Patient specific tumor growth prediction using multimodal images

Modeling free tumor growth: Discrete, continuum, and hybrid approaches to interpreting cancer development

Tumor growth dynamics serve as a critical aspect of understanding cancer progression and treatment response to mitigate one of the most pressing challenges in healthcare. The in silico approach to understanding tumor behavior computationally provides an efficient, cost-effective alternative to wet-lab examinations and are adaptable to different environmental conditions, time scales, and unique patient parameters. As a result, this paper explored modeling of free tumor growth in cancer, surveying contemporary literature on continuum, discrete, and hybrid approaches. Factors like predictive power and high-resolution simulation competed against drawbacks like simulation load and parameter feasibility in these models. Understanding tumor behavior in different scenarios and contexts became the first step in advancing cancer research and revolutionizing clinical outcomes.

Diagnostic and Therapeutic Issues in Glioma Using Imaging Data: The Challenge of Numerical Twinning

Glial tumors represent the leading etiology of primary brain tumors. Their particularities lie in (i) their location in a highly functional organ that is difficult to access surgically, including for biopsy, and (ii) their rapid, anisotropic mode of extension, notably via the fiber bundles of the white matter, which further limits the possibilities of resection. The use of mathematical tools enables the development of numerical models representative of the oncotype, genotype, evolution, and therapeutic response of lesions. The significant development of digital technologies linked to high-resolution NMR exploration, coupled with the possibilities offered by AI, means that we can envisage the creation of digital twins of tumors and their host organs, thus reducing the use of physical sampling.

ConvLSTM coordinated longitudinal transformer under spatio-temporal features for tumor growth prediction

Accurate quantification of tumor growth patterns can indicate the development process of the disease. According to the important features of tumor growth rate and expansion, physicians can intervene and diagnose patients more efficiently to improve the cure rate. However, the existing longitudinal growth model can not well analyze the dependence between tumor growth pixels in the long space-time, and fail to effectively fit the nonlinear growth law of tumors. So, we propose the ConvLSTM coordinated longitudinal Transformer (LCTformer) under spatiotemporal features for tumor growth prediction. We design the Adaptive Edge Enhancement Module (AEEM) to learn static spatial features of different size tumors under time series and make the depth model more focused on tumor edge regions. In addition, we propose the Growth Prediction Module (GPM) to characterize the future growth trend of tumors. It consists of a Longitudinal Transformer and ConvLSTM. Based on the adaptive abstract features of current tumors, Longitudinal Transformer explores the dynamic growth patterns between spatiotemporal CT sequences and learns the future morphological features of tumors under the dual views of residual information and sequence motion relationship in parallel. ConvLSTM can better learn the location information of target tumors, and it complements Longitudinal Transformer to jointly predict future imaging of tumors to reduce the loss of growth information. Finally, Channel Enhancement Fusion Module (CEFM) performs the dense fusion of the generated tumor feature images in the channel and spatial dimensions and realizes accurate quantification of the whole tumor growth process. Our model has been strictly trained and tested on the NLST dataset. The average prediction accuracy can reach 88.52% (Dice score), 89.64% (Recall), and 11.06 (RMSE), which can improve the work efficiency of doctors.

Prediction of brain tumor recurrence location based on multi-modal fusion and nonlinear correlation learning

Brain tumor is one of the leading causes of cancer death. The high-grade brain tumors are easier to recurrent even after standard treatment. Therefore, developing a method to predict brain tumor recurrence location plays an important role in the treatment planning and it can potentially prolong patient's survival time. There is still little work to deal with this issue. In this paper, we present a deep learning-based brain tumor recurrence location prediction network. Since the dataset is usually small, we propose to use transfer learning to improve the prediction. We first train a multi-modal brain tumor segmentation network on the public dataset BraTS 2021. Then, the pre-trained encoder is transferred to our private dataset for extracting the rich semantic features. Following that, a multi-scale multi-channel feature fusion model and a nonlinear correlation learning module are developed to learn the effective features. The correlation between multi-channel features is modeled by a nonlinear equation. To measure the similarity between the distributions of original features of one modality and the estimated correlated features of another modality, we propose to use Kullback-Leibler divergence. Based on this divergence, a correlation loss function is designed to maximize the similarity between the two feature distributions. Finally, two decoders are constructed to jointly segment the present brain tumor and predict its future tumor recurrence location. To the best of our knowledge, this is the first work that can segment the present tumor and at the same time predict future tumor recurrence location, making the treatment planning more efficient and precise. The experimental results demonstrated the effectiveness of our proposed method to predict the brain tumor recurrence location from the limited dataset.

Integrating mechanism-based modeling with biomedical imaging to build practical digital twins for clinical oncology

Digital twins employ mathematical and computational models to virtually represent a physical object (e.g., planes and human organs), predict the behavior of the object, and enable decision-making to optimize the future behavior of the object. While digital twins have been widely used in engineering for decades, their applications to oncology are only just emerging. Due to advances in experimental techniques quantitatively characterizing cancer, as well as advances in the mathematical and computational sciences, the notion of building and applying digital twins to understand tumor dynamics and personalize the care of cancer patients has been increasingly appreciated. In this review, we present the opportunities and challenges of applying digital twins in clinical oncology, with a particular focus on integrating medical imaging with mechanism-based, tissue-scale mathematical modeling. Specifically, we first introduce the general digital twin framework and then illustrate existing applications of image-guided digital twins in healthcare. Next, we detail both the imaging and modeling techniques that provide practical opportunities to build patient-specific digital twins for oncology. We then describe the current challenges and limitations in developing image-guided, mechanism-based digital twins for oncology along with potential solutions. We conclude by outlining five fundamental questions that can serve as a roadmap when designing and building a practical digital twin for oncology and attempt to provide answers for a specific application to brain cancer. We hope that this contribution provides motivation for the imaging science, oncology, and computational communities to develop practical digital twin technologies to improve the care of patients battling cancer.

Post-Radiotherapy PET Image Outcome Prediction by Deep Learning Under Biological Model Guidance: A Feasibility Study of Oropharyngeal Cancer Application

Purpose

To develop a method of biologically guided deep learning for post-radiation 18FDG-PET image outcome prediction based on pre-radiation images and radiotherapy dose information.

Methods

Based on the classic reaction–diffusion mechanism, a novel biological model was proposed using a partial differential equation that incorporates spatial radiation dose distribution as a patient-specific treatment information variable. A 7-layer encoder–decoder-based convolutional neural network (CNN) was designed and trained to learn the proposed biological model. As such, the model could generate post-radiation 18FDG-PET image outcome predictions with breakdown biological components for enhanced explainability. The proposed method was developed using 64 oropharyngeal patients with paired 18FDG-PET studies before and after 20-Gy delivery (2 Gy/day fraction) by intensity-modulated radiotherapy (IMRT). In a two-branch deep learning execution, the proposed CNN learns specific terms in the biological model from paired 18FDG-PET images and spatial dose distribution in one branch, and the biological model generates post-20-Gy 18FDG-PET image prediction in the other branch. As in 2D execution, 718/233/230 axial slices from 38/13/13 patients were used for training/validation/independent test. The prediction image results in test cases were compared with the ground-truth results quantitatively.

Results

The proposed method successfully generated post-20-Gy 18FDG-PET image outcome prediction with breakdown illustrations of biological model components. Standardized uptake value (SUV) mean values in 18FDG high-uptake regions of predicted images (2.45 ± 0.25) were similar to ground-truth results (2.51 ± 0.33). In 2D-based Gamma analysis, the median/mean Gamma Index (<1) passing rate of test images was 96.5%/92.8% using the 5%/5 mm criterion; such result was improved to 99.9%/99.6% when 10%/10 mm was adopted.

Conclusion

The developed biologically guided deep learning method achieved post-20-Gy 18FDG-PET image outcome predictions in good agreement with ground-truth results. With the breakdown biological modeling components, the outcome image predictions could be used in adaptive radiotherapy decision-making to optimize personalized plans for the best outcome in the future.

Artificial Intelligence and Machine Learning in the Diagnosis and Management of Gastroenteropancreatic Neuroendocrine Neoplasms-A Scoping Review

Neuroendocrine neoplasms (NENs) and tumors (NETs) are rare neoplasms that may affect any part of the gastrointestinal system. In this scoping review, we attempt to map existing evidence on the role of artificial intelligence, machine learning and deep learning in the diagnosis and management of NENs of the gastrointestinal system. After implementation of inclusion and exclusion criteria, we retrieved 44 studies with 53 outcome analyses. We then classified the papers according to the type of studied NET (26 Pan-NETs, 59.1%; 3 metastatic liver NETs (6.8%), 2 small intestinal NETs, 4.5%; colorectal, rectal, non-specified gastroenteropancreatic and non-specified gastrointestinal NETs had from 1 study each, 2.3%). The most frequently used AI algorithms were Supporting Vector Classification/Machine (14 analyses, 29.8%), Convolutional Neural Network and Random Forest (10 analyses each, 21.3%), Random Forest (9 analyses, 19.1%), Logistic Regression (8 analyses, 17.0%), and Decision Tree (6 analyses, 12.8%). There was high heterogeneity on the description of the prediction model, structure of datasets, and performance metrics, whereas the majority of studies did not report any external validation set. Future studies should aim at incorporating a uniform structure in accordance with existing guidelines for purposes of reproducibility and research quality, which are prerequisites for integration into clinical practice.

Quantitative magnetic resonance imaging and tumor forecasting of breast cancer patients in the community setting

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.

Hyperpolarized Magnetic Resonance and Artificial Intelligence: Frontiers of Imaging in Pancreatic Cancer

BACKGROUND

There is an unmet need for noninvasive imaging markers that can help identify the aggressive subtype(s) of pancreatic ductal adenocarcinoma (PDAC) at diagnosis and at an earlier time point, and evaluate the efficacy of therapy prior to tumor reduction. In the past few years, there have been two major developments with potential for a significant impact in establishing imaging biomarkers for PDAC and pancreatic cancer premalignancy: (1) hyperpolarized metabolic (HP)-magnetic resonance (MR), which increases the sensitivity of conventional MR by over 10,000-fold, enabling real-time metabolic measurements; and (2) applications of artificial intelligence (AI).

OBJECTIVE

Our objective of this review was to discuss these two exciting but independent developments (HP-MR and AI) in the realm of PDAC imaging and detection from the available literature to date.

METHODS

A systematic review following the PRISMA extension for Scoping Reviews (PRISMA-ScR) guidelines was performed. Studies addressing the utilization of HP-MR and/or AI for early detection, assessment of aggressiveness, and interrogating the early efficacy of therapy in patients with PDAC cited in recent clinical guidelines were extracted from the PubMed and Google Scholar databases. The studies were reviewed following predefined exclusion and inclusion criteria, and grouped based on the utilization of HP-MR and/or AI in PDAC diagnosis.

RESULTS

Part of the goal of this review was to highlight the knowledge gap of early detection in pancreatic cancer by any imaging modality, and to emphasize how AI and HP-MR can address this critical gap. We reviewed every paper published on HP-MR applications in PDAC, including six preclinical studies and one clinical trial. We also reviewed several HP-MR-related articles describing new probes with many functional applications in PDAC. On the AI side, we reviewed all existing papers that met our inclusion criteria on AI applications for evaluating computed tomography (CT) and MR images in PDAC. With the emergence of AI and its unique capability to learn across multimodal data, along with sensitive metabolic imaging using HP-MR, this knowledge gap in PDAC can be adequately addressed. CT is an accessible and widespread imaging modality worldwide as it is affordable; because of this reason alone, most of the data discussed are based on CT imaging datasets. Although there were relatively few MR-related papers included in this review, we believe that with rapid adoption of MR imaging and HP-MR, more clinical data on pancreatic cancer imaging will be available in the near future.

CONCLUSIONS

Integration of AI, HP-MR, and multimodal imaging information in pancreatic cancer may lead to the development of real-time biomarkers of early detection, assessing aggressiveness, and interrogating early efficacy of therapy in PDAC.

Modeling of Glioma Growth with Mass Effect by Longitudinal Magnetic Resonance Imaging

It is well-known that expanding glioblastomas typically induce significant deformations of the surrounding parenchyma (i.e., the so-called ?mass effect?). In this study, we evaluate the performance of three mathematical models of tumor growth: 1) a reaction-diffusion-advection model which accounts for mass effect (RDAM), 2) a reaction-diffusion model with mass effect that is consistent only in the case of small deformations (RDM), and 3) a reaction-diffusion model that does not include the mass effect (RD). The models were calibrated with magnetic resonance imaging (MRI) data obtained during tumor development in a murine model of glioma (n = 9). We obtained T₂-weighted and contrast-enhanced T₁-weighted MRI at 6 time points over 10 days to determine the spatiotemporal variation in the mass effect and tumor concentration, respectively. We calibrated the three models using data 1) at the first four, 2) only at the first and fourth, and 3) only at the third and fourth time points. Each of these calibrations were run forward in time to predict the volume fraction of tumor cells at the conclusion of the experiment. The diffusion coefficient for the RDAM model (median of 10.65 ? 10^-3 mm²d^-1) is significantly less than those for the RD and RDM models (17.46 ? 10^-3 mm²d^-1 and 19.38 ? 10^-3 mm²d^-1, respectively). The tumor concentrations for the RD, RDM, and RDAM models have medians of 40.2%, 32.1%, and 44.7%, respectively, for the calibration using data from the first four time points. The RDM model most accurately predicts tumor growth, while the RDAM model presents the least variation in its estimates of the diffusion coefficient and proliferation rate. This study demonstrates that the mathematical models capture both tumor development and mass effect observed in experiments.

Integrating Quantitative Assays with Biologically Based Mathematical Modeling for Predictive Oncology

We provide an overview on the use of biological assays to calibrate and initialize mechanism-based models of cancer phenomena. Although artificial intelligence methods currently dominate the landscape in computational oncology, mathematical models that seek to explicitly incorporate biological mechanisms into their formalism are of increasing interest. These models can guide experimental design and provide insights into the underlying mechanisms of cancer progression. Historically, these models have included a myriad of parameters that have been difficult to quantify in biologically relevant systems, limiting their practical insights. Recently, however, there has been much interest calibrating biologically based models with the quantitative measurements available from (for example) RNA sequencing, time-resolved microscopy, and in vivo imaging. In this contribution, we summarize how a variety of experimental methods quantify tumor characteristics from the molecular to tissue scales and describe how such data can be directly integrated with mechanism-based models to improve predictions of tumor growth and treatment response.

Evaluating patient-specific neoadjuvant regimens for breast cancer via a mathematical model constrained by quantitative magnetic resonance imaging data

The ability to accurately predict response and then rigorously optimize a therapeutic regimen on a patient-specific basis, would transform oncology. Toward this end, we have developed an experimental-mathematical framework that integrates quantitative magnetic resonance imaging (MRI) data into a biophysical model to predict patient-specific treatment response of locally advanced breast cancer to neoadjuvant therapy. Diffusion-weighted and dynamic contrast-enhanced MRI data is collected prior to therapy, after 1 cycle of therapy, and at the completion of the first therapeutic regimen. The model is initialized and calibrated with the first 2 patient-specific MRI data sets to predict response at the third, which is then compared to patient outcomes (N = 18). The model's predictions for total cellularity, total volume, and the longest axis at the completion of the regimen are significant within expected measurement precision (P< 0.05) and strongly correlated with measured response (P < 0.01). Further, we use the model to investigate, in silico, a range of (practical) alternative treatment plans to achieve the greatest possible tumor control for each individual in a subgroup of patients (N = 13). The model identifies alternative dosing strategies predicted to achieve greater tumor control compared to the standard of care for 12 of 13 patients (P < 0.01). In summary, a predictive, mechanism-based mathematical model has demonstrated the ability to identify alternative treatment regimens that are forecasted to outperform the therapeutic regimens the patients clinically. This has important implications for clinical trial design with the opportunity to alter oncology care in the future.

Towards integration of 64Cu-DOTA-trastuzumab PET-CT and MRI with mathematical modeling to predict response to neoadjuvant therapy in HER2 + breast cancer

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.

Integrated Biophysical Modeling and Image Analysis: Application to Neuro-Oncology

Central nervous system (CNS) tumors come with vastly heterogeneous histologic, molecular, and radiographic landscapes, rendering their precise characterization challenging. The rapidly growing fields of biophysical modeling and radiomics have shown promise in better characterizing the molecular, spatial, and temporal heterogeneity of tumors. Integrative analysis of CNS tumors, including clinically acquired multi-parametric magnetic resonance imaging (mpMRI) and the inverse problem of calibrating biophysical models to mpMRI data, assists in identifying macroscopic quantifiable tumor patterns of invasion and proliferation, potentially leading to improved (a) detection/segmentation of tumor subregions and (b) computer-aided diagnostic/prognostic/predictive modeling. This article presents a summary of (a) biophysical growth modeling and simulation,(b) inverse problems for model calibration, (c) these models' integration with imaging workflows, and (d) their application to clinically relevant studies. We anticipate that such quantitative integrative analysis may even be beneficial in a future revision of the World Health Organization (WHO) classification for CNS tumors, ultimately improving patient survival prospects.

IMAGE-DRIVEN BIOPHYSICAL TUMOR GROWTH MODEL CALIBRATION

We present a novel formulation for the calibration of a biophysical tumor growth model from a single-time snapshot, multiparametric magnetic resonance imaging (MRI) scan of a glioblastoma patient. Tumor growth models are typically nonlinear parabolic partial differential equations (PDEs). Thus, we have to generate a second snapshot to be able to extract significant information from a single patient snapshot. We create this two-snapshot scenario as follows. We use an atlas (an average of several scans of healthy individuals) as a substitute for an earlier, pretumor, MRI scan of the patient. Then, using the patient scan and the atlas, we combine image-registration algorithms and parameter estimation algorithms to achieve a better estimate of the healthy patient scan and the tumor growth parameters that are consistent with the data. Our scheme is based on our recent work (Scheufele et al., Comput. Methods Appl. Mech. Engrg., to appear), but we apply a different and novel scheme where the tumor growth simulation in contrast to the previous work is executed in the patient brain domain and not in the atlas domain yielding more meaningful patient-specific results. As a basis, we use a PDE-constrained optimization framework. We derive a modified Picard-iteration-type solution strategy in which we alternate between registration and tumor parameter estimation in a new way. In addition, we consider an ℓ ₁ sparsity constraint on the initial condition for the tumor and integrate it with the new joint inversion scheme. We solve the sub-problems with a reduced space, inexact Gauss-Newton-Krylov/quasi-Newton method. We present results using real brain data with synthetic tumor data that show that the new scheme reconstructs the tumor parameters in a more accurate and reliable way compared to our earlier scheme.

Optimal Control Theory for Personalized Therapeutic Regimens in Oncology: Background, History, Challenges, and Opportunities

Optimal control theory is branch of mathematics that aims to optimize a solution to a dynamical system. While the concept of using optimal control theory to improve treatment regimens in oncology is not novel, many of the early applications of this mathematical technique were not designed to work with routinely available data or produce results that can eventually be translated to the clinical setting. The purpose of this review is to discuss clinically relevant considerations for formulating and solving optimal control problems for treating cancer patients. Our review focuses on two of the most widely used cancer treatments, radiation therapy and systemic therapy, as they naturally lend themselves to optimal control theory as a means to personalize therapeutic plans in a rigorous fashion. To provide context for optimal control theory to address either of these two modalities, we first discuss the major limitations and difficulties oncologists face when considering alternate regimens for their patients. We then provide a brief introduction to optimal control theory before formulating the optimal control problem in the context of radiation and systemic therapy. We also summarize examples from the literature that illustrate these concepts. Finally, we present both challenges and opportunities for dramatically improving patient outcomes via the integration of clinically relevant, patient-specific, mathematical models and optimal control theory.

Spatio-Temporal Convolutional LSTMs for Tumor Growth Prediction by Learning 4D Longitudinal Patient Data

Prognostic tumor growth modeling via volumetric medical imaging observations can potentially lead to better outcomes of tumor treatment management and surgical planning. Recent advances of convolutional networks (ConvNets) have demonstrated higher accuracy than traditional mathematical models can be achieved in predicting future tumor volumes. This indicates that deep learning based data-driven techniques may have great potentials on addressing such problem. However, current 2D image patch based modeling approaches can not make full use of the spatio-temporal imaging context of the tumor's longitudinal 4D (3D + time) patient data. Moreover, they are incapable to predict clinically-relevant tumor properties, other than the tumor volumes. In this paper, we exploit to formulate the tumor growth process through convolutional Long Short-Term Memory (ConvLSTM) that extract tumor's static imaging appearances and simultaneously capture its temporal dynamic changes within a single network. We extend ConvLSTM into the spatio-temporal domain (ST-ConvLSTM) by jointly learning the inter-slice 3D contexts and the longitudinal or temporal dynamics from multiple patient studies. Our approach can incorporate other non-imaging patient information in an end-to-end trainable manner. Experiments are conducted on the largest 4D longitudinal tumor dataset of 33 patients to date. Results validate that the proposed ST-ConvLSTM model produces a Dice score of 83.2%±5.1% and a RVD of 11.2%±10.8%, both statistically significantly outperforming (p < 0.05) other compared methods of traditional linear model, ConvLSTM, and generative adversarial network (GAN) under the metric of predicting future tumor volumes. Additionally, our new method enables the prediction of both cell density and CT intensity numbers. Last, we demonstrate the generalizability of ST-ConvLSTM by employing it in 4D medical image segmentation task, which achieves an averaged Dice score of 86.3%±1.2% for left-ventricle segmentation in 4D ultrasound with 3 seconds per patient case.

From tumour perfusion to drug delivery and clinical translation of in silico cancer models

In silico cancer models have demonstrated great potential as a tool to improve drug design, optimise the delivery of drugs to target sites in the host tissue and, hence, improve therapeutic efficacy and patient outcome. However, there are significant barriers to the successful translation of in silico technology from bench to bedside. More precisely, the specification of unknown model parameters, the necessity for models to adequately reflect in vivo conditions, and the limited amount of pertinent validation data to evaluate models' accuracy and assess their reliability, pose major obstacles in the path towards their clinical translation. This review aims to capture the state-of-the-art in in silico cancer modelling of vascularised solid tumour growth, and identify the important advances and barriers to success of these models in clinical oncology. Particular emphasis has been put on continuum-based models of cancer since they - amongst the class of mechanistic spatio-temporal modelling approaches - are well-established in simulating transport phenomena and the biomechanics of tissues, and have demonstrated potential for clinical translation. Three important avenues in in silico modelling are considered in this contribution: first, since systemic therapy is a major cancer treatment approach, we start with an overview of the tumour perfusion and angiogenesis in silico models. Next, we present the state-of-the-art in silico work encompassing the delivery of chemotherapeutic agents to cancer nanomedicines through the bloodstream, and then review continuum-based modelling approaches that demonstrate great promise for successful clinical translation. We conclude with a discussion of what we view to be the key challenges and opportunities for in silico modelling in personalised and precision medicine.

Personalized image-based tumor growth prediction in a convection-diffusion-reaction model

Inter-individual heterogeneity of tumors leads to non-effectiveness of unique therapy plans. This issue has caused a growing interest in the field of personalized medicine and its application in tumor growth evaluation. Accordingly, in this paper, a framework of personalized medicine is presented for growth prediction of brain glioma tumors. A convection-diffusion-reaction model is used as the patient-specific tumor growth model which is associated with multimodal magnetic resonance images (MRIs). Two parameters of intracellular area fraction (ICAF) and metabolic rate have been used to incorporate the physiological data obtained from medical images into the model. The framework is tested on the data of two cases of glioma tumors to document the approach; parameter estimation is made using particle swarm optimization (PSO) and genetic algorithm (GA) and the model is evaluated by comparing the predicted tumors with the observed tumors in terms of root mean square error of the ICAF maps (IRMSE), relative area difference (RAD) and Dice's coefficient (DC). Results show the differences of IRMSE, RAD and DC in 4.1 ∓ 1.15%, 0.099 ∓ 0.041 and 85.5 ∓ 7.5%, respectively. Survival times are estimated by assuming the tumor radius of 35 mm as the fatal burden. Results confirm that less-diffusive tumors lead to higher survival times. The represented framework makes it possible to personally predict the growth behavior of glioma tumors only based on patients' routine MRIs and provides a basis for modeling the personalized therapy and walking in the path of personalized medicine.

Using mathematics in MRI data management for glioma assesment

Our aim is to review the mathematical tools usefulness in MR data management for glioma diagnosis and treatment optimization. MRI does not give access to organs variations in hours or days. However a lot of multiparametric data are generated. Mathematics could help to override this paradox, the aim of this article is to show how. We first make a review on mathematical modelling using equations. Afterwards we present statistical analysis. We provide detailed examples in both sections. We finally conclude, giving some clues on in silico models.

Coupling brain-tumor biophysical models and diffeomorphic image registration

We present SIBIA (Scalable Integrated Biophysics-based Image Analysis), a framework for joint image registration and biophysical inversion and we apply it to analyze MR images of glioblastomas (primary brain tumors). We have two applications in mind. The first one is normal-to-abnormal image registration in the presence of tumor-induced topology differences. The second one is biophysical inversion based on single-time patient data. The underlying optimization problem is highly non-linear and non-convex and has not been solved before with a gradient-based approach. Given the segmentation of a normal brain MRI and the segmentation of a cancer patient MRI, we determine tumor growth parameters and a registration map so that if we "grow a tumor" (using our tumor model) in the normal brain and then register it to the patient image, then the registration mismatch is as small as possible. This "coupled problem" two-way couples the biophysical inversion and the registration problem. In the image registration step we solve a large-deformation diffeomorphic registration problem parameterized by an Eulerian velocity field. In the biophysical inversion step we estimate parameters in a reaction-diffusion tumor growth model that is formulated as a partial differential equation (PDE). In SIBIA, we couple these two sub-components in an iterative manner. We first presented the components of SIBIA in "Gholami et al., Framework for Scalable Biophysics-based Image Analysis, IEEE/ACM Proceedings of the SC2017", in which we derived parallel distributed memory algorithms and software modules for the decoupled registration and biophysical inverse problems. In this paper, our contributions are the introduction of a PDE-constrained optimization formulation of the coupled problem, and the derivation of a Picard iterative solution scheme. We perform extensive tests to experimentally assess the performance of our method on synthetic and clinical datasets. We demonstrate the convergence of the SIBIA optimization solver in different usage scenarios. We demonstrate that using SIBIA, we can accurately solve the coupled problem in three dimensions (256³ resolution) in a few minutes using 11 dual-x86 nodes.

Mechanism-Based Modeling of Tumor Growth and Treatment Response Constrained by Multiparametric Imaging Data

Multiparametric imaging is a critical tool in the noninvasive study and assessment of cancer. Imaging methods have evolved over the past several decades to provide quantitative measures of tumor and healthy tissue characteristics related to, for example, cell number, blood volume fraction, blood flow, hypoxia, and metabolism. Mechanistic models of tumor growth also have matured to a point where the incorporation of patient-specific measures could provide clinically relevant predictions of tumor growth and response. In this review, we identify and discuss approaches that use multiparametric imaging data, including diffusion-weighted magnetic resonance imaging, dynamic contrast-enhanced magnetic resonance imaging, diffusion tensor imaging, contrast-enhanced computed tomography, [18F]fluorodeoxyglucose positron emission tomography, and [18F]fluoromisonidazole positron emission tomography to initialize and calibrate mechanistic models of tumor growth and response. We focus the discussion on brain and breast cancers; however, we also identify three emerging areas of application in kidney, pancreatic, and lung cancers. We conclude with a discussion of the future directions for incorporating multiparametric imaging data and mechanistic modeling into clinical decision making for patients with cancer.

Computer simulations suggest that prostate enlargement due to benign prostatic hyperplasia mechanically impedes prostate cancer growth

Prostate cancer and benign prostatic hyperplasia are common genitourinary diseases in aging men. Both pathologies may coexist and share numerous similarities, which have suggested several connections or some interplay between them. However, solid evidence confirming their existence is lacking. Recent studies on extensive series of prostatectomy specimens have shown that tumors originating in larger prostates present favorable pathological features. Hence, large prostates may exert a protective effect against prostate cancer. In this work, we propose a mechanical explanation for this phenomenon. The mechanical stress fields that originate as tumors enlarge have been shown to slow down their dynamics. Benign prostatic hyperplasia contributes to these mechanical stress fields, hence further restraining prostate cancer growth. We derived a tissue-scale, patient-specific mechanically coupled mathematical model to qualitatively investigate the mechanical interaction of prostate cancer and benign prostatic hyperplasia. This model was calibrated by studying the deformation caused by each disease independently. Our simulations show that a history of benign prostatic hyperplasia creates mechanical stress fields in the prostate that impede prostatic tumor growth and limit its invasiveness. The technology presented herein may assist physicians in the clinical management of benign prostate hyperplasia and prostate cancer by predicting pathological outcomes on a tissue-scale, patient-specific basis.

Towards patient-specific modeling of brain tumor growth and formation of secondary nodes guided by DTI-MRI

Previous studies to simulate brain tumor progression, often investigate either temporal changes in cancer cell density or the overall tissue-level growth of the tumor mass. Here, we developed a computational model to bridge these two approaches. The model incorporates the tumor biomechanical response at the tissue level and accounts for cellular events by modeling cancer cell proliferation, infiltration to surrounding tissues, and invasion to distant locations. Moreover, acquisition of high resolution human data from anatomical magnetic resonance imaging, diffusion tensor imaging and perfusion imaging was employed within the simulations towards a realistic and patient specific model. The model predicted the intratumoral mechanical stresses to range from 20 to 34 kPa, which caused an up to 4.5 mm displacement to the adjacent healthy tissue. Furthermore, the model predicted plausible cancer cell invasion patterns within the brain along the white matter fiber tracts. Finally, by varying the tumor vascular density and its invasive outer ring thickness, our model showed the potential of these parameters for guiding the timing (83–90 days) of cancer cell distant invasion as well as the number (0–2 sites) and location (temportal and/or parietal lobe) of the invasion sites.

Precision Medicine with Imprecise Therapy: Computational Modeling for Chemotherapy in Breast Cancer

Medical oncology is in need of a mathematical modeling toolkit that can leverage clinically-available measurements to optimize treatment selection and schedules for patients. Just as the therapeutic choice has been optimized to match tumor genetics, the delivery of those therapeutics should be optimized based on patient-specific pharmacokinetic/pharmacodynamic properties. Under the current approach to treatment response planning and assessment, there does not exist an efficient method to consolidate biomarker changes into a holistic understanding of treatment response. While the majority of research on chemotherapies focus on cellular and genetic mechanisms of resistance, there are numerous patient-specific and tumor-specific measures that contribute to treatment response. New approaches that consolidate multimodal information into actionable data are needed. Mathematical modeling offers a solution to this problem. In this perspective, we first focus on the particular case of breast cancer to highlight how mathematical models have shaped the current approaches to treatment. Then we compare chemotherapy to radiation therapy. Finally, we identify opportunities to improve chemotherapy treatments using the model of radiation therapy. We posit that mathematical models can improve the application of anticancer therapeutics in the era of precision medicine. By highlighting a number of historical examples of the contributions of mathematical models to cancer therapy, we hope that this contribution serves to engage investigators who may not have previously considered how mathematical modeling can provide real insights into breast cancer therapy.

Biophysical Modeling of In Vivo Glioma Response After Whole-Brain Radiation Therapy in a Murine Model of Brain Cancer

PURPOSE

To develop and investigate a set of biophysical models based on a mechanically coupled reaction-diffusion model of the spatiotemporal evolution of tumor growth after radiation therapy.

METHODS AND MATERIALS

Post-radiation therapy response is modeled using a cell death model (Md), a reduced proliferation rate model (Mp), and cell death and reduced proliferation model (Mdp). To evaluate each model, rats (n = 12) with C6 gliomas were imaged with diffusion-weighted magnetic resonance imaging (MRI) and contrast-enhanced MRI at 7 time points over 2 weeks. Rats received either 20 or 40 Gy between the third and fourth imaging time point. Diffusion-weighted MRI was used to estimate tumor cell number within enhancing regions in contrast-enhanced MRI data. Each model was fit to the spatiotemporal evolution of tumor cell number from time point 1 to time point 5 to estimate model parameters. The estimated model parameters were then used to predict tumor growth at the final 2 imaging time points. The model prediction was evaluated by calculating the error in tumor volume estimates, average surface distance, and voxel-based cell number.

RESULTS

For both the rats treated with either 20 or 40 Gy, significantly lower error in tumor volume, average surface distance, and voxel-based cell number was observed for the Mdp and Mp models compared with the Md model. The Mdp model fit, however, had significantly lower sum squared error compared with the Mp and Md models.

CONCLUSIONS

The results of this study indicate that for both doses, the Mp and Mdp models result in accurate predictions of tumor growth, whereas the Md model poorly describes response to radiation therapy.

Translational models of tumor angiogenesis: A nexus of in silico and in vitro models

Emerging evidence shows that endothelial cells are not only the building blocks of vascular networks that enable oxygen and nutrient delivery throughout a tissue but also serve as a rich resource of angiocrine factors. Endothelial cells play key roles in determining cancer progression and response to anti-cancer drugs. Furthermore, the endothelium-specific deposition of extracellular matrix is a key modulator of the availability of angiocrine factors to both stromal and cancer cells. Considering tumor vascular network as a decisive factor in cancer pathogenesis and treatment response, these networks need to be an inseparable component of cancer models. Both computational and in vitro experimental models have been extensively developed to model tumor-endothelium interactions. While informative, they have been developed in different communities and do not yet represent a comprehensive platform. In this review, we overview the necessity of incorporating vascular networks for both in vitro and in silico cancer models and discuss recent progresses and challenges of in vitro experimental microfluidic cancer vasculature-on-chip systems and their in silico counterparts. We further highlight how these two approaches can merge together with the aim of presenting a predictive combinatorial platform for studying cancer pathogenesis and testing the efficacy of single or multi-drug therapeutics for cancer treatment.

Convolutional Invasion and Expansion Networks for Tumor Growth Prediction

Tumor growth is associated with cell invasion and mass-effect, which are traditionally formulated by mathematical models, namely reaction-diffusion equations and biomechanics. Such models can be personalized based on clinical measurements to build the predictive models for tumor growth. In this paper, we investigate the possibility of using deep convolutional neural networks to directly represent and learn the cell invasion and mass-effect, and to predict the subsequent involvement regions of a tumor. The invasion network learns the cell invasion from information related to metabolic rate, cell density, and tumor boundary derived from multimodal imaging data. The expansion network models the mass-effect from the growing motion of tumor mass. We also study different architectures that fuse the invasion and expansion networks, in order to exploit the inherent correlations among them. Our network can easily be trained on population data and personalized to a target patient, unlike most previous mathematical modeling methods that fail to incorporate population data. Quantitative experiments on a pancreatic tumor data set show that the proposed method substantially outperforms a state-of-the-art mathematical model-based approach in both accuracy and efficiency, and that the information captured by each of the two subnetworks is complementary.

Predicting tumour growth and its impact on survival in gemcitabine-treated patients with advanced pancreatic cancer

The aim of this evaluation was to characterize the impact of the tumour size (TS) effects driven by the anticancer drug gemcitabine on overall survival (OS) in patients with advanced pancreatic cancer by building and validating a predictive semi-mechanistic joint TS-OS model. TS and OS data were obtained from one phase II and one phase III study where gemcitabine was administered (1000-1250 mg/kg over 30-60 min i.v infusion) as single agent to patients (n = 285) with advanced pancreatic cancer. Drug exposure, TS and OS were linked using the population approach with NONMEM 7.3. Pancreatic tumour progression was characterized by exponential growth (doubling time = 67 weeks), and tumour response to treatment was described as a function of the weekly area under the gemcitabine triphosphate concentration vs time curve (AUC), including treatment-related resistance development. The typical predicted percentage of tumour growth inhibition with respect to no treatment was 22.3% at the end of 6 chemotherapy cycles. Emerging resistance elicited a 57% decrease in drug effects during the 6th chemotherapy cycle. Predicted TS profile was identified as main prognostic factor of OS, with tumours responders' profiles improving median OS by 30 weeks compared to stable-disease TS profiles. Results of NCT00574275 trial were predicted using this modelling framework, thereby validating the approach as a prediction tool in clinical development. Our analyses show that despite the advanced stage of the disease in this patient population, the modelling framework herein can be used to predict the likelihood of treatment success using early clinical data.

Mechanically Coupled Reaction-Diffusion Model to Predict Glioma Growth: Methodological Details

Biophysical models designed to predict the growth and response of tumors to treatment have the potential to become a valuable tool for clinicians in care of cancer patients. Specifically, individualized tumor forecasts could be used to predict response or resistance early in the course of treatment, thereby providing an opportunity for treatment selection or adaption. This chapter discusses an experimental and modeling framework in which noninvasive imaging data is used to initialize and parameterize a subject-specific model of tumor growth. This modeling approach is applied to an analysis of murine models of glioma growth.

A mechanically coupled reaction-diffusion model that incorporates intra-tumoural heterogeneity to predict in vivo glioma growth

While gliomas have been extensively modelled with a reaction-diffusion (RD) type equation it is most likely an oversimplification. In this study, three mathematical models of glioma growth are developed and systematically investigated to establish a framework for accurate prediction of changes in tumour volume as well as intra-tumoural heterogeneity. Tumour cell movement was described by coupling movement to tissue stress, leading to a mechanically coupled (MC) RD model. Intra-tumour heterogeneity was described by including a voxel-specific carrying capacity (CC) to the RD model. The MC and CC models were also combined in a third model. To evaluate these models, rats (n = 14) with C6 gliomas were imaged with diffusion-weighted magnetic resonance imaging over 10 days to estimate tumour cellularity. Model parameters were estimated from the first three imaging time points and then used to predict tumour growth at the remaining time points which were then directly compared to experimental data. The results in this work demonstrate that mechanical-biological effects are a necessary component of brain tissue tumour modelling efforts. The results are suggestive that a variable tissue carrying capacity is a needed model component to capture tumour heterogeneity. Lastly, the results advocate the need for additional effort towards capturing tumour-to-tissue infiltration.

A Predictive Mathematical Modeling Approach for the Study of Doxorubicin Treatment in Triple Negative Breast Cancer

Doxorubicin forms the basis of chemotherapy regimens for several malignancies, including triple negative breast cancer (TNBC). Here, we present a coupled experimental/modeling approach to establish an in vitro pharmacokinetic/pharmacodynamic model to describe how the concentration and duration of doxorubicin therapy shape subsequent cell population dynamics. This work features a series of longitudinal fluorescence microscopy experiments that characterize (1) doxorubicin uptake dynamics in a panel of TNBC cell lines, and (2) cell population response to doxorubicin over 30 days. We propose a treatment response model, fully parameterized with experimental imaging data, to describe doxorubicin uptake and predict subsequent population dynamics. We found that a three compartment model can describe doxorubicin pharmacokinetics, and pharmacokinetic parameters vary significantly among the cell lines investigated. The proposed model effectively captures population dynamics and translates well to a predictive framework. In a representative cell line (SUM-149PT) treated for 12 hours with doxorubicin, the mean percent errors of the best-fit and predicted models were 14% (±10%) and 16% (±12%), which are notable considering these statistics represent errors over 30 days following treatment. More generally, this work provides both a template for studies quantitatively investigating treatment response and a scalable approach toward predictions of tumor response in vivo.

Three-dimensional Image-based Mechanical Modeling for Predicting the Response of Breast Cancer to Neoadjuvant Therapy

The use of quantitative medical imaging data to initialize and constrain mechanistic mathematical models of tumor growth has demonstrated a compelling strategy for predicting therapeutic response. More specifically, we have demonstrated a data-driven framework for prediction of residual tumor burden following neoadjuvant therapy in breast cancer that uses a biophysical mathematical model combining reaction-diffusion growth/therapy dynamics and biomechanical effects driven by early time point imaging data. Whereas early work had been based on a limited dimensionality reduction (two-dimensional planar modeling analysis) to simplify the numerical implementation, in this work, we extend our framework to a fully volumetric, three-dimensional biophysical mathematical modeling approach in which parameter estimates are generated by an inverse problem based on the adjoint state method for numerical efficiency. In an in silico performance study, we show accurate parameter estimation with error less than 3% as compared to ground truth. We apply the approach to patient data from a patient with pathological complete response and a patient with residual tumor burden and demonstrate technical feasibility and predictive potential with direct comparisons between imaging data observation and model predictions of tumor cellularity and volume. Comparisons to our previous two-dimensional modeling framework reflect enhanced model prediction of residual tumor burden through the inclusion of additional imaging slices of patient-specific data.

Pancreatic Tumor Growth Prediction With Elastic-Growth Decomposition, Image-Derived Motion, and FDM-FEM Coupling

Pancreatic neuroendocrine tumors are abnormal growths of hormone-producing cells in the pancreas. Unlike the brain which is protected by the skull, the pancreas can be significantly deformed by its surrounding organs. Consequently, the tumor shape differences observable from images at different time points arise from both tumor growth and pancreatic motion, and tumor growth model personalization may be compromised if such motion is ignored. Therefore, we incorporate pancreatic motion information derived from deformable image registration in model personalization. For more accurate mechanical interactions between tumor growth and pancreatic motion, elastic-growth decomposition is used with a hyperelastic constitutive law to model the mass effect, which allows growth modeling while conserving the mechanical properties. Furthermore, a way of coupling the finite difference method and the finite element method is proposed to greatly reduce the computation time. With both 2-[18F]-fluoro-2-deoxy-D-glucose positron emission tomographic and contrast-enhanced computed tomographic images, functional, structural, and motion data are combined for a patient-specific model. Experiments on synthetic and clinical data show the importance of image-derived motion on estimating pathophysiologically plausible mechanical properties and the promising performance of our framework. From seven patient data sets, the recall, precision, Dice coefficient, relative volume difference, and average surface distance between the personalized tumor growth simulations and the measurements were 83.2 ±8.8%, 86.9 ±8.3%, 84.4 ±4.0%, 13.9 ±9.8%, and 0.6 ±0.1 mm, respectively.

Image based modeling of tumor growth

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.

Predicting in vivo glioma growth with the reaction diffusion equation constrained by quantitative magnetic resonance imaging data

Reaction-diffusion models have been widely used to model glioma growth. However, it has not been shown how accurately this model can predict future tumor status using model parameters (i.e., tumor cell diffusion and proliferation) estimated from quantitative in vivo imaging data. To this end, we used in silico studies to develop the methods needed to accurately estimate tumor specific reaction-diffusion model parameters, and then tested the accuracy with which these parameters can predict future growth. The analogous study was then performed in a murine model of glioma growth. The parameter estimation approach was tested using an in silico tumor 'grown' for ten days as dictated by the reaction-diffusion equation. Parameters were estimated from early time points and used to predict subsequent growth. Prediction accuracy was assessed at global (total volume and Dice value) and local (concordance correlation coefficient, CCC) levels. Guided by the in silico study, rats (n = 9) with C6 gliomas, imaged with diffusion weighted magnetic resonance imaging, were used to evaluate the model's accuracy for predicting in vivo tumor growth. The in silico study resulted in low global (tumor volume error <8.8%, Dice >0.92) and local (CCC values >0.80) level errors for predictions up to six days into the future. The in vivo study showed higher global (tumor volume error >11.7%, Dice <0.81) and higher local (CCC <0.33) level errors over the same time period. The in silico study shows that model parameters can be accurately estimated and used to accurately predict future tumor growth at both the global and local scale. However, the poor predictive accuracy in the experimental study suggests the reaction-diffusion equation is an incomplete description of in vivo C6 glioma biology and may require further modeling of intra-tumor interactions including segmentation of (for example) proliferative and necrotic regions.

Joint tumor growth prediction and tumor segmentation on therapeutic follow-up PET images

Tumor response to treatment varies among patients. Patient-specific prediction of tumor evolution based on medical images during the treatment can help to build and adapt patient's treatment planning in a non-invasive way. Personalized tumor growth modeling allows patient-specific prediction by estimating model parameters based on individual's images. The model parameters are often estimated by optimizing a cost function constructed based on the tumor delineations. In this paper, we propose a joint framework for tumor growth prediction and tumor segmentation in the context of patient's therapeutic follow ups. Throughout the treatment, a series of sequential positron emission tomography (PET) images are acquired for tumor response monitoring. We propose to take into account the predicted information, which is used in combination with the random walks (RW) algorithm, to develop an automatic tumor segmentation method on PET images. Moreover, we propose an iterative scheme of RW, making the segmentation more performant. Furthermore, the obtained segmentation is applied to the process of model parameter estimation so as to get the model based prediction of tumor evolution. We evaluate our methods on 7 lung tumor patients, totaling 29 PET exams, under radiotherapy by comparing the obtained tumor prediction and tumor segmentation with manual tumor delineation by expert. Our system produces promising results when compared to the state-of-the-art methods.

Tumor growth prediction with reaction-diffusion and hyperelastic biomechanical model by physiological data fusion

The goal of tumor growth prediction is to model the tumor growth process, which can be achieved by physiological modeling and model personalization from clinical measurements. Although image-driven frameworks have been proposed with promising results, several issues such as infinitesimal strain assumptions, complicated personalization procedures, and the lack of functional information, may limit their prediction accuracy. In view of these issues, we propose a framework for pancreatic neuroendocrine tumor growth prediction, which comprises a FEM-based tumor growth model with coupled reaction-diffusion equation and nonlinear biomechanics. Physiological data fusion of structural and functional images is used to improve the subject-specificity of model personalization, and a derivative-free global optimization algorithm is adopted to facilitate the complicated model and accommodate flexible choices of objective functions. With this flexibility, we propose an objective function accounting for both the tumor volume difference and the root-mean-squared error of intracellular volume fractions. Experiments were performed on synthetic and clinical data to verify the parameter estimation capability and the prediction performance. Comparisons of using different biomechanical models and objective functions were also performed. From the experimental results of eight patient data sets, the average recall, precision, Dice coefficient, and relative volume difference between predicted and measured tumor volumes were 84.5 ± 6.9%, 85.8 ± 8.2%, 84.6 ± 1.7%, and 14.2 ± 8.4%, respectively.

PET-specific parameters and radiotracers in theoretical tumour modelling

The innovation of computational techniques serves as an important step toward optimized, patient-specific management of cancer. In particular, in silico simulation of tumour growth and treatment response may eventually yield accurate information on disease progression, enhance the quality of cancer treatment, and explain why certain therapies are effective where others are not. In silico modelling is demonstrated to considerably benefit from information obtainable with PET and PET/CT. In particular, models have successfully integrated tumour glucose metabolism, cell proliferation, and cell oxygenation from multiple tracers in order to simulate tumour behaviour. With the development of novel radiotracers to image additional tumour phenomena, such as pH and gene expression, the value of PET and PET/CT data for use in tumour models will continue to grow. In this work, the use of PET and PET/CT information in in silico tumour models is reviewed. The various parameters that can be obtained using PET and PET/CT are detailed, as well as the radiotracers that may be used for this purpose, their utility, and limitations. The biophysical measures used to quantify PET and PET/CT data are also described. Finally, a list of in silico models that incorporate PET and/or PET/CT data is provided and reviewed.

The status of neuroendocrine tumor imaging: from darkness to light?

Diagnostic imaging plays a pivotal role in the diagnosis, staging, treatment selection and follow-up for neuroendocrine tumors. The available diagnostic strategies are morphologic imaging, including computed tomography, magnetic resonance imaging (MRI) and ultrasound techniques, and molecular imaging, including scintigraphy with (111)In-pentetreotide and positron emission tomography with (68)Ga-DOTA-peptides, (18)F-DOPA and (11)C-5-HTP. A combination of anatomic and functional techniques is routinely performed to optimize sensitivity and specificity. The introduction of diffusion-weighted MRI and dynamic contrast-enhanced techniques represents a promising advance in radiologic imaging, whereas new receptor-binding peptides, including somatostatin agonists and antagonists, represent the recent most favorable innovation in molecular imaging. Future development includes the short-term validation of these techniques, but in extension also a more comprehensive multilevel integration of biologic information pertaining to a specific tumor and patient, possibly encompassing genomic considerations, currently evolving as a new entity denoted 'precision medicine'. The ideal is a diagnostic sequence that captures the global status of an individual's tumor and encompasses a multidimensional characterization of tumor location, metabolic performance and target identification. To date, advances in imagery have focused on increasing resolution, discrimination and functional characterization. In the future, the fusion of imagery with the parallel analysis of biological and genomic information has the potential to considerably amplify diagnosis.

Patient specific image driven evaluation of the aggressiveness of metastases to the lung

Metastases to the lung are a therapeutic challenge because some are fast-evolving while others evolve slowly. Any insight that can be provided for which nodule has to be treated first would help clinicians. In this work, we evaluate the aggressiveness but also the response to treatment of these nodules using a calibrated mathematical model. This model is a macroscopic model describing tumoral growth through a set of nonlinear partial differential equations. It has to be calibrated to a specific patient and a specific nodule using a temporal sequence of CT scans. To this end, a new optimization technique based on a reduced order method is developed. Finally, results on two clinical cases are presented that give satisfactory numerical prognosis of the evolution of a nodule during different phases: growth, treatment and post-treatment relapse.