1
|
Hussain A, Muthuvalu MS, Faye I, Zafar M, Inc M, Afzal F, Iqbal MS. Numerical investigation of treated brain glioma model using a two-stage successive over-relaxation method. Comput Biol Med 2023; 153:106429. [PMID: 36587570 DOI: 10.1016/j.compbiomed.2022.106429] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2022] [Revised: 11/17/2022] [Accepted: 12/13/2022] [Indexed: 12/31/2022]
Abstract
A brain tumor is a dynamic system in which cells develop rapidly and abnormally, as is the case with most cancers. Cancer develops in the brain or inside the skull when aberrant and odd cells proliferate in the brain. By depriving the healthy cells of leisure, nutrition, and oxygen, these aberrant cells eventually cause the healthy cells to perish. This article investigated the development of glioma cells in treating brain tumors. Mathematically, reaction-diffusion models have been developed for brain glioma growth to quantify the diffusion and proliferation of the tumor cells within brain tissues. This study presents the formulation the two-stage successive over-relaxation (TSSOR) algorithm based on the finite difference approximation for solving the treated brain glioma model to predict glioma cells in treating the brain tumor. Also, the performance of TSSOR method is compared to the Gauss-Seidel (GS) and two-stage Gauss-Seidel (TSGS) methods in terms of the number of iterations, the amount of time it takes to process the data, and the rate at which glioma cells grow the fastest. The implementation of the TSSOR, TSGS, and GS methods predicts the growth of tumor cells under the treatment protocol. The results show that the number of glioma cells decreased initially and then increased gradually by the next day. The computational complexity analysis is also used and concludes that the TSSOR method is faster compared to the TSGS and GS methods. According to the results of the treated glioma development model, the TSSOR approach reduced the number of iterations by between 8.0 and 71.95%. In terms of computational time, the TSSOR approach is around 1.18-76.34% faster than the TSGS and GS methods.
Collapse
Affiliation(s)
- Abida Hussain
- Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak, Malaysia; Centre for Intelligent Signal and Imaging Research, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak, Malaysia
| | - Mohana Sundaram Muthuvalu
- Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak, Malaysia
| | - Ibrahima Faye
- Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak, Malaysia; Centre for Intelligent Signal and Imaging Research, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak, Malaysia
| | - Mudasar Zafar
- Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak, Malaysia; Centre for Research in Enhanced Oil Recovery, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak, Malaysia
| | - Mustafa Inc
- Firat University, Science Faculty, Department of Mathematics, 23119, Elazig, Turkey; Department of Medical Research, China Medical University, Taichung, Taiwan.
| | - Farkhanda Afzal
- Department of Humanities and Basic Sciences, MCS, National University of Sciences and Technology (NUST), Islamabad, Pakistan
| | - Muhammad Sajid Iqbal
- Department of Humanities and Basic Sciences, MCS, National University of Sciences and Technology (NUST), Islamabad, Pakistan
| |
Collapse
|
2
|
Duclos S, Golin A, Fox A, Chaudhary N, Camelo-Piragua S, Pandey A, Xu Z. Transcranial histotripsy parameter study in primary and metastatic murine brain tumor models. Int J Hyperthermia 2023; 40:2237218. [PMID: 37495214 PMCID: PMC10410615 DOI: 10.1080/02656736.2023.2237218] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Revised: 07/07/2023] [Accepted: 07/11/2023] [Indexed: 07/28/2023] Open
Abstract
OBJECTIVE This study investigated the effect of various histotripsy dosages on tumor cell kill and associated bleeding in two murine brain tumor models (glioma [Gl261] and lung metastasis [LL/2-Luc2]). METHODS AND MATERIALS GL261 or LL/2-Luc2 cells were cultured and implanted into the brains of C57BL/6 mice. Histotripsy (1-cycle pulses, 5 Hz PRF, 30 MPa-P) was performed using a 1 MHz transducer for five different dosages for each cell line: 5, 20 or 200 pulses per location (PPL) at a single treatment point, or 5 or 10-20 PPL at multiple treatment points. MRI, bioluminescence imaging and histology were used to assess tumor ablation and treatment effects within 4-6 h post-treatment. RESULTS All treatment groups resulted in a reduction of BLI intensity for the LL/2-Luc2 tumors, with significant signal reductions for the multi-point groups. The average pre-/post-treatment BLI flux (photons/s, ×108) for the different treatment groups were: 4.39/2.19 (5 PPL single-point), 5.49/1.80 (20 PPL single-point), 3.86/1.73 (200 PPL single-point), 2.44/1.11 (5 PPL multi-point) and 5.85/0.80 (10 PPL multi-point). MRI and H&E staining showed increased tumor damage and hemorrhagic effects with increasing histotripsy dose for both GL261 and LL/2-Luc2 tumors, but the increase in tumor damage was diminished beyond 10-20 PPL for single-point treatments and outweighed by increased hemorrhage. In general, hemorrhage was confined to be within 1 mm of the treatment boundary for all groups. CONCLUSIONS Our results suggest that a lower number of histotripsy pulses at fewer focal locations can achieve substantial tumor kill while minimizing hemorrhage.
Collapse
Affiliation(s)
- Sarah Duclos
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA
| | - Andrew Golin
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA
| | - Adam Fox
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA
- Department of Neurosurgery, University of Michigan, Ann Arbor, MI, USA
| | - Neeraj Chaudhary
- Department of Neurosurgery, University of Michigan, Ann Arbor, MI, USA
- Department of Radiology, University of Michigan, Ann Arbor, MI, USA
| | | | - Aditya Pandey
- Department of Neurosurgery, University of Michigan, Ann Arbor, MI, USA
| | - Zhen Xu
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA
| |
Collapse
|
3
|
Cherfils L, Gatti S, Guillevin C, Miranville A, Guillevin R. On a tumor growth model with brain lactate kinetics. MATHEMATICAL MEDICINE AND BIOLOGY : A JOURNAL OF THE IMA 2022; 39:382-409. [PMID: 35961012 DOI: 10.1093/imammb/dqac010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Revised: 05/10/2022] [Accepted: 07/25/2022] [Indexed: 01/01/2023]
Abstract
Our aim in this paper is to study a mathematical model for high grade gliomas, taking into account lactates kinetics, as well as chemotherapy and antiangiogenic treatment. In particular, we prove the existence and uniqueness of biologically relevant solutions. We also perform numerical simulations based on different therapeutical situations that can be found in the literature. These simulations are consistent with what is expected in these situations.
Collapse
Affiliation(s)
- Laurence Cherfils
- LaSIE UMR CNRS 7356, La Rochelle Université, Avenue Michel Crépeau, F-17042 La Rochelle Cedex, France
| | - Stefania Gatti
- Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Via Campi 213/B, I-41125 Modena, Italy
| | - Carole Guillevin
- Laboratoire I3M et Laboratoire de Mathématiques et Applications, Université de Poitiers, UMR CNRS 7348, Equipe DACTIM-MIS, Site du Futuroscope-Téléport 2 11 Boulevard Marie et Pierre Curie-Bâtiment H3-TSA 61125, 86073 Poitiers Cedex 9, France, and CHU de Poitiers, 2 rue de la Milétrie 86000 Poitiers, France
| | - Alain Miranville
- School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, P.R. China and Laboratoire I3M et Laboratoire de Mathématiques et Applications, Université de Poitiers, Equipe DACTIM-MIS, Site du Futuroscope-Téléport 2 11 Boulevard Marie et Pierre Curie-Bâtiment H3-TSA 61125, 86073 Poitiers Cedex 9, France
| | - Rémy Guillevin
- Laboratoire I3M et Laboratoire de Mathématiques et Applications, Université de Poitiers, UMR CNRS 7348, Equipe DACTIM-MIS, Site du Futuroscope-Téléport 2 11 Boulevard Marie et Pierre Curie-Bâtiment H3-TSA 61125, 86073 Poitiers Cedex 9, France, and CHU de Poitiers, 2 rue de la Milétrie 86000 Poitiers, France
| |
Collapse
|
4
|
Prediction of Lung Nodule Progression with an Uncertainty-Aware Hierarchical Probabilistic Network. Diagnostics (Basel) 2022; 12:diagnostics12112639. [DOI: 10.3390/diagnostics12112639] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2022] [Revised: 10/21/2022] [Accepted: 10/24/2022] [Indexed: 11/16/2022] Open
Abstract
Predicting whether a lung nodule will grow, remain stable or regress over time, especially early in its follow-up, would help doctors prescribe personalized treatments and better surgical planning. However, the multifactorial nature of lung tumour progression hampers the identification of growth patterns. In this work, we propose a deep hierarchical generative and probabilistic network that, given an initial image of the nodule, predicts whether it will grow, quantifies its future size and provides its expected semantic appearance at a future time. Unlike previous solutions, our approach also estimates the uncertainty in the predictions from the intrinsic noise in medical images and the inter-observer variability in the annotations. The evaluation of this method on an independent test set reported a future tumour growth size mean absolute error of 1.74 mm, a nodule segmentation Dice’s coefficient of 78% and a tumour growth accuracy of 84% on predictions made up to 24 months ahead. Due to the lack of similar methods for providing future lung tumour growth predictions, along with their associated uncertainty, we adapted equivalent deterministic and alternative generative networks (i.e., probabilistic U-Net, Bayesian test dropout and Pix2Pix). Our method outperformed all these methods, corroborating the adequacy of our approach.
Collapse
|
5
|
Coupling solid and fluid stresses with brain tumour growth and white matter tract deformations in a neuroimaging-informed model. Biomech Model Mechanobiol 2022; 21:1483-1509. [PMID: 35908096 PMCID: PMC9626445 DOI: 10.1007/s10237-022-01602-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2021] [Accepted: 06/17/2022] [Indexed: 11/29/2022]
Abstract
Brain tumours are among the deadliest types of cancer, since they display a strong ability to invade the surrounding tissues and an extensive resistance to common therapeutic treatments. It is therefore important to reproduce the heterogeneity of brain microstructure through mathematical and computational models, that can provide powerful instruments to investigate cancer progression. However, only a few models include a proper mechanical and constitutive description of brain tissue, which instead may be relevant to predict the progression of the pathology and to analyse the reorganization of healthy tissues occurring during tumour growth and, possibly, after surgical resection. Motivated by the need to enrich the description of brain cancer growth through mechanics, in this paper we present a mathematical multiphase model that explicitly includes brain hyperelasticity. We find that our mechanical description allows to evaluate the impact of the growing tumour mass on the surrounding healthy tissue, quantifying the displacements, deformations, and stresses induced by its proliferation. At the same time, the knowledge of the mechanical variables may be used to model the stress-induced inhibition of growth, as well as to properly modify the preferential directions of white matter tracts as a consequence of deformations caused by the tumour. Finally, the simulations of our model are implemented in a personalized framework, which allows to incorporate the realistic brain geometry, the patient-specific diffusion and permeability tensors reconstructed from imaging data and to modify them as a consequence of the mechanical deformation due to cancer growth.
Collapse
|
6
|
Martens C, Rovai A, Bonatto D, Metens T, Debeir O, Decaestecker C, Goldman S, Van Simaeys G. Deep Learning for Reaction-Diffusion Glioma Growth Modeling: Towards a Fully Personalized Model? Cancers (Basel) 2022; 14:cancers14102530. [PMID: 35626134 PMCID: PMC9139770 DOI: 10.3390/cancers14102530] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2022] [Revised: 05/11/2022] [Accepted: 05/18/2022] [Indexed: 11/30/2022] Open
Abstract
Simple Summary Mathematical tumor growth models have been proposed for decades to capture the growth of gliomas, an aggressive form of brain tumor. However, the estimation of the tumor cell-density distribution at diagnosis and model parameters from partial observations provided by magnetic resonance imaging are ill-posed problems. In this work, we propose a deep learning-based approach to address these problems. 1200 synthetic tumors are first generated using the mathematical model over brain geometries of 6 volunteers. Two deep convolutional neural networks are then trained to (i) reconstruct a whole tumor cell-density distribution and (ii) evaluate the model parameters from partial observations provided in the form of threshold-like imaging contours, with state-of-the-art results. From the estimated cell-density distribution and parameter values, the spatio-temporal evolution of the tumor can ultimately be accurately captured by the mathematical model. Such an approach could be of great interest for glioma characterization and therapy planning. Abstract Reaction-diffusion models have been proposed for decades to capture the growth of gliomas, the most common primary brain tumors. However, ill-posedness of the initialization at diagnosis time and parameter estimation of such models have restrained their clinical use as a personalized predictive tool. In this work, we investigate the ability of deep convolutional neural networks (DCNNs) to address commonly encountered pitfalls in the field. Based on 1200 synthetic tumors grown over real brain geometries derived from magnetic resonance (MR) data of six healthy subjects, we demonstrate the ability of DCNNs to reconstruct a whole tumor cell-density distribution from only two imaging contours at a single time point. With an additional imaging contour extracted at a prior time point, we also demonstrate the ability of DCNNs to accurately estimate the individual diffusivity and proliferation parameters of the model. From this knowledge, the spatio-temporal evolution of the tumor cell-density distribution at later time points can ultimately be precisely captured using the model. We finally show the applicability of our approach to MR data of a real glioblastoma patient. This approach may open the perspective of a clinical application of reaction-diffusion growth models for tumor prognosis and treatment planning.
Collapse
Affiliation(s)
- Corentin Martens
- Department of Nuclear Medicine, Hôpital Erasme, Université libre de Bruxelles, Route de Lennik 808, 1070 Brussels, Belgium; (A.R.); (S.G.); (G.V.S.)
- Center for Microscopy and Molecular Imaging (CMMI), Université libre de Bruxelles, Rue Adrienne Bolland 8, 6041 Charleroi, Belgium; (O.D.); (C.D.)
- Laboratory of Image Synthesis and Analysis (LISA), École Polytechnique de Bruxelles, Université libre de Bruxelles, Avenue Franklin Roosevelt 50, 1050 Brussels, Belgium; (D.B.); (T.M.)
- Correspondence:
| | - Antonin Rovai
- Department of Nuclear Medicine, Hôpital Erasme, Université libre de Bruxelles, Route de Lennik 808, 1070 Brussels, Belgium; (A.R.); (S.G.); (G.V.S.)
| | - Daniele Bonatto
- Laboratory of Image Synthesis and Analysis (LISA), École Polytechnique de Bruxelles, Université libre de Bruxelles, Avenue Franklin Roosevelt 50, 1050 Brussels, Belgium; (D.B.); (T.M.)
| | - Thierry Metens
- Laboratory of Image Synthesis and Analysis (LISA), École Polytechnique de Bruxelles, Université libre de Bruxelles, Avenue Franklin Roosevelt 50, 1050 Brussels, Belgium; (D.B.); (T.M.)
- Department of Radiology, Hôpital Erasme, Université libre de Bruxelles, Route de Lennik 808, 1070 Brussels, Belgium
| | - Olivier Debeir
- Center for Microscopy and Molecular Imaging (CMMI), Université libre de Bruxelles, Rue Adrienne Bolland 8, 6041 Charleroi, Belgium; (O.D.); (C.D.)
- Laboratory of Image Synthesis and Analysis (LISA), École Polytechnique de Bruxelles, Université libre de Bruxelles, Avenue Franklin Roosevelt 50, 1050 Brussels, Belgium; (D.B.); (T.M.)
| | - Christine Decaestecker
- Center for Microscopy and Molecular Imaging (CMMI), Université libre de Bruxelles, Rue Adrienne Bolland 8, 6041 Charleroi, Belgium; (O.D.); (C.D.)
- Laboratory of Image Synthesis and Analysis (LISA), École Polytechnique de Bruxelles, Université libre de Bruxelles, Avenue Franklin Roosevelt 50, 1050 Brussels, Belgium; (D.B.); (T.M.)
| | - Serge Goldman
- Department of Nuclear Medicine, Hôpital Erasme, Université libre de Bruxelles, Route de Lennik 808, 1070 Brussels, Belgium; (A.R.); (S.G.); (G.V.S.)
- Center for Microscopy and Molecular Imaging (CMMI), Université libre de Bruxelles, Rue Adrienne Bolland 8, 6041 Charleroi, Belgium; (O.D.); (C.D.)
| | - Gaetan Van Simaeys
- Department of Nuclear Medicine, Hôpital Erasme, Université libre de Bruxelles, Route de Lennik 808, 1070 Brussels, Belgium; (A.R.); (S.G.); (G.V.S.)
- Center for Microscopy and Molecular Imaging (CMMI), Université libre de Bruxelles, Rue Adrienne Bolland 8, 6041 Charleroi, Belgium; (O.D.); (C.D.)
| |
Collapse
|
7
|
Quader S, Kataoka K, Cabral H. Nanomedicine for brain cancer. Adv Drug Deliv Rev 2022; 182:114115. [PMID: 35077821 DOI: 10.1016/j.addr.2022.114115] [Citation(s) in RCA: 38] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2021] [Revised: 12/18/2021] [Accepted: 01/12/2022] [Indexed: 02/06/2023]
Abstract
CNS tumors remain among the deadliest forms of cancer, resisting conventional and new treatment approaches, with mortality rates staying practically unchanged over the past 30 years. One of the primary hurdles for treating these cancers is delivering drugs to the brain tumor site in therapeutic concentration, evading the blood-brain (tumor) barrier (BBB/BBTB). Supramolecular nanomedicines (NMs) are increasingly demonstrating noteworthy prospects for addressing these challenges utilizing their unique characteristics, such as improving the bioavailability of the payloadsviacontrolled pharmacokinetics and pharmacodynamics, BBB/BBTB crossing functions, superior distribution in the brain tumor site, and tumor-specific drug activation profiles. Here, we review NM-based brain tumor targeting approaches to demonstrate their applicability and translation potential from different perspectives. To this end, we provide a general overview of brain tumor and their treatments, the incidence of the BBB and BBTB, and their role on NM targeting, as well as the potential of NMs for promoting superior therapeutic effects. Additionally, we discuss critical issues of NMs and their clinical trials, aiming to bolster the potential clinical applications of NMs in treating these life-threatening diseases.
Collapse
Affiliation(s)
- Sabina Quader
- Innovation Center of NanoMedicine, Kawasaki Institute of Industrial Promotion, 3-25-14 Tonomachi, Kawasaki-ku, Kawasaki 212-0821, Japan
| | - Kazunori Kataoka
- Innovation Center of NanoMedicine, Kawasaki Institute of Industrial Promotion, 3-25-14 Tonomachi, Kawasaki-ku, Kawasaki 212-0821, Japan.
| | - Horacio Cabral
- Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
| |
Collapse
|
8
|
Khajanchi S, Nieto JJ. Spatiotemporal dynamics of a glioma immune interaction model. Sci Rep 2021; 11:22385. [PMID: 34789751 PMCID: PMC8599515 DOI: 10.1038/s41598-021-00985-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2021] [Accepted: 10/20/2021] [Indexed: 12/20/2022] Open
Abstract
We report a mathematical model which depicts the spatiotemporal dynamics of glioma cells, macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine TGF-β and immuno-stimulatory cytokine IFN-γ through a system of five coupled reaction-diffusion equations. We performed local stability analysis of the biologically based mathematical model for the growth of glioma cell population and their environment. The presented stability analysis of the model system demonstrates that the temporally stable positive interior steady state remains stable under the small inhomogeneous spatiotemporal perturbations. The irregular spatiotemporal dynamics of gliomas, macrophages and cytotoxic T-lymphocytes are discussed extensively and some numerical simulations are presented. Performed some numerical simulations in both one and two dimensional spaces. The occurrence of heterogeneous pattern formation of the system has both biological and mathematical implications and the concepts of glioma cell progression and invasion are considered. Simulation of the model shows that by increasing the value of time, the glioma cell population, macrophages and cytotoxic-T-lymphocytes spread throughout the domain.
Collapse
Affiliation(s)
- Subhas Khajanchi
- Department of Mathematics, Presidency University, 86/1 College Street, Kolkata, 700073, India.
| | - Juan J Nieto
- Instituto de Matem\acute{a}ticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
| |
Collapse
|
9
|
Quantitative magnetic resonance imaging and tumor forecasting of breast cancer patients in the community setting. Nat Protoc 2021; 16:5309-5338. [PMID: 34552262 PMCID: PMC9753909 DOI: 10.1038/s41596-021-00617-y] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2020] [Accepted: 08/12/2021] [Indexed: 02/07/2023]
Abstract
This protocol describes a complete data acquisition, analysis and computational forecasting pipeline for employing quantitative MRI data to predict the response of locally advanced breast cancer to neoadjuvant therapy in a community-based care setting. The methodology has previously been successfully applied to a heterogeneous patient population. The protocol details how to acquire the necessary images followed by registration, segmentation, quantitative perfusion and diffusion analysis, model calibration, and prediction. The data collection portion of the protocol requires ~25 min of scanning, postprocessing requires 2-3 h, and the model calibration and prediction components require ~10 h per patient depending on tumor size. The response of individual breast cancer patients to neoadjuvant therapy is forecast by application of a biophysical, reaction-diffusion mathematical model to these data. Successful application of the protocol results in coregistered MRI data from at least two scan visits that quantifies an individual tumor's size, cellularity and vascular properties. This enables a spatially resolved prediction of how a particular patient's tumor will respond to therapy. Expertise in image acquisition and analysis, as well as the numerical solution of partial differential equations, is required to carry out this protocol.
Collapse
|
10
|
Improving cancer treatments via dynamical biophysical models. Phys Life Rev 2021; 39:1-48. [PMID: 34688561 DOI: 10.1016/j.plrev.2021.10.001] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2021] [Accepted: 10/13/2021] [Indexed: 12/17/2022]
Abstract
Despite significant advances in oncological research, cancer nowadays remains one of the main causes of mortality and morbidity worldwide. New treatment techniques, as a rule, have limited efficacy, target only a narrow range of oncological diseases, and have limited availability to the general public due their high cost. An important goal in oncology is thus the modification of the types of antitumor therapy and their combinations, that are already introduced into clinical practice, with the goal of increasing the overall treatment efficacy. One option to achieve this goal is optimization of the schedules of drugs administration or performing other medical actions. Several factors complicate such tasks: the adverse effects of treatments on healthy cell populations, which must be kept tolerable; the emergence of drug resistance due to the intrinsic plasticity of heterogeneous cancer cell populations; the interplay between different types of therapies administered simultaneously. Mathematical modeling, in which a tumor and its microenvironment are considered as a single complex system, can address this complexity and can indicate potentially effective protocols, that would require experimental verification. In this review, we consider classical methods, current trends and future prospects in the field of mathematical modeling of tumor growth and treatment. In particular, methods of treatment optimization are discussed with several examples of specific problems related to different types of treatment.
Collapse
|
11
|
Kalra J, Baker J, Song J, Kyle A, Minchinton A, Bally M. Inter-Metastatic Heterogeneity of Tumor Marker Expression and Microenvironment Architecture in a Preclinical Cancer Model. Int J Mol Sci 2021; 22:6336. [PMID: 34199298 PMCID: PMC8231937 DOI: 10.3390/ijms22126336] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2021] [Revised: 05/25/2021] [Accepted: 06/09/2021] [Indexed: 11/30/2022] Open
Abstract
BACKGROUND Preclinical drug development studies rarely consider the impact of a candidate drug on established metastatic disease. This may explain why agents that are successful in subcutaneous and even orthotopic preclinical models often fail to demonstrate efficacy in clinical trials. It is reasonable to anticipate that sites of metastasis will be phenotypically unique, as each tumor will have evolved heterogeneously with respect to gene expression as well as the associated phenotypic outcome of that expression. The objective for the studies described here was to gain an understanding of the tumor heterogeneity that exists in established metastatic disease and use this information to define a preclinical model that is more predictive of treatment outcome when testing novel drug candidates clinically. METHODS Female NCr nude mice were inoculated with fluorescent (mKate), Her2/neu-positive human breast cancer cells (JIMT-mKate), either in the mammary fat pad (orthotopic; OT) to replicate a primary tumor, or directly into the left ventricle (intracardiac; IC), where cells eventually localize in multiple sites to create a model of established metastasis. Tumor development was monitored by in vivo fluorescence imaging (IVFI). Subsequently, animals were sacrificed, and tumor tissues were isolated and imaged ex vivo. Tumors within organ tissues were further analyzed via multiplex immunohistochemistry (mIHC) for Her2/neu expression, blood vessels (CD31), as well as a nuclear marker (Hoechst) and fluorescence (mKate) expressed by the tumor cells. RESULTS Following IC injection, JIMT-1mKate cells consistently formed tumors in the lung, liver, brain, kidney, ovaries, and adrenal glands. Disseminated tumors were highly variable when assessing vessel density (CD31) and tumor marker expression (mkate, Her2/neu). Interestingly, tumors which developed within an organ did not adopt a vessel microarchitecture that mimicked the organ where growth occurred, nor did the vessel microarchitecture appear comparable to the primary tumor. Rather, metastatic lesions showed considerable variability, suggesting that each secondary tumor is a distinct disease entity from a microenvironmental perspective. CONCLUSIONS The data indicate that more phenotypic heterogeneity in the tumor microenvironment exists in models of metastatic disease than has been previously appreciated, and this heterogeneity may better reflect the metastatic cancer in patients typically enrolled in early-stage Phase I/II clinical trials. Similar to the suggestion of others in the past, the use of models of established metastasis preclinically should be required as part of the anticancer drug candidate development process, and this may be particularly important for targeted therapeutics and/or nanotherapeutics.
Collapse
Affiliation(s)
- Jessica Kalra
- Experimental Therapeutics, BC Cancer Agency, Vancouver, BC V5Z 1L3, Canada;
- Applied Research Centre, Langara, Vancouver, BC V5Y 2Z6, Canada
- Department Anesthesia Pharmacology and Therapeutics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
- Faculty of Pharmaceutical Sciences, University of British Columbia, Vancouver, BC V6T 1Z4, Canada;
| | - Jennifer Baker
- Integrative Oncology, BC Cancer Agency, Vancouver, BC V5Z 1L3, Canada; (J.B.); (A.K.)
| | - Justin Song
- Chemical and Biomolecular Engineering Department, Vanderbilt University, Nashville, TN 37235, USA;
| | - Alastair Kyle
- Integrative Oncology, BC Cancer Agency, Vancouver, BC V5Z 1L3, Canada; (J.B.); (A.K.)
| | - Andrew Minchinton
- Faculty of Pharmaceutical Sciences, University of British Columbia, Vancouver, BC V6T 1Z4, Canada;
- Integrative Oncology, BC Cancer Agency, Vancouver, BC V5Z 1L3, Canada; (J.B.); (A.K.)
| | - Marcel Bally
- Experimental Therapeutics, BC Cancer Agency, Vancouver, BC V5Z 1L3, Canada;
- Faculty of Pharmaceutical Sciences, University of British Columbia, Vancouver, BC V6T 1Z4, Canada;
- Pathology and Laboratory Medicine, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
- Nanomedicine Innovation Network, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| |
Collapse
|
12
|
Chulián S, Martinez-Rubio Á, Gandarias ML, Rosa M. Lie point symmetries for generalised Fisher's equations describing tumour dynamics. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:3291-3312. [PMID: 34198386 DOI: 10.3934/mbe.2021164] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
A huge variety of phenomena are governed by ordinary differential equations (ODEs) and partial differential equations (PDEs). However, there is no general method to solve them. Obtaining solutions for differential equations is one of the greatest problem for both applied mathematics and physics. Multiple integration methods have been developed to the day to solve particular types of differential equations, specially those focused on physical or biological phenomena. In this work, we review several applications of the Lie method to obtain solutions of reaction-diffusion equations describing cell dynamics and tumour invasion.
Collapse
Affiliation(s)
- Salvador Chulián
- Departamento de Matemáticas, University of Cádiz, Cádiz, Spain; Instituto de Investigación e Innovación Biomédica de Cádiz (INiBICA), University of Cádiz, Cádiz, Spain
| | - Álvaro Martinez-Rubio
- Departamento de Matemáticas, University of Cádiz, Cádiz, Spain; Instituto de Investigación e Innovación Biomédica de Cádiz (INiBICA), University of Cádiz, Cádiz, Spain
| | | | - María Rosa
- Departamento de Matemáticas, University of Cádiz, Cádiz, Spain; Instituto de Investigación e Innovación Biomédica de Cádiz (INiBICA), University of Cádiz, Cádiz, Spain
| |
Collapse
|
13
|
Wang Y, Brodin E, Nishii K, Frieboes HB, Mumenthaler SM, Sparks JL, Macklin P. Impact of tumor-parenchyma biomechanics on liver metastatic progression: a multi-model approach. Sci Rep 2021; 11:1710. [PMID: 33462259 PMCID: PMC7813881 DOI: 10.1038/s41598-020-78780-7] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2020] [Accepted: 11/24/2020] [Indexed: 12/17/2022] Open
Abstract
Colorectal cancer and other cancers often metastasize to the liver in later stages of the disease, contributing significantly to patient death. While the biomechanical properties of the liver parenchyma (normal liver tissue) are known to affect tumor cell behavior in primary and metastatic tumors, the role of these properties in driving or inhibiting metastatic inception remains poorly understood, as are the longer-term multicellular dynamics. This study adopts a multi-model approach to study the dynamics of tumor-parenchyma biomechanical interactions during metastatic seeding and growth. We employ a detailed poroviscoelastic model of a liver lobule to study how micrometastases disrupt flow and pressure on short time scales. Results from short-time simulations in detailed single hepatic lobules motivate constitutive relations and biological hypotheses for a minimal agent-based model of metastatic growth in centimeter-scale tissue over months-long time scales. After a parameter space investigation, we find that the balance of basic tumor-parenchyma biomechanical interactions on shorter time scales (adhesion, repulsion, and elastic tissue deformation over minutes) and longer time scales (plastic tissue relaxation over hours) can explain a broad range of behaviors of micrometastases, without the need for complex molecular-scale signaling. These interactions may arrest the growth of micrometastases in a dormant state and prevent newly arriving cancer cells from establishing successful metastatic foci. Moreover, the simulations indicate ways in which dormant tumors could "reawaken" after changes in parenchymal tissue mechanical properties, as may arise during aging or following acute liver illness or injury. We conclude that the proposed modeling approach yields insight into the role of tumor-parenchyma biomechanics in promoting liver metastatic growth, and advances the longer term goal of identifying conditions to clinically arrest and reverse the course of late-stage cancer.
Collapse
Affiliation(s)
- Yafei Wang
- Department of Intelligent Systems Engineering, Indiana University, Bloomington, IN, USA
| | - Erik Brodin
- Department of Chemical, Paper and Biomedical Engineering, Miami University, Oxford, OH, USA
| | - Kenichiro Nishii
- Department of Chemical, Paper and Biomedical Engineering, Miami University, Oxford, OH, USA
| | - Hermann B Frieboes
- Department of Bioengineering, University of Louisville, Louisville, KY, USA
- James Graham Brown Cancer Center, University of Louisville, Louisville, KY, USA
- Center for Predictive Medicine, University of Louisville, Louisville, KY, USA
| | - Shannon M Mumenthaler
- Lawrence J. Ellison Institute for Transformative Medicine, University of Southern California, Los Angeles, CA, USA
| | - Jessica L Sparks
- Department of Chemical, Paper and Biomedical Engineering, Miami University, Oxford, OH, USA.
| | - Paul Macklin
- Department of Intelligent Systems Engineering, Indiana University, Bloomington, IN, USA.
| |
Collapse
|
14
|
Elazab A, Wang C, Gardezi SJS, Bai H, Hu Q, Wang T, Chang C, Lei B. GP-GAN: Brain tumor growth prediction using stacked 3D generative adversarial networks from longitudinal MR Images. Neural Netw 2020; 132:321-332. [DOI: 10.1016/j.neunet.2020.09.004] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2019] [Revised: 08/27/2020] [Accepted: 09/06/2020] [Indexed: 01/28/2023]
|
15
|
Jarrett AM, Hormuth DA, Adhikarla V, Sahoo P, Abler D, Tumyan L, Schmolze D, Mortimer J, Rockne RC, Yankeelov TE. Towards integration of 64Cu-DOTA-trastuzumab PET-CT and MRI with mathematical modeling to predict response to neoadjuvant therapy in HER2 + breast cancer. Sci Rep 2020; 10:20518. [PMID: 33239688 PMCID: PMC7688955 DOI: 10.1038/s41598-020-77397-0] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2020] [Accepted: 10/29/2020] [Indexed: 12/20/2022] Open
Abstract
While targeted therapies exist for human epidermal growth factor receptor 2 positive (HER2 +) breast cancer, HER2 + patients do not always respond to therapy. We present the results of utilizing a biophysical mathematical model to predict tumor response for two HER2 + breast cancer patients treated with the same therapeutic regimen but who achieved different treatment outcomes. Quantitative data from magnetic resonance imaging (MRI) and 64Cu-DOTA-trastuzumab positron emission tomography (PET) are used to estimate tumor density, perfusion, and distribution of HER2-targeted antibodies for each individual patient. MRI and PET data are collected prior to therapy, and follow-up MRI scans are acquired at a midpoint in therapy. Given these data types, we align the data sets to a common image space to enable model calibration. Once the model is parameterized with these data, we forecast treatment response with and without HER2-targeted therapy. By incorporating targeted therapy into the model, the resulting predictions are able to distinguish between the two different patient responses, increasing the difference in tumor volume change between the two patients by > 40%. This work provides a proof-of-concept strategy for processing and integrating PET and MRI modalities into a predictive, clinical-mathematical framework to provide patient-specific predictions of HER2 + treatment response.
Collapse
Affiliation(s)
- Angela M Jarrett
- Oden Institute for Computational Engineering and Sciences, The University of Texas At Austin, Austin, TX, USA
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, TX, USA
| | - David A Hormuth
- Oden Institute for Computational Engineering and Sciences, The University of Texas At Austin, Austin, TX, USA
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, TX, USA
| | - Vikram Adhikarla
- Division of Mathematical Oncology, Department of Computational and Quantitative Medicine, Beckman Research Institute, City of Hope National Medical Center, 1500 E Duarte Rd, Bldg. 74, Duarte, CA, 91010, USA
| | - Prativa Sahoo
- Division of Mathematical Oncology, Department of Computational and Quantitative Medicine, Beckman Research Institute, City of Hope National Medical Center, 1500 E Duarte Rd, Bldg. 74, Duarte, CA, 91010, USA
| | - Daniel Abler
- Division of Mathematical Oncology, Department of Computational and Quantitative Medicine, Beckman Research Institute, City of Hope National Medical Center, 1500 E Duarte Rd, Bldg. 74, Duarte, CA, 91010, USA
- ARTORG Center for Biomedical Engineering Research, University of Bern, Bern, Switzerland
| | - Lusine Tumyan
- Department of Radiology, City of Hope National Medical Center, Duarte, CA, USA
| | - Daniel Schmolze
- Department of Pathology, City of Hope National Medical Center, Duarte, CA, USA
| | - Joanne Mortimer
- Department of Medical Oncology & Therapeutics Research, City of Hope National Medical Center, Duarte, CA, USA
| | - Russell C Rockne
- Division of Mathematical Oncology, Department of Computational and Quantitative Medicine, Beckman Research Institute, City of Hope National Medical Center, 1500 E Duarte Rd, Bldg. 74, Duarte, CA, 91010, USA.
| | - Thomas E Yankeelov
- Oden Institute for Computational Engineering and Sciences, The University of Texas At Austin, Austin, TX, USA.
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, TX, USA.
- Department of Diagnostic Medicine, The University of Texas at Austin, Austin, TX, USA.
- Department of Oncology, The University of Texas at Austin, Austin, TX, USA.
- Department of Biomedical Engineering, The University of Texas at Austin, 107 W Dean Keeton Street Stop C0800, Austin, TX, 78712, USA.
- Department of Imaging Physics, The University of Texas MD Anderson Cancer Center, Houston, TX, USA.
| |
Collapse
|
16
|
Ebrahimi Zade A, Shahabi Haghighi S, Soltani M. Reinforcement learning for optimal scheduling of Glioblastoma treatment with Temozolomide. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2020; 193:105443. [PMID: 32311510 DOI: 10.1016/j.cmpb.2020.105443] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2019] [Revised: 02/17/2020] [Accepted: 03/08/2020] [Indexed: 06/11/2023]
Abstract
BACKGROUND Glioblastoma multiforme (GBM) is the most frequent primary brain tumor in adults and Temozolomide (TMZ) is an effective chemotherapeutic agent for its treatment. In Silico models of GBM growth provide an appropriate foundation for analysis and comparison of different regimens. We propose a mathematical frame for patient specific design of optimal chemotherapy regimens for GBM patients. METHODS The proposed frame includes online interaction of a virtual GBM with an optimizing agent. Spatiotemporal dynamics of GBM growth and its response to TMZ are simulated with a three dimensional hybrid cellular automaton. Q learning is tailored to the virtual GBM for treatment optimization aimed at minimizing tumor size at the end of treatment course. Q learning consists of a learning agent that interacts with the virtual GBM. System state is affected by the agent decisions and the obtained rewards guide Q learning to the optimal schedule. RESULTS Computational results confirm that the optimal chemotherapy schedule depends on some patient specific parameters including body weight, tumor size and its position in the brain. Furthermore, the algorithm is used for scheduling 2100 mg of TMZ on a virtual GBM and the obtained schedule is to administer150 mg of TMZ every other day. The obtained schedule is compared to the standard 7/14 regimen and the results show that it is superior to the 7/14 regimen in minimizing tumor size. CONCLUSION The proposed frame is an appropriate decision support system for patient specific design of TMZ administration regimens on GBM patients. Also, since the obtained optimal schedule outperforms the standard 7/14 regimen, it is worthy of further clinical testing.
Collapse
Affiliation(s)
- Amir Ebrahimi Zade
- Faculty of Industrial Engineering and Systems Management, Amirkabir University of Technology, Tehran, Iran
| | | | - Madjid Soltani
- Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran 1969764499, Iran; Advanced Bioengineering Initiative Center, Computational Medicine Center, K. N. Toosi University of Technology, Tehran, Iran; Centre for Biotechnology and Bioengineering (CBB), University of Waterloo, Waterloo, ON, Canada; Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada
| |
Collapse
|
17
|
Simulating glioblastoma growth consisting both visible and invisible parts of the tumor using a diffusion-reaction model followed by resection and radiotherapy. Acta Neurol Belg 2020; 120:629-637. [PMID: 29869778 DOI: 10.1007/s13760-018-0952-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2018] [Accepted: 05/23/2018] [Indexed: 02/04/2023]
Abstract
Glioblastoma is known to be among one of the deadliest brain tumors in the world today. There have been major improvements in the detection of cancerous cells in the twenty-first century. However, the threshold of detection of these cancerous cells varies in different scanning techniques such as magnetic resonance imaging (MRI) and computed tomography (CT). The growth of these tumors and different treatments have been modeled to assist medical experts in better predictions of the related tumor growth and in the selection of more accurate treatments. In clinical terms the tumor consisted of two parts known as the visible part, which is the part of the tumor that is above the threshold of the detecting device and the invisible part, which is below the detecting threshold. In this study, the common reaction-diffusion model of tumor growth is used to simulate the growth of the glioblastoma tumor. Also resection and radiotherapy have been modeled as methods to prevent the growth of the tumor. The results demonstrate that although the selected treatments were effective in reducing the number of cancerous cells to under the threshold of detection, they did not eliminate all cancerous cells and if no further treatments were applied, the cancerous cells would spread and become malignant again. Although previous studies have suggested that the ratio of proliferation to diffusion could describe the malignancy of the tumor, this study in addition shows the importance of each of the coefficients regarding the malignancy of the tumor.
Collapse
|
18
|
An optimized generic cerebral tumor growth modeling framework by coupling biomechanical and diffusive models with treatment effects. Appl Soft Comput 2019. [DOI: 10.1016/j.asoc.2019.04.034] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
|
19
|
Randall EC, Emdal KB, Laramy JK, Kim M, Roos A, Calligaris D, Regan MS, Gupta SK, Mladek AC, Carlson BL, Johnson AJ, Lu FK, Xie XS, Joughin BA, Reddy RJ, Peng S, Abdelmoula WM, Jackson PR, Kolluri A, Kellersberger KA, Agar JN, Lauffenburger DA, Swanson KR, Tran NL, Elmquist WF, White FM, Sarkaria JN, Agar NYR. Integrated mapping of pharmacokinetics and pharmacodynamics in a patient-derived xenograft model of glioblastoma. Nat Commun 2018; 9:4904. [PMID: 30464169 PMCID: PMC6249307 DOI: 10.1038/s41467-018-07334-3] [Citation(s) in RCA: 50] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2018] [Accepted: 10/23/2018] [Indexed: 12/13/2022] Open
Abstract
Therapeutic options for the treatment of glioblastoma remain inadequate despite concerted research efforts in drug development. Therapeutic failure can result from poor permeability of the blood-brain barrier, heterogeneous drug distribution, and development of resistance. Elucidation of relationships among such parameters could enable the development of predictive models of drug response in patients and inform drug development. Complementary analyses were applied to a glioblastoma patient-derived xenograft model in order to quantitatively map distribution and resulting cellular response to the EGFR inhibitor erlotinib. Mass spectrometry images of erlotinib were registered to histology and magnetic resonance images in order to correlate drug distribution with tumor characteristics. Phosphoproteomics and immunohistochemistry were used to assess protein signaling in response to drug, and integrated with transcriptional response using mRNA sequencing. This comprehensive dataset provides simultaneous insight into pharmacokinetics and pharmacodynamics and indicates that erlotinib delivery to intracranial tumors is insufficient to inhibit EGFR tyrosine kinase signaling.
Collapse
Affiliation(s)
- Elizabeth C Randall
- Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, 02115, USA
| | - Kristina B Emdal
- Department of Biological Engineering, Koch Institute for Integrative Cancer Research, Massachusetts Institute of Technology, 500 Main St, Cambridge, MA, 02142, USA
| | - Janice K Laramy
- Department of Pharmaceutics, College of Pharmacy, University of Minnesota, Minneapolis, MN, 55455, USA
| | - Minjee Kim
- Department of Pharmaceutics, College of Pharmacy, University of Minnesota, Minneapolis, MN, 55455, USA
| | - Alison Roos
- Department of Cancer Biology, Mayo Clinic, 13400 E. Shea Blvd.MCCRB 03-055, Scottsdale, AZ, 85259, USA
| | - David Calligaris
- Department of Neurosurgery, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, 02115, USA
| | - Michael S Regan
- Department of Neurosurgery, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, 02115, USA
| | - Shiv K Gupta
- Department of Radiation Oncology, Mayo Clinic, 200 First St SW, Rochester, MN, 55902, USA
| | - Ann C Mladek
- Department of Radiation Oncology, Mayo Clinic, 200 First St SW, Rochester, MN, 55902, USA
| | - Brett L Carlson
- Department of Radiation Oncology, Mayo Clinic, 200 First St SW, Rochester, MN, 55902, USA
| | - Aaron J Johnson
- Department of Immunology, Mayo Clinic, 200 First St SW, Rochester, MN, 55902, USA
| | - Fa-Ke Lu
- Department of Neurosurgery, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, 02115, USA
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, 02138, USA
- Department of Biomedical Engineering, Binghamton University, State University of New York, Binghamton, NY, 13902, USA
| | - X Sunney Xie
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, 02138, USA
| | - Brian A Joughin
- Department of Biological Engineering, Koch Institute for Integrative Cancer Research, Massachusetts Institute of Technology, 500 Main St, Cambridge, MA, 02142, USA
| | - Raven J Reddy
- Department of Biological Engineering, Koch Institute for Integrative Cancer Research, Massachusetts Institute of Technology, 500 Main St, Cambridge, MA, 02142, USA
| | - Sen Peng
- Cancer and Cell Biology Division, Translational Genomics Research Institute, Phoenix, AZ, 85004, USA
| | - Walid M Abdelmoula
- Department of Neurosurgery, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, 02115, USA
| | - Pamela R Jackson
- Mathematical NeuroOncology Lab, Department of Neurosurgery, Mayo Clinic, 5777 E. Mayo Blvd, Phoenix, AZ, 85054, USA
| | - Aarti Kolluri
- Mathematical NeuroOncology Lab, Department of Neurosurgery, Mayo Clinic, 5777 E. Mayo Blvd, Phoenix, AZ, 85054, USA
| | | | - Jeffrey N Agar
- Department of Chemistry and Chemical Biology, Northeastern University, 412 TF (140 The Fenway), Boston, MA, 02111, USA
| | - Douglas A Lauffenburger
- Department of Biological Engineering, Koch Institute for Integrative Cancer Research, Massachusetts Institute of Technology, 500 Main St, Cambridge, MA, 02142, USA
| | - Kristin R Swanson
- Mathematical NeuroOncology Lab, Department of Neurosurgery, Mayo Clinic, 5777 E. Mayo Blvd, Phoenix, AZ, 85054, USA
| | - Nhan L Tran
- Department of Cancer Biology, Mayo Clinic, 13400 E. Shea Blvd.MCCRB 03-055, Scottsdale, AZ, 85259, USA
| | - William F Elmquist
- Department of Pharmaceutics, College of Pharmacy, University of Minnesota, Minneapolis, MN, 55455, USA
| | - Forest M White
- Department of Biological Engineering, Koch Institute for Integrative Cancer Research, Massachusetts Institute of Technology, 500 Main St, Cambridge, MA, 02142, USA
| | - Jann N Sarkaria
- Department of Radiation Oncology, Mayo Clinic, 200 First St SW, Rochester, MN, 55902, USA
| | - Nathalie Y R Agar
- Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, 02115, USA.
- Department of Neurosurgery, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, 02115, USA.
- Department of Cancer Biology, Dana-Farber Cancer Institute, Harvard Medical School, Boston, MA, 02115, USA.
| |
Collapse
|
20
|
Elazab A, Bai H, Yang M, Hu Q, Le MH, Wang T, Lei B. A Coupled Modified Reaction Diffusion and Biomechanical Models for Cerebral Tumor Growth Modeling in Presence of Treatment. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2018; 2018:758-761. [PMID: 30440506 DOI: 10.1109/embc.2018.8512324] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Tumor growth modeling at macroscopic level from multimodal images can help in predicting the future evolution of tumor and the treatment planning. This can be achieved using mathematical models where multi time-point images are available. In this paper, we propose a coupled modified reaction diffusion model that measures tumor invasion and infiltration with biomechanical model to consider tumor mass effect. In addition, our model considers treatment effects from radiotherapy and/or chemotherapy if any. The chemotherapy effect is included via a modified log-kill method to consider tissue heterogeneity while radiotherapy effect is considered using the linear quadratic model. We test the proposed model on both synthetic and 6 real datasets of low grade glioma cases with and without treatments. Experimental results of the proposed model on the clinical magnetic resonance images show that our model can simulate the tumor growth with good accuracy and effectively include the treatment effects.
Collapse
|
21
|
Jarrett AM, Hormuth DA, Barnes SL, Feng X, Huang W, Yankeelov TE. Incorporating drug delivery into an imaging-driven, mechanics-coupled reaction diffusion model for predicting the response of breast cancer to neoadjuvant chemotherapy: theory and preliminary clinical results. Phys Med Biol 2018; 63:105015. [PMID: 29697054 PMCID: PMC5985823 DOI: 10.1088/1361-6560/aac040] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
Clinical methods for assessing tumor response to therapy are largely rudimentary, monitoring only temporal changes in tumor size. Our goal is to predict the response of breast tumors to therapy using a mathematical model that utilizes magnetic resonance imaging (MRI) data obtained non-invasively from individual patients. We extended a previously established, mechanically coupled, reaction-diffusion model for predicting tumor response initialized with patient-specific diffusion weighted MRI (DW-MRI) data by including the effects of chemotherapy drug delivery, which is estimated using dynamic contrast-enhanced (DCE-) MRI data. The extended, drug incorporated, model is initialized using patient-specific DW-MRI and DCE-MRI data. Data sets from five breast cancer patients were used-obtained before, after one cycle, and at mid-point of neoadjuvant chemotherapy. The DCE-MRI data was used to estimate spatiotemporal variations in tumor perfusion with the extended Kety-Tofts model. The physiological parameters derived from DCE-MRI were used to model changes in delivery of therapy drugs within the tumor for incorporation in the extended model. We simulated the original model and the extended model in both 2D and 3D and compare the results for this five-patient cohort. Preliminary results show reductions in the error of model predicted tumor cellularity and size compared to the experimentally-measured results for the third MRI scan when therapy was incorporated. Comparing the two models for agreement between the predicted total cellularity and the calculated total cellularity (from the DW-MRI data) reveals an increased concordance correlation coefficient from 0.81 to 0.98 for the 2D analysis and 0.85 to 0.99 for the 3D analysis (p < 0.01 for each) when the extended model was used in place of the original model. This study demonstrates the plausibility of using DCE-MRI data as a means to estimate drug delivery on a patient-specific basis in predictive models and represents a step toward the goal of achieving individualized prediction of tumor response to therapy.
Collapse
Affiliation(s)
- Angela M. Jarrett
- Institute for Computational Engineering and Sciences, The University of Texas at Austin Austin, Texas USA
| | - David A. Hormuth
- Institute for Computational Engineering and Sciences, The University of Texas at Austin Austin, Texas USA
| | - Stephane L. Barnes
- Institute for Computational Engineering and Sciences, The University of Texas at Austin Austin, Texas USA
| | - Xinzeng Feng
- Institute for Computational Engineering and Sciences, The University of Texas at Austin Austin, Texas USA
| | - Wei Huang
- Advanced Imaging Research Center Oregon Health and Science University Portland, Oregon USA
| | - Thomas E. Yankeelov
- Institute for Computational Engineering and Sciences, The University of Texas at Austin Austin, Texas USA
- Livestrong Cancer Institutes, The University of Texas at Austin Austin, Texas USA
- Department of Biomedical Engineering, The University of Texas at Austin Austin, Texas USA
- Department of Oncology, The University of Texas at Austin Austin, Texas USA
- Department of Diagnostic Medicine, The University of Texas at Austin Austin, Texas USA
| |
Collapse
|
22
|
Bratus A, Samokhin I, Yegorov I, Yurchenko D. Maximization of viability time in a mathematical model of cancer therapy. Math Biosci 2017; 294:110-119. [PMID: 29074355 DOI: 10.1016/j.mbs.2017.10.011] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2017] [Revised: 10/12/2017] [Accepted: 10/20/2017] [Indexed: 01/07/2023]
Abstract
In this paper, we study a dynamic optimization problem for a general nonlinear mathematical model for therapy of a lethal form of cancer. The model describes how the populations of cancer and normal cells evolve under the influence of the concentrations of nutrients (oxygen, glucose, etc.) and the applied therapeutic agent (drug). Regulated intensity of the therapy is interpreted as a time-dependent control strategy. The therapy (control) goal is to maximize the viability time, i. e., the duration of staying in a so-called safety region (which specifies safe living conditions of a patient in terms of constraints on the amounts of cancer and normal cells), subject to limited resources of the therapeutic agent. In a specific benchmark case, a novel optimality principle for admissible therapy strategies is established. It states that the optimal trajectories should finally reach a certain corner of the safety region or at least the upper constraint on the quantity of cancer cells. The results of numerical simulations appear to be in good agreement with the proposed principle. Typical qualitative structures of optimal treatment strategies are also obtained. Furthermore, important characteristics of the model are the competition coefficient (describing the negative influence of cancer cells on normal cells), the upper bound in the drug integral constraint, and the ratio between the therapy and damage coefficients (i. e., the ratio between the positive primary and negative side effects of the therapy).
Collapse
Affiliation(s)
- Alexander Bratus
- Lomonosov Moscow State University, Leninskie Gory, MSU, 2nd educational building, Moscow, 119991, Russia; Moscow State University of Railway Engineering, Obraztsova 15, Moscow, 127994, Russia.
| | - Igor Samokhin
- Lomonosov Moscow State University, Leninskie Gory, MSU, 2nd educational building, Moscow, 119991, Russia.
| | - Ivan Yegorov
- Inria Sophia Antipolis - Méditerranée (as a part of Université Côte d'Azur, Inria, INRA, CNRS, UPMC Univ Paris 06), Borel building, 2004, route des Lucioles - BP 93, 06 902 Sophia Antipolis Cedex, France.
| | | |
Collapse
|
23
|
Elazab A. Low grade glioma growth modeling considering chemotherapy and radiotherapy effects from magnetic resonance images. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2017; 2017:3077-3080. [PMID: 29060548 DOI: 10.1109/embc.2017.8037507] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Studying tumor growth using mathematical models from magnetic resonance (MR) images is an important application that is believed to play a major role in cancer treatment by predicting tumor evolution, quantifying the response to therapy, and treatment planning. Reaction diffusion is the most popular model because of its simplicity and consistency with the biological growth process. However, most of the current growth models focus on presurgical images and likely without treatment. In this paper, we propose a new reaction diffusion model to consider the chemotherapy and radiotherapy effects on the tumor growth modelling for patients with low grade glioma. The proposed model does not consider the tensor information from diffusion tensor imaging. Instead it uses a weighted parameter to promote higher diffusivity in white matter. The radiotherapy and chemotherapy effects are considered as a loss terms in the proposed model. The preliminary results of the proposed model on synthetic and 2 real MR images show that, our model can effectively simulate tumor growth with high accuracies when treatments are administrated to low grade glioma patients.
Collapse
|
24
|
Elazab A, Bai H, Abdulazeem YM, Abdelhamid T, Zhou S, Wong KKL, Hu Q. Post-Surgery Glioma Growth Modeling from Magnetic Resonance Images for Patients with Treatment. Sci Rep 2017; 7:1222. [PMID: 28450707 PMCID: PMC5430870 DOI: 10.1038/s41598-017-01189-2] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2017] [Accepted: 03/22/2017] [Indexed: 01/17/2023] Open
Abstract
Reaction diffusion is the most common growth modelling methodology due to its simplicity and consistency with the biological tumor growth process. However, current extensions of the reaction diffusion model lack one or more of the following: efficient inclusion of treatments' effects, taking into account the viscoelasticity of brain tissues, and guaranteed stability of the numerical solution. We propose a new model to overcome the aforementioned drawbacks. Guided by directional information derived from diffusion tensor imaging, our model relates tissue heterogeneity with the absorption of the chemotherapy, adopts the linear-quadratic term to simulate the radiotherapy effect, employs Maxwell-Weichert model to incorporate brain viscoelasticity, and ensures the stability of the numerical solution. The performance is verified through experiments on synthetic and real MR images. Experiments on 9 MR datasets of patients with low grade gliomas undergoing surgery with different treatment regimens are carried out and validated using Jaccard score and Dice coefficient. The growth simulation accuracies of the proposed model are in ranges of [0.673 0.822] and [0.805 0.902] for Jaccard scores and Dice coefficients, respectively. The accuracies decrease up to 4% and 2.4% when ignoring treatment effects and the tensor information, while brain viscoelasticity has no significant impact on the accuracies.
Collapse
Affiliation(s)
- Ahmed Elazab
- Research Laboratory for Medical Imaging and Digital Surgery, Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences, Shenzhen, China
- Department of Computer Science, Faculty Computers and Information, Mansoura University, Mansoura City, Egypt
- Department of Computer Science, Misr Higher Institute for commerce and computers, Mansoura City, Egypt
| | - Hongmin Bai
- Department of Neurosurgery, Guangzhou General Hospital of Guangzhou Military Command, Guangzhou, China
| | - Yousry M Abdulazeem
- Department of Computer Engineering, Misr Higher Institute for Engineering and Technology, Mansoura City, Egypt
| | - Talaat Abdelhamid
- Department of Physics and Mathematical Engineering, Faculty of Electronic Engineering, Menoufiya University, Al Minufiyah, Egypt
| | - Sijie Zhou
- Department of Neurosurgery, Guangzhou General Hospital of Guangzhou Military Command, Guangzhou, China
| | - Kelvin K L Wong
- School of Medicine, Western Sydney University, Campbelltown, New South Wales, Australia.
| | - Qingmao Hu
- Research Laboratory for Medical Imaging and Digital Surgery, Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences, Shenzhen, China.
- Key Laboratory of Human-Machine Intelligence-Synergy Systems, Chinese Academy of Sciences, Shenzhen, China.
| |
Collapse
|
25
|
|
26
|
Alfonso JCL, Köhn-Luque A, Stylianopoulos T, Feuerhake F, Deutsch A, Hatzikirou H. Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights. Sci Rep 2016; 6:37283. [PMID: 27876890 PMCID: PMC5120360 DOI: 10.1038/srep37283] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2016] [Accepted: 10/26/2016] [Indexed: 12/18/2022] Open
Abstract
Gliomas are highly invasive brain tumours characterised by poor prognosis and limited response to therapy. There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve tumour blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation induced by blood vessel occlusion/collapse. In contrast, the therapeutic intention of normalising the abnormal tumour vasculature is to improve the efficacy of conventional treatment modalities. Although these strategies have shown therapeutic potential, it remains unclear why they both often fail to control glioma growth. To shed some light on this issue, we propose a mathematical model based on the migration/proliferation dichotomy of glioma cells in order to investigate why vaso-modulatory interventions have shown limited success in terms of tumour clearance. We found the existence of a critical cell proliferation/diffusion ratio that separates glioma responses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the front speed and increase the infiltration width, for those in the other regime, the invasion speed increases and infiltration width decreases. We discuss how these in silico findings can be used to guide individualised vaso-modulatory approaches to improve treatment success rates.
Collapse
Affiliation(s)
- J C L Alfonso
- Braunschweig Integrated Centre of Systems Biology and Helmholtz Center for Infectious Research, Braunschweig, Germany.,Center for Information Services and High Performance Computing, Technische Universität Dresden, Germany
| | - A Köhn-Luque
- Department of Biostatistics, Faculty of Medicine, University of Oslo, Norway.,BigInsight, Centre for Research-based Innovation (SFI), Oslo, Norway
| | - T Stylianopoulos
- Cancer Biophysics Laboratory, Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia, Cyprus
| | - F Feuerhake
- Institute of Pathology, Medical School of Hannover, Germany.,Institute of Neuropathology, University Clinic Freiburg, Germany
| | - A Deutsch
- Center for Information Services and High Performance Computing, Technische Universität Dresden, Germany
| | - H Hatzikirou
- Braunschweig Integrated Centre of Systems Biology and Helmholtz Center for Infectious Research, Braunschweig, Germany
| |
Collapse
|
27
|
Meghdadi N, Soltani M, Niroomand-Oscuii H, Ghalichi F. Image based modeling of tumor growth. AUSTRALASIAN PHYSICAL & ENGINEERING SCIENCES IN MEDICINE 2016; 39:601-13. [PMID: 27596102 DOI: 10.1007/s13246-016-0475-5] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2016] [Accepted: 08/16/2016] [Indexed: 01/11/2023]
Abstract
Tumors are a main cause of morbidity and mortality worldwide. Despite the efforts of the clinical and research communities, little has been achieved in the past decades in terms of improving the treatment of aggressive tumors. Understanding the underlying mechanism of tumor growth and evaluating the effects of different therapies are valuable steps in predicting the survival time and improving the patients' quality of life. Several studies have been devoted to tumor growth modeling at different levels to improve the clinical outcome by predicting the results of specific treatments. Recent studies have proposed patient-specific models using clinical data usually obtained from clinical images and evaluating the effects of various therapies. The aim of this review is to highlight the imaging role in tumor growth modeling and provide a worthwhile reference for biomedical and mathematical researchers with respect to tumor modeling using the clinical data to develop personalized models of tumor growth and evaluating the effect of different therapies.
Collapse
Affiliation(s)
- N Meghdadi
- Division of Biomechanics, Department of Mechanical Engineering, Sahand University of Technology, East Azerbaijan, Tabriz, Iran.,Computational Medicine Institute, Tehran, Iran
| | - M Soltani
- Division of Nuclear Medicine, Department of Radiology and Radiological Science, Johns Hopkins University School of Medicine, Baltimore, MD, 21287-0807, USA. .,Department of Mechanical Engineering, K. N. T. University of Technology, Tehran, Iran. .,Cancer Biology Research Center, Tehran University of Medical Sciences, Tehran, Iran. .,Computational Medicine Institute, Tehran, Iran.
| | - H Niroomand-Oscuii
- Division of Biomechanics, Department of Mechanical Engineering, Sahand University of Technology, East Azerbaijan, Tabriz, Iran.
| | - F Ghalichi
- Division of Biomechanics, Department of Mechanical Engineering, Sahand University of Technology, East Azerbaijan, Tabriz, Iran
| |
Collapse
|
28
|
Cai Y, Wu J, Li Z, Long Q. Mathematical Modelling of a Brain Tumour Initiation and Early Development: A Coupled Model of Glioblastoma Growth, Pre-Existing Vessel Co-Option, Angiogenesis and Blood Perfusion. PLoS One 2016; 11:e0150296. [PMID: 26934465 PMCID: PMC4774981 DOI: 10.1371/journal.pone.0150296] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2015] [Accepted: 02/11/2016] [Indexed: 01/12/2023] Open
Abstract
We propose a coupled mathematical modelling system to investigate glioblastoma growth in response to dynamic changes in chemical and haemodynamic microenvironments caused by pre-existing vessel co-option, remodelling, collapse and angiogenesis. A typical tree-like architecture network with different orders for vessel diameter is designed to model pre-existing vasculature in host tissue. The chemical substances including oxygen, vascular endothelial growth factor, extra-cellular matrix and matrix degradation enzymes are calculated based on the haemodynamic environment which is obtained by coupled modelling of intravascular blood flow with interstitial fluid flow. The haemodynamic changes, including vessel diameter and permeability, are introduced to reflect a series of pathological characteristics of abnormal tumour vessels including vessel dilation, leakage, angiogenesis, regression and collapse. Migrating cells are included as a new phenotype to describe the migration behaviour of malignant tumour cells. The simulation focuses on the avascular phase of tumour development and stops at an early phase of angiogenesis. The model is able to demonstrate the main features of glioblastoma growth in this phase such as the formation of pseudopalisades, cell migration along the host vessels, the pre-existing vasculature co-option, angiogenesis and remodelling. The model also enables us to examine the influence of initial conditions and local environment on the early phase of glioblastoma growth.
Collapse
Affiliation(s)
- Yan Cai
- State Key Laboratory of Bioelectronics, Southeast University, Nanjing, China
- School of Biological Science and Medical Engineering, Southeast University, Nanjing, China
- * E-mail:
| | - Jie Wu
- School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai, China
| | - Zhiyong Li
- State Key Laboratory of Bioelectronics, Southeast University, Nanjing, China
- School of Biological Science and Medical Engineering, Southeast University, Nanjing, China
| | - Quan Long
- Brunel Institute for Bioengineering, School of Engineering and Design, Brunel University, Uxbridge, Middlesex, United Kingdom
- * E-mail:
| |
Collapse
|
29
|
Colombo MC, Giverso C, Faggiano E, Boffano C, Acerbi F, Ciarletta P. Towards the Personalized Treatment of Glioblastoma: Integrating Patient-Specific Clinical Data in a Continuous Mechanical Model. PLoS One 2015; 10:e0132887. [PMID: 26186462 PMCID: PMC4505854 DOI: 10.1371/journal.pone.0132887] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2015] [Accepted: 06/22/2015] [Indexed: 12/31/2022] Open
Abstract
Glioblastoma multiforme (GBM) is the most aggressive and malignant among brain tumors. In addition to uncontrolled proliferation and genetic instability, GBM is characterized by a diffuse infiltration, developing long protrusions that penetrate deeply along the fibers of the white matter. These features, combined with the underestimation of the invading GBM area by available imaging techniques, make a definitive treatment of GBM particularly difficult. A multidisciplinary approach combining mathematical, clinical and radiological data has the potential to foster our understanding of GBM evolution in every single patient throughout his/her oncological history, in order to target therapeutic weapons in a patient-specific manner. In this work, we propose a continuous mechanical model and we perform numerical simulations of GBM invasion combining the main mechano-biological characteristics of GBM with the micro-structural information extracted from radiological images, i.e. by elaborating patient-specific Diffusion Tensor Imaging (DTI) data. The numerical simulations highlight the influence of the different biological parameters on tumor progression and they demonstrate the fundamental importance of including anisotropic and heterogeneous patient-specific DTI data in order to obtain a more accurate prediction of GBM evolution. The results of the proposed mathematical model have the potential to provide a relevant benefit for clinicians involved in the treatment of this particularly aggressive disease and, more importantly, they might drive progress towards improving tumor control and patient’s prognosis.
Collapse
Affiliation(s)
- Maria Cristina Colombo
- MOX-Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy; Fondazione CEN, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - Chiara Giverso
- MOX-Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy; Fondazione CEN, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - Elena Faggiano
- MOX-Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy; Labs-Department of Chemistry, Materials and Chemical Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - Carlo Boffano
- Neuroradiology-Fondazione I.R.C.C.S. Istituto Neurologico Carlo Besta, Via Celoria 11, 20133 Milano, Italy
| | - Francesco Acerbi
- Department of Neurosurgery-Fondazione I.R.C.C.S. Istituto Neurologico Carlo Besta, Via Celoria 11, 20133 Milano, Italy
| | - Pasquale Ciarletta
- Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France
| |
Collapse
|
30
|
Banerjee S, Khajanchi S, Chaudhuri S. A mathematical model to elucidate brain tumor abrogation by immunotherapy with T11 target structure. PLoS One 2015; 10:e0123611. [PMID: 25955428 PMCID: PMC4425651 DOI: 10.1371/journal.pone.0123611] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2014] [Accepted: 02/19/2015] [Indexed: 11/17/2022] Open
Abstract
T11 Target structure (T11TS), a membrane glycoprotein isolated from sheep erythrocytes, reverses the immune suppressed state of brain tumor induced animals by boosting the functional status of the immune cells. This study aims at aiding in the design of more efficacious brain tumor therapies with T11 target structure. We propose a mathematical model for brain tumor (glioma) and the immune system interactions, which aims in designing efficacious brain tumor therapy. The model encompasses considerations of the interactive dynamics of glioma cells, macrophages, cytotoxic T-lymphocytes (CD8+ T-cells), TGF-β, IFN-γ and the T11TS. The system undergoes sensitivity analysis, that determines which state variables are sensitive to the given parameters and the parameters are estimated from the published data. Computer simulations were used for model verification and validation, which highlight the importance of T11 target structure in brain tumor therapy.
Collapse
Affiliation(s)
- Sandip Banerjee
- Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee - 247667, Uttaranchal, India
| | - Subhas Khajanchi
- Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee - 247667, Uttaranchal, India
| | - Swapna Chaudhuri
- Department of Laboratory Medicine, School of Tropical Medicine, Kolkata-700073, West Bengal, India
| |
Collapse
|
31
|
Mi H, Petitjean C, Dubray B, Vera P, Ruan S. Prediction of lung tumor evolution during radiotherapy in individual patients with PET. IEEE TRANSACTIONS ON MEDICAL IMAGING 2014; 33:995-1003. [PMID: 24710167 DOI: 10.1109/tmi.2014.2301892] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We propose a patient-specific model based on partial differential equation to predict the evolution of lung tumors during radiotherapy. The evolution of tumor cell density is formulated by three terms: 1) advection describing the advective flux transport of tumor cells, 2) proliferation representing the tumor cell proliferation modeled as Gompertz differential equation, and 3) treatment quantifying the radiotherapeutic efficacy from linear quadratic formulation. We consider that tumor cell density variation can be derived from positron emission tomography images, the novel idea is to model the advection term by calculating 3D optical flow field from sequential images. To estimate patient-specific parameters, we propose an optimization between the predicted and observed images, under a global constraint that the tumor volume decreases exponentially as radiation dose increases. A thresholding on the predicted tumor cell densities is then used to define tumor contours, tumor volumes and maximum standardized uptake values (SUVmax). Results obtained on seven patients show a satisfying agreement between the predicted tumor contours and those drawn by an expert.
Collapse
|
32
|
Groh CM, Hubbard ME, Jones PF, Loadman PM, Periasamy N, Sleeman BD, Smye SW, Twelves CJ, Phillips RM. Mathematical and computational models of drug transport in tumours. J R Soc Interface 2014; 11:20131173. [PMID: 24621814 DOI: 10.1098/rsif.2013.1173] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
The ability to predict how far a drug will penetrate into the tumour microenvironment within its pharmacokinetic (PK) lifespan would provide valuable information about therapeutic response. As the PK profile is directly related to the route and schedule of drug administration, an in silico tool that can predict the drug administration schedule that results in optimal drug delivery to tumours would streamline clinical trial design. This paper investigates the application of mathematical and computational modelling techniques to help improve our understanding of the fundamental mechanisms underlying drug delivery, and compares the performance of a simple model with more complex approaches. Three models of drug transport are developed, all based on the same drug binding model and parametrized by bespoke in vitro experiments. Their predictions, compared for a 'tumour cord' geometry, are qualitatively and quantitatively similar. We assess the effect of varying the PK profile of the supplied drug, and the binding affinity of the drug to tumour cells, on the concentration of drug reaching cells and the accumulated exposure of cells to drug at arbitrary distances from a supplying blood vessel. This is a contribution towards developing a useful drug transport modelling tool for informing strategies for the treatment of tumour cells which are 'pharmacokinetically resistant' to chemotherapeutic strategies.
Collapse
Affiliation(s)
- C M Groh
- Klinik und Poliklinik für Strahlentherapie (Medizinische Physik), Universitätsklinikum Würzburg, , Josef-Schneider-Strasse 11, 97080 Würzburg, Germany
| | | | | | | | | | | | | | | | | |
Collapse
|
33
|
Bratus A, Fimmel E, Kovalenko S. On assessing quality of therapy in non-linear distributed mathematical models for brain tumor growth dynamics. Math Biosci 2014; 248:88-96. [DOI: 10.1016/j.mbs.2013.12.007] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2012] [Revised: 12/12/2013] [Accepted: 12/16/2013] [Indexed: 10/25/2022]
|
34
|
Unkelbach J, Menze BH, Konukoglu E, Dittmann F, Le M, Ayache N, Shih HA. Radiotherapy planning for glioblastoma based on a tumor growth model: improving target volume delineation. Phys Med Biol 2014; 59:747-70. [PMID: 24440875 DOI: 10.1088/0031-9155/59/3/747] [Citation(s) in RCA: 45] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
Glioblastoma differ from many other tumors in the sense that they grow infiltratively into the brain tissue instead of forming a solid tumor mass with a defined boundary. Only the part of the tumor with high tumor cell density can be localized through imaging directly. In contrast, brain tissue infiltrated by tumor cells at low density appears normal on current imaging modalities. In current clinical practice, a uniform margin, typically two centimeters, is applied to account for microscopic spread of disease that is not directly assessable through imaging. The current treatment planning procedure can potentially be improved by accounting for the anisotropy of tumor growth, which arises from different factors: anatomical barriers such as the falx cerebri represent boundaries for migrating tumor cells. In addition, tumor cells primarily spread in white matter and infiltrate gray matter at lower rate. We investigate the use of a phenomenological tumor growth model for treatment planning. The model is based on the Fisher-Kolmogorov equation, which formalizes these growth characteristics and estimates the spatial distribution of tumor cells in normal appearing regions of the brain. The target volume for radiotherapy planning can be defined as an isoline of the simulated tumor cell density. This paper analyzes the model with respect to implications for target volume definition and identifies its most critical components. A retrospective study involving ten glioblastoma patients treated at our institution has been performed. To illustrate the main findings of the study, a detailed case study is presented for a glioblastoma located close to the falx. In this situation, the falx represents a boundary for migrating tumor cells, whereas the corpus callosum provides a route for the tumor to spread to the contralateral hemisphere. We further discuss the sensitivity of the model with respect to the input parameters. Correct segmentation of the brain appears to be the most crucial model input. We conclude that the tumor growth model provides a method to account for anisotropic growth patterns of glioma, and may therefore provide a tool to make target delineation more objective and automated.
Collapse
Affiliation(s)
- Jan Unkelbach
- Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, MA, USA
| | | | | | | | | | | | | |
Collapse
|
35
|
Belmonte-Beitia J, Woolley T, Scott J, Maini P, Gaffney E. Modelling biological invasions: Individual to population scales at interfaces. J Theor Biol 2013; 334:1-12. [DOI: 10.1016/j.jtbi.2013.05.033] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2012] [Revised: 05/24/2013] [Accepted: 05/28/2013] [Indexed: 11/27/2022]
|
36
|
Hawkins-Daarud A, Rockne RC, Anderson ARA, Swanson KR. Modeling Tumor-Associated Edema in Gliomas during Anti-Angiogenic Therapy and Its Impact on Imageable Tumor. Front Oncol 2013; 3:66. [PMID: 23577324 PMCID: PMC3616256 DOI: 10.3389/fonc.2013.00066] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2012] [Accepted: 03/14/2013] [Indexed: 12/22/2022] Open
Abstract
Glioblastoma, the most aggressive form of primary brain tumor, is predominantly assessed with gadolinium-enhanced T1-weighted (T1Gd) and T2-weighted magnetic resonance imaging (MRI). Pixel intensity enhancement on the T1Gd image is understood to correspond to the gadolinium contrast agent leaking from the tumor-induced neovasculature, while hyperintensity on the T2/FLAIR images corresponds with edema and infiltrated tumor cells. None of these modalities directly show tumor cells; rather, they capture abnormalities in the microenvironment caused by the presence of tumor cells. Thus, assessing disease response after treatments impacting the microenvironment remains challenging through the obscuring lens of MR imaging. Anti-angiogenic therapies have been used in the treatment of gliomas with spurious results ranging from no apparent response to significant imaging improvement with the potential for extremely diffuse patterns of tumor recurrence on imaging and autopsy. Anti-angiogenic treatment normalizes the vasculature, effectively decreasing vessel permeability and thus reducing tumor-induced edema, drastically altering T2-weighted MRI. We extend a previously developed mathematical model of glioma growth to explicitly incorporate edema formation allowing us to directly characterize and potentially predict the effects of anti-angiogenics on imageable tumor growth. A comparison of simulated glioma growth and imaging enhancement with and without bevacizumab supports the current understanding that anti-angiogenic treatment can serve as a surrogate for steroids and the clinically driven hypothesis that anti-angiogenic treatment may not have any significant effect on the growth dynamics of the overall tumor cell populations. However, the simulations do illustrate a potentially large impact on the level of edematous extracellular fluid, and thus on what would be imageable on T2/FLAIR MR. Additionally, by evaluating virtual tumors with varying growth kinetics, we see tumors with lower proliferation rates will have the most reduction in swelling from such treatments.
Collapse
|
37
|
Baldock AL, Rockne RC, Boone AD, Neal ML, Hawkins-Daarud A, Corwin DM, Bridge CA, Guyman LA, Trister AD, Mrugala MM, Rockhill JK, Swanson KR. From patient-specific mathematical neuro-oncology to precision medicine. Front Oncol 2013; 3:62. [PMID: 23565501 PMCID: PMC3613895 DOI: 10.3389/fonc.2013.00062] [Citation(s) in RCA: 64] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2012] [Accepted: 03/07/2013] [Indexed: 01/28/2023] Open
Abstract
Gliomas are notoriously aggressive, malignant brain tumors that have variable response to treatment. These patients often have poor prognosis, informed primarily by histopathology. Mathematical neuro-oncology (MNO) is a young and burgeoning field that leverages mathematical models to predict and quantify response to therapies. These mathematical models can form the basis of modern “precision medicine” approaches to tailor therapy in a patient-specific manner. Patient-specific models (PSMs) can be used to overcome imaging limitations, improve prognostic predictions, stratify patients, and assess treatment response in silico. The information gleaned from such models can aid in the construction and efficacy of clinical trials and treatment protocols, accelerating the pace of clinical research in the war on cancer. This review focuses on the growing translation of PSM to clinical neuro-oncology. It will also provide a forward-looking view on a new era of patient-specific MNO.
Collapse
Affiliation(s)
- A L Baldock
- Department of Neurological Surgery, Northwestern University Chicago, IL, USA ; Brain Tumor Institute, Northwestern University Chicago, IL, USA
| | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
38
|
Chakrabarti A, Verbridge S, Stroock AD, Fischbach C, Varner JD. Multiscale models of breast cancer progression. Ann Biomed Eng 2012; 40:2488-500. [PMID: 23008097 DOI: 10.1007/s10439-012-0655-8] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2012] [Accepted: 09/04/2012] [Indexed: 12/13/2022]
Abstract
Breast cancer initiation, invasion and metastasis span multiple length and time scales. Molecular events at short length scales lead to an initial tumorigenic population, which left unchecked by immune action, acts at increasingly longer length scales until eventually the cancer cells escape from the primary tumor site. This series of events is highly complex, involving multiple cell types interacting with (and shaping) the microenvironment. Multiscale mathematical models have emerged as a powerful tool to quantitatively integrate the convective-diffusion-reaction processes occurring on the systemic scale, with the molecular signaling processes occurring on the cellular and subcellular scales. In this study, we reviewed the current state of the art in cancer modeling across multiple length scales, with an emphasis on the integration of intracellular signal transduction models with pro-tumorigenic chemical and mechanical microenvironmental cues. First, we reviewed the underlying biomolecular origin of breast cancer, with a special emphasis on angiogenesis. Then, we summarized the development of tissue engineering platforms which could provide high-fidelity ex vivo experimental models to identify and validate multiscale simulations. Lastly, we reviewed top-down and bottom-up multiscale strategies that integrate subcellular networks with the microenvironment. We present models of a variety of cancers, in addition to breast cancer specific models. Taken together, we expect as the sophistication of the simulations increase, that multiscale modeling and bottom-up agent-based models in particular will become an increasingly important platform technology for basic scientific discovery, as well as the identification and validation of potentially novel therapeutic targets.
Collapse
Affiliation(s)
- Anirikh Chakrabarti
- School of Chemical and Biomolecular Engineering, 244 Olin Hall, Cornell University, Ithaca, NY 14853, USA
| | | | | | | | | |
Collapse
|
39
|
Murray JD. Vignettes from the field of mathematical biology: the application of mathematics to biology and medicine. Interface Focus 2012; 2:397-406. [PMID: 23919124 DOI: 10.1098/rsfs.2011.0102] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2011] [Accepted: 01/05/2012] [Indexed: 11/12/2022] Open
Abstract
The application of mathematical models in biology and medicine has a long history. From the sparse number of papers in the first half of the twentieth century with a few scientists working in the field it has become vast with thousands of active researchers. We give a brief, and far from definitive history, of how some parts of the field have developed and how the type of research has changed. We describe in more detail just two examples of specific models which are directly related to real biological problems, namely animal coat patterns and the growth and image enhancement of glioblastoma brain tumours.
Collapse
Affiliation(s)
- J D Murray
- Applied and Computational Mathematics and Ecology and Evolutionary Biology , Princeton University , Princeton, NJ 08544-1003 , USA
| |
Collapse
|
40
|
In silico modelling of tumour margin diffusion and infiltration: review of current status. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2012; 2012:672895. [PMID: 22919432 PMCID: PMC3418724 DOI: 10.1155/2012/672895] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/13/2012] [Accepted: 04/11/2012] [Indexed: 11/17/2022]
Abstract
As a result of advanced treatment techniques, requiring precise target definitions, a need for more accurate delineation of the Clinical Target Volume (CTV) has arisen. Mathematical modelling is found to be a powerful tool to provide fairly accurate predictions for the Microscopic Extension (ME) of a tumour to be incorporated in a CTV. In general terms, biomathematical models based on a sequence of observations or development of a hypothesis assume some links between biological mechanisms involved in cancer development and progression to provide quantitative or qualitative measures of tumour behaviour as well as tumour response to treatment. Generally, two approaches are taken: deterministic and stochastic modelling. In this paper, recent mathematical models, including deterministic and stochastic methods, are reviewed and critically compared. It is concluded that stochastic models are more promising to provide a realistic description of cancer tumour behaviour due to being intrinsically probabilistic as well as discrete, which enables incorporation of patient-specific biomedical data such as tumour heterogeneity and anatomical boundaries.
Collapse
|
41
|
Murray JD. Glioblastoma brain tumours: estimating the time from brain tumour initiation and resolution of a patient survival anomaly after similar treatment protocols. JOURNAL OF BIOLOGICAL DYNAMICS 2012; 6 Suppl 2:118-127. [PMID: 22882019 DOI: 10.1080/17513758.2012.678392] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
A practical mathematical model for glioblastomas (brain tumours), which incorporates the two key parameters of tumour growth, namely the cancer cell diffusion and the cell proliferation rate, has been shown to be clinically useful and predictive. Previous studies explain why multifocal recurrence is inevitable and show how various treatment scenarios have been incorporated in the model. In most tumours, it is not known when the cancer started. Based on patient in vivo parameters, obtained from two brain scans, it is shown how to estimate the time, after initial detection, when the tumour started. This is an input of potential importance in any future controlled clinical study of any connection between cell phone radiation and brain tumour incidence. It is also used to estimate more accurately survival times from detection. Finally, based on patient parameters, the solution of the model equation of the tumour growth helps to explain why certain patients live longer than others after similar treatment protocols specifically surgical resection (removal) and irradiation.
Collapse
Affiliation(s)
- J D Murray
- Applied and Computational Mathematics, Princeton University, Princeton, NJ, USA.
| |
Collapse
|
42
|
Gevertz J. Optimization of vascular-targeting drugs in a computational model of tumor growth. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:041914. [PMID: 22680505 DOI: 10.1103/physreve.85.041914] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2011] [Indexed: 06/01/2023]
Abstract
A biophysical tool is introduced that seeks to provide a theoretical basis for helping drug design teams assess the most promising drug targets and design optimal treatment strategies. The tool is grounded in a previously validated computational model of the feedback that occurs between a growing tumor and the evolving vasculature. In this paper, the model is particularly used to explore the therapeutic effectiveness of two drugs that target the tumor vasculature: angiogenesis inhibitors (AIs) and vascular disrupting agents (VDAs). Using sensitivity analyses, the impact of VDA dosing parameters is explored, as is the effects of administering a VDA with an AI. Further, a stochastic optimization scheme is utilized to identify an optimal dosing schedule for treatment with an AI and a chemotherapeutic. The treatment regimen identified can successfully halt simulated tumor growth, even after the cessation of therapy.
Collapse
Affiliation(s)
- Jana Gevertz
- Department of Mathematics and Statistics, The College of New Jersey, Ewing, New Jersey 08628, USA.
| |
Collapse
|
43
|
Roniotis A, Sakkalis V, Karatzanis I, Zervakis ME, Marias K. In-depth analysis and evaluation of diffusive glioma models. ACTA ACUST UNITED AC 2012; 16:299-307. [PMID: 22287245 DOI: 10.1109/titb.2012.2185704] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Glioma is one of the most aggressive types of brain tumor. Several mathematical models have been developed during the past two decades, toward simulating the mechanisms that govern the development of glioma. The most common models use the diffusion-reaction equation (DRE) for simulating the spatiotemporal variation of tumor cell concentration. Nevertheless, despite the applications presented, there has been little work on studying the details of the mathematical solution and implementation of the 3-D diffusion model and presenting a qualitative analysis of the algorithmic results. This paper presents a complete mathematical framework on the solution of the DRE using different numerical schemes. This framework takes into account all characteristics of the latest models, such as brain tissue heterogeneity, anisotropic tumor cell migration, chemotherapy, and resection modeling. The different numerical schemes presented have been evaluated based upon the degree to which the DRE exact solution is approximated. Experiments have been conducted both on real datasets and a test case for which there is a known algebraic expression of the solution. Thus, it is possible to calculate the accuracy of the different models.
Collapse
Affiliation(s)
- Alexandros Roniotis
- Institute of Computer Science, Foundation for Research and Technology, Heraklion, Greece.
| | | | | | | | | |
Collapse
|
44
|
ROCKNE RUSSELL, ALVORD ELLSWORTHC, REED PJ, SWANSON KRISTINR. MODELING THE GROWTH AND INVASION OF GLIOMAS, FROM SIMPLE TO COMPLEX: THE GOLDIE LOCKS PARADIGM. ACTA ACUST UNITED AC 2011. [DOI: 10.1142/s1793048008000642] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
As with all mathematical modeling, the scope of the question to be explored determines the scope of the most appropriate model. The case is no different for the modeling of primary brain tumors (gliomas), ranging from too simple, not accounting for the major feature of gliomas (extensive invasion), to too complicated, with too many variables and no easy way to translate from culture media in vitro to brain tissue in vivo. We settle on a "just right" approach which utilizes currently available magnetic resonance imaging (MRI) to estimate two defining characteristics, net rates of proliferation (ρ) and diffusion (D). Most importantly, these parameters are predictive of clinical behavior, and can be tailored to individual patients in vivo and in real time. These two rates combine to generate a linear radial growth pattern of the MRI visible portion of each glioma. Further, we introduce a novel method for the calculation of glioma invasion through grey and white matter.
Collapse
Affiliation(s)
- RUSSELL ROCKNE
- Department of Pathology, University of Washington, 1959 N.E. Pacific St., Seattle WA 98195, USA
| | - ELLSWORTH C. ALVORD
- Department of Pathology, University of Washington, 1959 N.E. Pacific St., Seattle WA 98195, USA
| | - P. J. REED
- Department of Pathology, University of Washington, 1959 N.E. Pacific St., Seattle WA 98195, USA
| | - KRISTIN R. SWANSON
- Department of Pathology, University of Washington, 1959 N.E. Pacific St., Seattle WA 98195, USA
| |
Collapse
|
45
|
Swanson KR, Rockne RC, Claridge J, Chaplain MA, Alvord EC, Anderson ARA. Quantifying the role of angiogenesis in malignant progression of gliomas: in silico modeling integrates imaging and histology. Cancer Res 2011; 71:7366-75. [PMID: 21900399 DOI: 10.1158/0008-5472.can-11-1399] [Citation(s) in RCA: 139] [Impact Index Per Article: 10.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Gliomas are uniformly fatal forms of primary brain neoplasms that vary from low- to high-grade (glioblastoma). Whereas low-grade gliomas are weakly angiogenic, glioblastomas are among the most angiogenic tumors. Thus, interactions between glioma cells and their tissue microenvironment may play an important role in aggressive tumor formation and progression. To quantitatively explore how tumor cells interact with their tissue microenvironment, we incorporated the interactions of normoxic glioma cells, hypoxic glioma cells, vascular endothelial cells, diffusible angiogenic factors, and necrosis formation into a first-generation, biologically based mathematical model for glioma growth and invasion. Model simulations quantitatively described the spectrum of in vivo dynamics of gliomas visualized with medical imaging. Furthermore, we investigated how proliferation and dispersal of glioma cells combine to induce increasing degrees of cellularity, mitoses, hypoxia-induced neoangiogenesis and necrosis, features that characterize increasing degrees of "malignancy," and we found that changes in the net rates of proliferation (ρ) and invasion (D) are not always necessary for malignant progression. Thus, although other factors, including the accumulation of genetic mutations, can change cellular phenotype (e.g., proliferation and invasion rates), this study suggests that these are not required for malignant progression. Simulated results are placed in the context of the current clinical World Health Organization grading scheme for studying specific patient examples. This study suggests that through the application of the proposed model for tumor-microenvironment interactions, predictable patterns of dynamic changes in glioma histology distinct from changes in cellular phenotype (e.g., proliferation and invasion rates) may be identified, thus providing a powerful clinical tool.
Collapse
Affiliation(s)
- Kristin R Swanson
- Department of Pathology, University of Washington School of Medicine, Seattle, Washington, USA.
| | | | | | | | | | | |
Collapse
|
46
|
Bohman LE, Swanson KR, Moore JL, Rockne R, Mandigo C, Hankinson T, Assanah M, Canoll P, Bruce JN. Magnetic resonance imaging characteristics of glioblastoma multiforme: implications for understanding glioma ontogeny. Neurosurgery 2011; 67:1319-27; discussion 1327-8. [PMID: 20871424 DOI: 10.1227/neu.0b013e3181f556ab] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
BACKGROUND Identifying the origin of gliomas carries important implications for advancing the treatment of these recalcitrant tumors. Recent research promotes the hypothesis of a subventricular zone (SVZ) origin for the stemlike gliomagenic cells identified within human glioma specimens. However, conflicting evidence suggests that SVZ-like cells are not uniquely gliomagenic but this capacity may be shared by cycling progenitors distributed throughout the subcortical white matter (SCWM). OBJECTIVE To review radiological evidence in glioblastoma multiforme (GBM) patients to provide insight into the question of glioma ontogeny. METHODS We explored whether GBMs at first diagnosis demonstrated a pattern of anatomic distribution consistent with origin at the SVZ through retrospective analysis of preoperative contrast-enhanced T1-weighted magnetic resonance images in 63 patients. We then examined the relationship of tumor volume, point of origin, and proximity to the ventricles using a computer model of glioma growth. RESULTS Fewer than half of the GBMs analyzed had contrast-enhancing portions that contacted the ventricle on preoperative imaging. A strong correlation was found between tumor volume and the distance between the contrast-enhancing edge of the tumor and the ventricle, demonstrating that tumors abutting the ventricle are significantly larger than those that do not. The lesions simulated by the computer model validated our assumption that tumors that are radiographically distant from the ventricles are unlikely to have originated in the SVZ and supported our hypothesis that as they grow, the edges of all tumors will near the ventricles, regardless of their point of origin. CONCLUSION This work offers further support for the hypothesis that the origins of GBMs are at sites distributed throughout the white matter and are not limited to the region of the SVZ.
Collapse
Affiliation(s)
- Leif-Erik Bohman
- Department of Neurological Surgery, Columbia University College of Physicians and Surgeons, New York, New York, USA
| | | | | | | | | | | | | | | | | |
Collapse
|
47
|
Ellingson BM, Cloughesy TF, Lai A, Nghiemphu PL, Pope WB. Cell invasion, motility, and proliferation level estimate (CIMPLE) maps derived from serial diffusion MR images in recurrent glioblastoma treated with bevacizumab. J Neurooncol 2011; 105:91-101. [PMID: 21442275 DOI: 10.1007/s11060-011-0567-8] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2010] [Accepted: 03/17/2011] [Indexed: 01/27/2023]
Abstract
Microscopic invasion of tumor cells and undetected tumor proliferation is the primary reason for a dismal prognosis in glioblastoma patients. Identification and quantification of spatially localized brain regions undergoing high rates of cell migration and proliferation is critical for improving patient survival; however, there are currently no non-invasive imaging biomarkers for estimating proliferation and migration rates of human gliomas in vivo. To accomplish this, we developed CIMPLE (cell invasion, motility, and proliferation level estimates) image maps using serial diffusion MRI scans and a solution to a glioma growth model equation. CIMPLE represent a novel method of quantifying the level of aggressive malignant behavior. In the current pilot study, we demonstrate the utility of CIMPLE maps to predict progression free survival (PFS) and overall survival (OS) in 26 recurrent glioblastoma patients treated with bevacizumab from our Neuro-Oncology database. Voxel-wise estimates of cell proliferation rate predicted spatial regions of contrast enhancement in 35% of patients. A linear correlation was found between the mean proliferation rate and progression-free survival (PFS; P < 0.0001) as well as overall survival (OS; P = 0.0093). Similarly, the mean proliferation rate was able to stratify patients with early and late PFS as well as OS.
Collapse
Affiliation(s)
- Benjamin M Ellingson
- Department of Radiological Sciences, David Geffen School of Medicine, University of California Los Angeles, Los Angeles, CA 90024, USA.
| | | | | | | | | |
Collapse
|
48
|
Ellingson BM, LaViolette PS, Rand SD, Malkin MG, Connelly JM, Mueller WM, Prost RW, Schmainda KM. Spatially quantifying microscopic tumor invasion and proliferation using a voxel-wise solution to a glioma growth model and serial diffusion MRI. Magn Reson Med 2010; 65:1131-43. [PMID: 21413079 DOI: 10.1002/mrm.22688] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2010] [Revised: 09/20/2010] [Accepted: 09/26/2010] [Indexed: 01/15/2023]
Abstract
The purpose of this study was to develop a voxel-wise analytical solution to a glioma growth model using serial diffusion MRI. These cell invasion, motility, and proliferation level estimates (CIMPLE maps) provide quantitative estimates of microscopic tumor growth dynamics. After an analytical solution was found, noise simulations were performed to predict the effects that perturbations in apparent diffusion coefficient values and the time between apparent diffusion coefficient map acquisitions would have on the accuracy of CIMPLE maps. CIMPLE maps were then created for 53 patients with gliomas with WHO grades of II-IV. MR spectroscopy estimates of the choline-to-N-acetylaspartate ratio were compared to cell proliferation estimates in CIMPLE maps using Pearson's correlation analysis. Median differences in cell proliferation and diffusion rates between WHO grades were compared. A strong correlation (R(2) = 0.9714) and good spatial correspondence were observed between MR spectroscopy measurements of the choline-to-N-acetylaspartate ratio and CIMPLE map cell proliferation rate estimates. Estimates of cell proliferation and diffusion rates appear to be significantly different between low- (WHO II) and high-grade (WHO III-IV) gliomas. Cell diffusion rate (motility) estimates are highly dependent on the time interval between apparent diffusion coefficient map acquisitions, whereas cell proliferation rate estimates are additionally influenced by the level of noise present in apparent diffusion coefficient maps.
Collapse
Affiliation(s)
- Benjamin M Ellingson
- Department of Radiological Sciences, David Geffen School of Medicine at UCLA, Los Angeles, California, USA
| | | | | | | | | | | | | | | |
Collapse
|
49
|
Rockne R, Rockhill JK, Mrugala M, Spence AM, Kalet I, Hendrickson K, Lai A, Cloughesy T, Alvord EC, Swanson KR. Predicting the efficacy of radiotherapy in individual glioblastoma patients in vivo: a mathematical modeling approach. Phys Med Biol 2010; 55:3271-85. [PMID: 20484781 DOI: 10.1088/0031-9155/55/12/001] [Citation(s) in RCA: 170] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Glioblastoma multiforme (GBM) is the most malignant form of primary brain tumors known as gliomas. They proliferate and invade extensively and yield short life expectancies despite aggressive treatment. Response to treatment is usually measured in terms of the survival of groups of patients treated similarly, but this statistical approach misses the subgroups that may have responded to or may have been injured by treatment. Such statistics offer scant reassurance to individual patients who have suffered through these treatments. Furthermore, current imaging-based treatment response metrics in individual patients ignore patient-specific differences in tumor growth kinetics, which have been shown to vary widely across patients even within the same histological diagnosis and, unfortunately, these metrics have shown only minimal success in predicting patient outcome. We consider nine newly diagnosed GBM patients receiving diagnostic biopsy followed by standard-of-care external beam radiation therapy (XRT). We present and apply a patient-specific, biologically based mathematical model for glioma growth that quantifies response to XRT in individual patients in vivo. The mathematical model uses net rates of proliferation and migration of malignant tumor cells to characterize the tumor's growth and invasion along with the linear-quadratic model for the response to radiation therapy. Using only routinely available pre-treatment MRIs to inform the patient-specific bio-mathematical model simulations, we find that radiation response in these patients, quantified by both clinical and model-generated measures, could have been predicted prior to treatment with high accuracy. Specifically, we find that the net proliferation rate is correlated with the radiation response parameter (r = 0.89, p = 0.0007), resulting in a predictive relationship that is tested with a leave-one-out cross-validation technique. This relationship predicts the tumor size post-therapy to within inter-observer tumor volume uncertainty. The results of this study suggest that a mathematical model can create a virtual in silico tumor with the same growth kinetics as a particular patient and can not only predict treatment response in individual patients in vivo but also provide a basis for evaluation of response in each patient to any given therapy.
Collapse
Affiliation(s)
- R Rockne
- Department of Pathology, University of Washington, 1959 NE Pacific St, Seattle, WA 98195, USA
| | | | | | | | | | | | | | | | | | | |
Collapse
|
50
|
Vital-Lopez FG, Armaou A, Hutnik M, Maranas CD. Modeling the effect of chemotaxis on glioblastoma tumor progression. AIChE J 2010. [DOI: 10.1002/aic.12296] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|