Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

Autonomous learning of pathologists' cancer grading rules

Deep learning (DL) algorithms have demonstrated remarkable proficiency in histopathology classification tasks, presenting an opportunity to discover disease-related features escaping visual inspection. However, the "black box" nature of DL obfuscates the basis of the classification. Here, we develop an algorithm for interpretable Deep Learning (IDL) that sheds light on the links between tissue morphology and cancer biology. We make use of a generative model trained to represent images via a combination of a semantic latent space and a noise vector to capture low level image details. We traversed the latent space so as to induce prototypical image changes associated with the disease state, which we identified via a second DL model. Applied to a dataset of clear cell renal cell carcinoma (ccRCC) tissue images the AI system pinpoints nuclear size and nucleolus density in tumor cells (but not other cell types) as the decisive features of tumor progression from grade 1 to grade 4 - mirroring the rules that have been used for decades in the clinic and are taught in textbooks. Moreover, the AI system posits a decrease in vasculature with increasing grade. While the association has been illustrated by some previous reports, the correlation is not part of currently implemented grading systems. These results indicate the potential of IDL to autonomously formalize the connection between the histopathological presentation of a disease and the underlying tissue architectural drivers.

Mathematical modeling in radiotherapy for cancer: a comprehensive narrative review

Mathematical modeling has long been a cornerstone of radiotherapy for cancer, guiding treatment prescription, planning, and delivery through versatile applications. As we enter the era of medical big data, where the integration of molecular, imaging, and clinical data at both the tumor and patient levels could promise more precise and personalized cancer treatment, the role of mathematical modeling has become even more critical. This comprehensive narrative review aims to summarize the main applications of mathematical modeling in radiotherapy, bridging the gap between classical models and the latest advancements. The review covers a wide range of applications, including radiobiology, clinical workflows, stereotactic radiosurgery/stereotactic body radiotherapy (SRS/SBRT), spatially fractionated radiotherapy (SFRT), FLASH radiotherapy (FLASH-RT), immune-radiotherapy, and the emerging concept of radiotherapy digital twins. Each of these areas is explored in depth, with a particular focus on how newer trends and innovations are shaping the future of radiation cancer treatment. By examining these diverse applications, this review provides a comprehensive overview of the current state of mathematical modeling in radiotherapy. It also highlights the growing importance of these models in the context of personalized medicine and multi-scale, multi-modal data integration, offering insights into how they can be leveraged to enhance treatment precision and patient outcomes. As radiotherapy continues to evolve, the insights gained from this review will help guide future research and clinical practice, ensuring that mathematical modeling continues to propel innovations in radiation cancer treatment.

Validating the predictions of mathematical models describing tumor growth and treatment response

Despite advances in methods to interrogate tumor biology, the observational and population-based approach of classical cancer research and clinical oncology does not enable anticipation of tumor outcomes to hasten the discovery of cancer mechanisms and personalize disease management. To address these limitations, individualized cancer forecasts have been shown to predict tumor growth and therapeutic response, inform treatment optimization, and guide experimental efforts. These predictions are obtained via computer simulations of mathematical models that are constrained with data from a patient's cancer and experiments. This book chapter addresses the validation of these mathematical models to forecast tumor growth and treatment response. We start with an overview of mathematical modeling frameworks, model selection techniques, and fundamental metrics. We then describe the usual strategies employed to validate cancer forecasts in preclinical and clinical scenarios. Finally, we discuss existing barriers in validating these predictions along with potential strategies to address them.

A mathematical model for predicting the spatiotemporal response of breast cancer cells treated with doxorubicin

Tumor heterogeneity contributes significantly to chemoresistance, a leading cause of treatment failure. To better personalize therapies, it is essential to develop tools capable of identifying and predicting intra- and inter-tumor heterogeneities. Biology-inspired mathematical models are capable of attacking this problem, but tumor heterogeneity is often overlooked in in-vivo modeling studies, while phenotypic considerations capturing spatial dynamics are not typically included in in-vitro modeling studies. We present a data assimilation-prediction pipeline with a two-phenotype model that includes a spatiotemporal component to characterize and predict the evolution of in-vitro breast cancer cells and their heterogeneous response to chemotherapy. Our model assumes that the cells can be divided into two subpopulations: surviving cells unaffected by the treatment, and irreversibly damaged cells undergoing treatment-induced death. MCF7 breast cancer cells were previously cultivated in wells for up to 1000 hours, treated with various concentrations of doxorubicin and imaged with time-resolved microscopy to record spatiotemporally-resolved cell count data. Images were used to generate cell density maps. Treatment response predictions were initialized by a training set and updated by weekly measurements. Our mathematical model successfully calibrated the spatiotemporal cell growth dynamics, achieving median [range] concordance correlation coefficients of > .99 [.88, >.99] and .73 [.58, .85] across the whole well and individual pixels, respectively. Our proposed data assimilation-prediction approach achieved values of .97 [.44, >.99] and .69 [.35, .79] for the whole well and individual pixels, respectively. Thus, our model can capture and predict the spatiotemporal dynamics of MCF7 cells treated with doxorubicin in an in-vitro setting.

Angiogenesis-elicited spectral responses of early invasive skin melanoma: Implications for the evaluation of lesion progression

Early invasive skin melanoma (EISM) associated with partial tumor invasion to the thin and optically complex papillary dermis (PD) represents a critical stage before the onset of metastasis. EISM lesions may be accompanied by angiogenesis, which can alter the PD's blood and fibril contents. A comprehensive understanding about these interconnected processes is essential for enhancing the efficacy of EISM optical evaluation methodologies. Employing a first-principles computational approach supported by measured data, we systematically assess the impact that angiogenesis can have on the EISM's spectral responses. Our findings indicate that these responses are discernibly affected by angiogenesis under distinct physiological conditions, with more substantial tissue alterations leading to accentuated spectral changes in the 550-600 nm region. Accordingly, we propose the use of a customized low-cost spectral index to monitor these processes. Furthermore, our investigation provides a high-fidelity in silico platform for interdisciplinary research on the photobiology of evolving skin melanomas.

Modelling radiobiology

Radiotherapy has played an essential role in cancer treatment for over a century, and remains one of the best-studied methods of cancer treatment. Because of its close links with the physical sciences, it has been the subject of extensive quantitative mathematical modelling, but a complete understanding of the mechanisms of radiotherapy has remained elusive. In part this is because of the complexity and range of scales involved in radiotherapy-from physical radiation interactions occurring over nanometres to evolution of patient responses over months and years. This review presents the current status and ongoing research in modelling radiotherapy responses across these scales, including basic physical mechanisms of DNA damage, the immediate biological responses this triggers, and genetic- and patient-level determinants of response. Finally, some of the major challenges in this field and potential avenues for future improvements are also discussed.

In Silico Approach to Model Heat Distribution of Magnetic Hyperthermia in the Tumoral and Healthy Vascular Network Using Tumor-on-a-Chip to Evaluate Effective Therapy

Glioblastoma multiforme (GBM) is the most severe form of brain cancer in adults, characterized by its complex vascular network that contributes to resistance to conventional therapies. Thermal therapies, such as magnetic hyperthermia (MHT), emerge as promising alternatives, using heat to selectively target tumor cells while minimizing damage to healthy tissues. The organ-on-a-chip can replicate this complex vascular network of GBM, allowing for detailed investigations of heat dissipation in MHT, while computational simulations refine treatment parameters. In this in silico study, tumor-on-a-chip models were used to optimize MHT therapy by comparing heat dissipation in normal and abnormal vascular networks, considering geometries, flow rates, and concentrations of magnetic nanoparticles (MNPs). In the high vascular complexity model, the maximum velocity was 19 times lower than in the normal vasculature model and 4 times lower than in the low-complexity tumor model, highlighting the influence of vascular complexity on velocity and temperature distribution. The MHT simulation showed greater heat intensity in the central region, with a flow rate of 1 µL/min and 0.5 mg/mL of MNPs being the best conditions to achieve the therapeutic temperature. The complex vasculature model had the lowest heat dissipation, reaching 44.15 °C, compared to 42.01 °C in the low-complexity model and 37.80 °C in the normal model. These results show that greater vascular complexity improves heat retention, making it essential to consider this heterogeneity to optimize MHT treatment. Therefore, for an efficient MHT process, it is necessary to simulate ideal blood flow and MNP conditions to ensure heat retention at the tumor site, considering its irregular vascularization and heat dissipation for effective destruction.

Systematic evaluation of MRI-based characterization of tumor-associated vascular morphology and hemodynamics via a dynamic digital phantom

Purpose

Validation of quantitative imaging biomarkers is a challenging task, due to the difficulty in measuring the ground truth of the target biological process. A digital phantom-based framework is established to systematically validate the quantitative characterization of tumor-associated vascular morphology and hemodynamics based on dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI).

Approach

A digital phantom is employed to provide a ground-truth vascular system within which 45 synthetic tumors are simulated. Morphological analysis is performed on high-spatial resolution DCE-MRI data (spatial/temporal resolution = 30 to 300    μ m / 60    s ) to determine the accuracy of locating the arterial inputs of tumor-associated vessels (TAVs). Hemodynamic analysis is then performed on the combination of high-spatial resolution and high-temporal resolution (spatial/temporal resolution = 60 to 300    μ m / 1 to 10 s) DCE-MRI data, determining the accuracy of estimating tumor-associated blood pressure, vascular extraction rate, interstitial pressure, and interstitial flow velocity.

Results

The observed effects of acquisition settings demonstrate that, when optimizing the DCE-MRI protocol for the morphological analysis, increasing the spatial resolution is helpful but not necessary, as the location and arterial input of TAVs can be recovered with high accuracy even with the lowest investigated spatial resolution. When optimizing the DCE-MRI protocol for hemodynamic analysis, increasing the spatial resolution of the images used for vessel segmentation is essential, and the spatial and temporal resolutions of the images used for the kinetic parameter fitting require simultaneous optimization.

Conclusion

An in silico validation framework was generated to systematically quantify the effects of image acquisition settings on the ability to accurately estimate tumor-associated characteristics.

Radiomics Multifactorial in Silico Model for Spatial Prediction of Glioblastoma Progression and Recurrence: A Proof-of-Concept

BACKGROUND

Radiomics-based prediction of glioblastoma spatial progression and recurrence may improve personalized strategies. However, most prototypes are based on limited monofactorial Gompertzian models of tumor growth. The present study consists of a proof of concept on the accuracy of a radiomics multifactorial in silico model in predicting short-term spatial growth and recurrence of glioblastoma.

METHODS

A radiomics-based biomathematical multifactorial in silico model was developed using magnetic resonance imaging (MRI) data from a 53-year-old patient with newly diagnosed glioblastoma of the right supramarginal gyrus. Raw and optimized models were derived from the MRI at diagnosis and matched to the preoperative MRI obtained 28 days after diagnosis to test the accuracy in predicting the short-term spatial growth of the tumor. An additional optimized model was derived from the early postoperative MRI and matched to the MRI documenting tumor recurrence to test spatial accuracy in predicting the location of recurrence. The spatial prediction accuracy of the model was reported as an average Jaccard index.

RESULTS

Optimized models yielded an average Jaccard index of 0.69 and 0.26 for short-term tumor growth and long-term recurrence site, respectively.

CONCLUSIONS

The present radiomics-based multifactorial in silico model was feasible, reliable, and accurate for short-term spatial prediction of glioblastoma progression. The predictive value for the spatial location of recurrence was still low, and refinements in the description of tissue reorganization in the peritumoral and resected areas may be critical to optimize accuracy further.

A Pilot Study on Patient-specific Computational Forecasting of Prostate Cancer Growth during Active Surveillance Using an Imaging-informed Biomechanistic Model

Active surveillance (AS) is a suitable management option for newly diagnosed prostate cancer, which usually presents low to intermediate clinical risk. Patients enrolled in AS have their tumor monitored via longitudinal multiparametric MRI (mpMRI), PSA tests, and biopsies. Hence, treatment is prescribed when these tests identify progression to higher-risk prostate cancer. However, current AS protocols rely on detecting tumor progression through direct observation according to population-based monitoring strategies. This approach limits the design of patient-specific AS plans and may delay the detection of tumor progression. Here, we present a pilot study to address these issues by leveraging personalized computational predictions of prostate cancer growth. Our forecasts are obtained with a spatiotemporal biomechanistic model informed by patient-specific longitudinal mpMRI data (T2-weighted MRI and apparent diffusion coefficient maps from diffusion-weighted MRI). Our results show that our technology can represent and forecast the global tumor burden for individual patients, achieving concordance correlation coefficients from 0.93 to 0.99 across our cohort (n = 7). In addition, we identify a model-based biomarker of higher-risk prostate cancer: the mean proliferation activity of the tumor (P = 0.041). Using logistic regression, we construct a prostate cancer risk classifier based on this biomarker that achieves an area under the ROC curve of 0.83. We further show that coupling our tumor forecasts with this prostate cancer risk classifier enables the early identification of prostate cancer progression to higher-risk disease by more than 1 year. Thus, we posit that our predictive technology constitutes a promising clinical decision-making tool to design personalized AS plans for patients with prostate cancer.

SIGNIFICANCE

Personalization of a biomechanistic model of prostate cancer with mpMRI data enables the prediction of tumor progression, thereby showing promise to guide clinical decision-making during AS for each individual patient.

Enhanced perfusion following exposure to radiotherapy: A theoretical investigation

Tumour angiogenesis leads to the formation of blood vessels that are structurally and spatially heterogeneous. Poor blood perfusion, in conjunction with increased hypoxia and oxygen heterogeneity, impairs a tumour's response to radiotherapy. The optimal strategy for enhancing tumour perfusion remains unclear, preventing its regular deployment in combination therapies. In this work, we first identify vascular architectural features that correlate with enhanced perfusion following radiotherapy, using in vivo imaging data from vascular tumours. Then, we present a novel computational model to determine the relationship between these architectural features and blood perfusion in silico. If perfusion is defined to be the proportion of vessels that support blood flow, we find that vascular networks with small mean diameters and large numbers of angiogenic sprouts show the largest increases in perfusion post-irradiation for both biological and synthetic tumours. We also identify cases where perfusion increases due to the pruning of hypoperfused vessels, rather than blood being rerouted. These results indicate the importance of considering network composition when determining the optimal irradiation strategy. In the future, we aim to use our findings to identify tumours that are good candidates for perfusion enhancement and to improve the efficacy of combination therapies.

Mathematical model of oxygen, nutrient, and drug transport in tuberculosis granulomas

Physiological abnormalities in pulmonary granulomas-pathological hallmarks of tuberculosis (TB)-compromise the transport of oxygen, nutrients, and drugs. In prior studies, we demonstrated mathematically and experimentally that hypoxia and necrosis emerge in the granuloma microenvironment (GME) as a direct result of limited oxygen availability. Building on our initial model of avascular oxygen diffusion, here we explore additional aspects of oxygen transport, including the roles of granuloma vasculature, transcapillary transport, plasma dilution, and interstitial convection, followed by cellular metabolism. Approximate analytical solutions are provided for oxygen and glucose concentration, interstitial fluid velocity, interstitial fluid pressure, and the thickness of the convective zone. These predictions are in agreement with prior experimental results from rabbit TB granulomas and from rat carcinoma models, which share similar transport limitations. Additional drug delivery predictions for anti-TB-agents (rifampicin and clofazimine) strikingly match recent spatially-resolved experimental results from a mouse model of TB. Finally, an approach to improve molecular transport in granulomas by modulating interstitial hydraulic conductivity is tested in silico.

Designing clinical trials for patients who are not average

The heterogeneity inherent in cancer means that even a successful clinical trial merely results in a therapeutic regimen that achieves, on average, a positive result only in a subset of patients. The only way to optimize an intervention for an individual patient is to reframe their treatment as their own, personalized trial. Toward this goal, we formulate a computational framework for performing personalized trials that rely on four mathematical techniques. First, mathematical models that can be calibrated with patient-specific data to make accurate predictions of response. Second, digital twins built on these models capable of simulating the effects of interventions. Third, optimal control theory applied to the digital twins to optimize outcomes. Fourth, data assimilation to continually update and refine predictions in response to therapeutic interventions. In this perspective, we describe each of these techniques, quantify their "state of readiness", and identify use cases for personalized clinical trials.

Ultrasound-mediated nano-sized drug delivery systems for cancer treatment: Multi-scale and multi-physics computational modeling

Computational modeling enables researchers to study and understand various complex biological phenomena in anticancer drug delivery systems (DDSs), especially nano-sized DDSs (NSDDSs). The combination of NSDDSs and therapeutic ultrasound (TUS), that is, focused ultrasound and low-intensity pulsed ultrasound, has made significant progress in recent years, opening many opportunities for cancer treatment. Multiple parameters require tuning and optimization to develop effective DDSs, such as NSDDSs, in which mathematical modeling can prove advantageous. In silico computational modeling of ultrasound-responsive DDS typically involves a complex framework of acoustic interactions, heat transfer, drug release from nanoparticles, fluid flow, mass transport, and pharmacodynamic governing equations. Owing to the rapid development of computational tools, modeling the different phenomena in multi-scale complex problems involved in drug delivery to tumors has become possible. In the present study, we present an in-depth review of recent advances in the mathematical modeling of TUS-mediated DDSs for cancer treatment. A detailed discussion is also provided on applying these computational models to improve the clinical translation for applications in cancer treatment. This article is categorized under: Nanotechnology Approaches to Biology > Nanoscale Systems in Biology Therapeutic Approaches and Drug Discovery > Nanomedicine for Oncologic Disease.

Computational Multi-Scale Modeling of Drug Delivery into an Anti-Angiogenic Therapy-Treated Tumor

The present study develops a numerical model, which is the most complex one, in comparison to previous research to investigate drug delivery accompanied by the anti-angiogenesis effect. This paper simulates intravascular blood flow and interstitial fluid flow using a dynamic model. The model accounts for the non-Newtonian behavior of blood and incorporates the adaptation of the diameter of a heterogeneous microvascular network derived from modeling the evolution of endothelial cells toward a circular tumor sprouting from two-parent vessels, with and without imposing the inhibitory effect of angiostatin on a modified discrete angiogenesis model. The average solute exposure and its uniformity in solid tumors of different sizes are studied by numerically solving the convection-diffusion equation. Three different methodologies are considered for simulating anti-angiogenesis: modifying the capillary network, updating the transport properties, and considering both microvasculature and transport properties modifications. It is shown that anti-angiogenic therapy decreases drug wash-out in the periphery of the tumor. Results show the decisive role of microvascular structure, particularly its distribution, and interstitial transport properties modifications induced via vascular normalization on the quality of drug delivery, such that it is improved by 39% in uniformity by the second approach in R = 0.2 cm.

Predictive digital twin for optimizing patient-specific radiotherapy regimens under uncertainty in high-grade gliomas

We develop a methodology to create data-driven predictive digital twins for optimal risk-aware clinical decision-making. We illustrate the methodology as an enabler for an anticipatory personalized treatment that accounts for uncertainties in the underlying tumor biology in high-grade gliomas, where heterogeneity in the response to standard-of-care (SOC) radiotherapy contributes to sub-optimal patient outcomes. The digital twin is initialized through prior distributions derived from population-level clinical data in the literature for a mechanistic model's parameters. Then the digital twin is personalized using Bayesian model calibration for assimilating patient-specific magnetic resonance imaging data. The calibrated digital twin is used to propose optimal radiotherapy treatment regimens by solving a multi-objective risk-based optimization under uncertainty problem. The solution leads to a suite of patient-specific optimal radiotherapy treatment regimens exhibiting varying levels of trade-off between the two competing clinical objectives: (i) maximizing tumor control (characterized by minimizing the risk of tumor volume growth) and (ii) minimizing the toxicity from radiotherapy. The proposed digital twin framework is illustrated by generating an in silico cohort of 100 patients with high-grade glioma growth and response properties typically observed in the literature. For the same total radiation dose as the SOC, the personalized treatment regimens lead to median increase in tumor time to progression of around six days. Alternatively, for the same level of tumor control as the SOC, the digital twin provides optimal treatment options that lead to a median reduction in radiation dose by 16.7% (10 Gy) compared to SOC total dose of 60 Gy. The range of optimal solutions also provide options with increased doses for patients with aggressive cancer, where SOC does not lead to sufficient tumor control.

High-temporal resolution DCE-MRI improves assessment of intra- and peri-breast lesions categorized as BI-RADS 4

BACKGROUND

BI-RADS 4 breast lesions are suspicious for malignancy with a range from 2 to 95%, indicating that numerous benign lesions are unnecessarily biopsied. Thus, we aimed to investigate whether high-temporal-resolution dynamic contrast-enhanced MRI (H_DCE-MRI) would be superior to conventional low-temporal-resolution DCE-MRI (L_DCE-MRI) in the diagnosis of BI-RADS 4 breast lesions.

METHODS

This single-center study was approved by the IRB. From April 2015 to June 2017, patients with breast lesions were prospectively included and randomly assigned to undergo either H_DCE-MRI, including 27 phases, or L_DCE-MRI, including 7 phases. Patients with BI-RADS 4 lesions were diagnosed by the senior radiologist in this study. Using a two-compartment extended Tofts model and a three-dimensional volume of interest, several pharmacokinetic parameters reflecting hemodynamics, including K^trans, K_ep, V_e, and V_p, were obtained from the intralesional, perilesional and background parenchymal enhancement areas, which were labeled the Lesion, Peri and BPE areas, respectively. Models were developed based on hemodynamic parameters, and the performance of these models in discriminating between benign and malignant lesions was evaluated by receiver operating characteristic (ROC) curve analysis.

RESULTS

A total of 140 patients were included in the study and underwent H_DCE-MRI (n = 62) or L_DCE-MRI (n = 78) scans; 56 of these 140 patients had BI-RADS 4 lesions. Some pharmacokinetic parameters from H_DCE-MRI (Lesion_K^trans, K_ep, and V_p; Peri_K^trans, K_ep, and V_p) and from L_DCE-MRI (Lesion_K_ep, Peri_V_p, BPE_K^trans and BPE_V_p) were significantly different between benign and malignant breast lesions (P < 0.01). ROC analysis showed that Lesion_K^trans (AUC = 0.866), Lesion_K_ep (AUC = 0.929), Lesion_V_p (AUC = 0.872), Peri_K^trans (AUC = 0.733), Peri_K_ep (AUC = 0.810), and Peri_V_p (AUC = 0.857) in the H_DCE-MRI group had good discrimination performance. Parameters from the BPE area showed no differentiating ability in the H_DCE-MRI group. Lesion_K_ep (AUC = 0.767), Peri_V_p (AUC = 0.726), and BPE_K^trans and BPE_V_p (AUC = 0.687 and 0.707) could differentiate between benign and malignant breast lesions in the L_DCE-MRI group. The models were compared with the senior radiologist's assessment for the identification of BI-RADS 4 breast lesions. The AUC, sensitivity and specificity of Lesion_K_ep (0.963, 100.0%, and 88.9%, respectively) in the H_DCE-MRI group were significantly higher than those of the same parameter in the L_DCE-MRI group (0.663, 69.6% and 75.0%, respectively) for the assessment of BI-RADS 4 breast lesions. The DeLong test was conducted, and there was a significant difference only between Lesion_K_ep in the H_DCE-MRI group and the senior radiologist (P = 0.04).

CONCLUSIONS

Pharmacokinetic parameters (K^trans, K_ep and V_p) from the intralesional and perilesional regions on high-temporal-resolution DCE-MRI, especially the intralesional K_ep parameter, can improve the assessment of benign and malignant BI-RADS 4 breast lesions to avoid unnecessary biopsy.

Mechanotransduction in tumor dynamics modeling

Mechanotherapy is a groundbreaking approach to impact carcinogenesis. Cells sense and respond to mechanical stimuli, translating them into biochemical signals in a process known as mechanotransduction. The impact of stress on tumor growth has been studied in the last three decades, and many papers highlight the role of mechanics as a critical self-inducer of tumor fate at the in vitro and in vivo biological levels. Meanwhile, mathematical models attempt to determine laws to reproduce tumor dynamics. This review discusses biological mechanotransduction mechanisms and mathematical-biomechanical models together. The aim is to provide a common framework for the different approaches that have emerged in the literature from the perspective of tumor avascularity and to provide insight into emerging mechanotherapies that have attracted interest in recent years.

Cellular-automaton model for tumor growth dynamics: Virtualization of different scenarios

Mathematical Oncology has emerged as a research field that applies either continuous or discrete models to mathematically describe cancer-related phenomena. Such methods are usually expressed in terms of differential equations, however tumor composition involves specific cellular structure and can demonstrate probabilistic nature, often requiring tailor-made approaches. In this context, cell-based models allow monitoring independent single parameters, which might vary in both time and space. By relying on extant tumor growth models in the literature, this study introduces cellular-automata simulation strategies that admit heterogeneous cell population while capturing both single-cell and cluster-cell behaviors. In this agent-based computational model, tumor cells are limited to follow four possible courses of action, namely: proliferation, migration, apoptosis or quiescence. Despite the apparent simplicity of those actions, the model can represent different complex tumor features depending on parameter settings. This study virtualized five different scenarios, showcasing model capabilities of representing tumor dynamics including alternate dormancy periods, cell death instability and cluster formation. Implementation techniques are also explored together with prospective model expansion towards deterministic features. The proposed stochastic cellular automaton model is able to effectively simulate different scenarios regarding tumor growth effectively, figuring as an interesting tool for in silico modeling, with promising capabilities of expansion to support research in mathematical oncology, thus improving diagnosis tools and/or personalized treatment.

A hybrid spatiotemporal model of PCa dynamics and insights into optimal therapeutic strategies

Using a hybrid cellular automaton with stochastic elements, we investigate the effectiveness of multiple drug therapies on prostate cancer (PCa) growth. The ability of Androgen Deprivation Therapy to reduce PCa growth represents a milestone in prostate cancer treatment, nonetheless most patients eventually become refractory and develop castration-resistant prostate cancer. In recent years, a "second generation" drug called enzalutamide has been used to treat advanced PCa, or patients already exposed to chemotherapy that stopped responding to it. However, tumour resistance to enzalutamide is not well understood, and in this context, preclinical models and in silico experiments (numerical simulations) are key to understanding the mechanisms of resistance and to assessing therapeutic settings that may delay or prevent the onset of resistance. In our mathematical system, we incorporate cell phenotype switching to model the development of increased drug resistance, and consider the effect of the micro-environment dynamics on necrosis and apoptosis of the tumour cells. The therapeutic strategies that we explore include using a single drug (enzalutamide), and drug combinations (enzalutamide and everolimus or cabazitaxel) with different treatment schedules. Our results highlight the effectiveness of alternating therapies, especially alternating enzalutamide and cabazitaxel over a year, and a comparison is made with data taken from TRAMP mice to verify our findings.

Towards integration of time-resolved confocal microscopy of a 3D in vitro microfluidic platform with a hybrid multiscale model of tumor angiogenesis

The goal of this study is to calibrate a multiscale model of tumor angiogenesis with time-resolved data to allow for systematic testing of mathematical predictions of vascular sprouting. The multi-scale model consists of an agent-based description of tumor and endothelial cell dynamics coupled to a continuum model of vascular endothelial growth factor concentration. First, we calibrate ordinary differential equation models to time-resolved protein concentration data to estimate the rates of secretion and consumption of vascular endothelial growth factor by endothelial and tumor cells, respectively. These parameters are then input into the multiscale tumor angiogenesis model, and the remaining model parameters are then calibrated to time resolved confocal microscopy images obtained within a 3D vascularized microfluidic platform. The microfluidic platform mimics a functional blood vessel with a surrounding collagen matrix seeded with inflammatory breast cancer cells, which induce tumor angiogenesis. Once the multi-scale model is fully parameterized, we forecast the spatiotemporal distribution of vascular sprouts at future time points and directly compare the predictions to experimentally measured data. We assess the ability of our model to globally recapitulate angiogenic vasculature density, resulting in an average relative calibration error of 17.7% ± 6.3% and an average prediction error of 20.2% ± 4% and 21.7% ± 3.6% using one and four calibrated parameters, respectively. We then assess the model's ability to predict local vessel morphology (individualized vessel structure as opposed to global vascular density), initialized with the first time point and calibrated with two intermediate time points. In this study, we have rigorously calibrated a mechanism-based, multiscale, mathematical model of angiogenic sprouting to multimodal experimental data to make specific, testable predictions.

A data assimilation framework to predict the response of glioma cells to radiation

We incorporate a practical data assimilation methodology into our previously established experimental-computational framework to predict the heterogeneous response of glioma cells receiving fractionated radiation treatment. Replicates of 9L and C6 glioma cells grown in 96-well plates were irradiated with six different fractionation schemes and imaged via time-resolved microscopy to yield 360- and 286-time courses for the 9L and C6 lines, respectively. These data were used to calibrate a biology-based mathematical model and then make predictions within two different scenarios. For Scenario 1, 70% of the time courses are fit to the model and the resulting parameter values are averaged. These average values, along with the initial cell number, initialize the model to predict the temporal evolution for each test time course (10% of the data). In Scenario 2, the predictions for the test cases are made with model parameters initially assigned from the training data, but then updated with new measurements every 24 hours via four versions of a data assimilation framework. We then compare the predictions made from Scenario 1 and the best version of Scenario 2 to the experimentally measured microscopy measurements using the concordance correlation coefficient (CCC). Across all fractionation schemes, Scenario 1 achieved a CCC value (mean ± standard deviation) of 0.845 ± 0.185 and 0.726 ± 0.195 for the 9L and C6 cell lines, respectively. For the best data assimilation version from Scenario 2 (validated with the last 20% of the data), the CCC values significantly increased to 0.954 ± 0.056 (p = 0.002) and 0.901 ± 0.061 (p = 8.9e-5) for the 9L and C6 cell lines, respectively. Thus, we have developed a data assimilation approach that incorporates an experimental-computational system to accurately predict the in vitro response of glioma cells to fractionated radiation therapy.

Optimizing combination therapy in a murine model of HER2+ breast cancer

Human epidermal growth factor receptor 2 positive (HER2+) breast cancer is frequently treated with drugs that target the HER2 receptor, such as trastuzumab, in combination with chemotherapy, such as doxorubicin. However, an open problem in treatment design is to determine the therapeutic regimen that optimally combines these two treatments to yield optimal tumor control. Working with data quantifying temporal changes in tumor volume due to different trastuzumab and doxorubicin treatment protocols in a murine model of human HER2+ breast cancer, we propose a complete framework for model development, calibration, selection, and treatment optimization to find the optimal treatment protocol. Through different assumptions for the drug-tumor interactions, we propose ten different models to characterize the dynamic relationship between tumor volume and drug availability, as well as the drug-drug interaction. Using a Bayesian framework, each of these models are calibrated to the dataset and the model with the highest Bayesian information criterion weight is selected to represent the biological system. The selected model captures the inhibition of trastuzumab due to pre-treatment with doxorubicin, as well as the increase in doxorubicin efficacy due to pre-treatment with trastuzumab. We then apply optimal control theory (OCT) to this model to identify two optimal treatment protocols. In the first optimized protocol, we fix the maximum dosage for doxorubicin and trastuzumab to be the same as the maximum dose delivered experimentally, while trying to minimize tumor burden. Within this constraint, optimal control theory indicates the optimal regimen is to first deliver two doses of trastuzumab on days 35 and 36, followed by two doses of doxorubicin on days 37 and 38. This protocol predicts an additional 45% reduction in tumor burden compared to that achieved with the experimentally delivered regimen. In the second optimized protocol we fix the tumor control to be the same as that obtained experimentally, and attempt to reduce the doxorubicin dose. Within this constraint, the optimal regimen is the same as the first optimized protocol but uses only 43% of the doxorubicin dose used experimentally. This protocol predicts tumor control equivalent to that achieved experimentally. These results strongly suggest the utility of mathematical modeling and optimal control theory for identifying therapeutic regimens maximizing efficacy and minimizing toxicity.

Towards Patient-Specific Optimization of Neoadjuvant Treatment Protocols for Breast Cancer Based on Image-Guided Fluid Dynamics

OBJECTIVE

This study establishes a fluid dynamics model personalized with patient-specific imaging data to optimize neoadjuvant therapy (i.e., doxorubicin) protocols for breast cancers.

METHODS

Ten patients recruited at the University of Chicago were included in this study. Quantitative dynamic contrast-enhanced and diffusion weighted magnetic resonance imaging data are leveraged to estimate patient-specific hemodynamic properties, which are then used to constrain the mechanism-based drug delivery model. Then, computer simulations of this model yield the subsequent drug distribution throughout the breast. By systematically varying the dosing schedule, we identify an optimized regimen for each patient using the maximum safe therapeutic duration (MSTD), which is a metric balancing treatment efficacy and toxicity.

RESULTS

With an individually optimized dose (range = 12.11-15.11 mg/m2 per injection), a 3-week regimen consisting of a uniform daily injection significantly outperforms all other scheduling strategies (P < 0.001). In particular, the optimal protocol is predicted to significantly outperform the standard protocol (P < 0.001), improving the MSTD by an average factor of 9.93 (range = 6.63 to 14.17).

CONCLUSION

A clinical-mathematical framework was developed by integrating quantitative MRI data, advanced image processing, and computational fluid dynamics to predict the efficacy and toxicity of neoadjuvant therapy protocols, thus enabling the rational identification of an optimal therapeutic regimen on a patient-specific basis.

SIGNIFICANCE

Our clinical-computational approach has the potential to enable optimization of therapeutic regimens on a patient-specific basis and provide guidance for prospective clinical trials aimed at refining neoadjuvant therapy protocols for breast cancers.

MRI-Based Digital Models Forecast Patient-Specific Treatment Responses to Neoadjuvant Chemotherapy in Triple-Negative Breast Cancer

Triple-negative breast cancer (TNBC) is persistently refractory to therapy, and methods to improve targeting and evaluation of responses to therapy in this disease are needed. Here, we integrate quantitative MRI data with biologically based mathematical modeling to accurately predict the response of TNBC to neoadjuvant systemic therapy (NAST) on an individual basis. Specifically, 56 patients with TNBC enrolled in the ARTEMIS trial (NCT02276443) underwent standard-of-care doxorubicin/cyclophosphamide (A/C) and then paclitaxel for NAST, where dynamic contrast-enhanced MRI and diffusion-weighted MRI were acquired before treatment and after two and four cycles of A/C. A biologically based model was established to characterize tumor cell movement, proliferation, and treatment-induced cell death. Two evaluation frameworks were investigated using: (i) images acquired before and after two cycles of A/C for calibration and predicting tumor status after A/C, and (ii) images acquired before, after two cycles, and after four cycles of A/C for calibration and predicting response following NAST. For Framework 1, the concordance correlation coefficients between the predicted and measured patient-specific, post-A/C changes in tumor cellularity and volume were 0.95 and 0.94, respectively. For Framework 2, the biologically based model achieved an area under the receiver operator characteristic curve of 0.89 (sensitivity/specificity = 0.72/0.95) for differentiating pathological complete response (pCR) from non-pCR, which is statistically superior (P &lt; 0.05) to the value of 0.78 (sensitivity/specificity = 0.72/0.79) achieved by tumor volume measured after four cycles of A/C. Overall, this model successfully captured patient-specific, spatiotemporal dynamics of TNBC response to NAST, providing highly accurate predictions of NAST response.

SIGNIFICANCE

Integrating MRI data with biologically based mathematical modeling successfully predicts breast cancer response to chemotherapy, suggesting digital twins could facilitate a paradigm shift from simply assessing response to predicting and optimizing therapeutic efficacy.

Replacement in angiogenesis research: Studying mechanisms of blood vessel development by animal-free in vitro, in vivo and in silico approaches

Angiogenesis, the development of new blood vessels from pre-existing ones, is an essential process determining numerous physiological and pathological conditions. Accordingly, there is a high demand for research approaches allowing the investigation of angiogenic mechanisms and the assessment of pro- and anti-angiogenic therapeutics. The present review provides a selective overview and critical discussion of such approaches, which, in line with the 3R principle, all share the common feature that they are not based on animal experiments. They include in vitro assays to study the viability, proliferation, migration, tube formation and sprouting activity of endothelial cells in two- and three-dimensional environments, the degradation of extracellular matrix compounds as well as the impact of hemodynamic forces on blood vessel formation. These assays can be complemented by in vivo analyses of microvascular network formation in the chorioallantoic membrane assay and early stages of zebrafish larvae. In addition, the combination of experimental data and physical laws enables the mathematical modeling of tissue-specific vascularization, blood flow patterns, interstitial fluid flow as well as oxygen, nutrient and drug distribution. All these animal-free approaches markedly contribute to an improved understanding of fundamental biological mechanisms underlying angiogenesis. Hence, they do not only represent essential tools in basic science but also in early stages of drug development. Moreover, their advancement bears the great potential to analyze angiogenesis in all its complexity and, thus, to make animal experiments superfluous in the future.

Opportunities for improving brain cancer treatment outcomes through imaging-based mathematical modeling of the delivery of radiotherapy and immunotherapy

Immunotherapy has become a fourth pillar in the treatment of brain tumors and, when combined with radiation therapy, may improve patient outcomes and reduce the neurotoxicity. As with other combination therapies, the identification of a treatment schedule that maximizes the synergistic effect of radiation- and immune-therapy is a fundamental challenge. Mechanism-based mathematical modeling is one promising approach to systematically investigate therapeutic combinations to maximize positive outcomes within a rigorous framework. However, successful clinical translation of model-generated combinations of treatment requires patient-specific data to allow the models to be meaningfully initialized and parameterized. Quantitative imaging techniques have emerged as a promising source of high quality, spatially and temporally resolved data for the development and validation of mathematical models. In this review, we will present approaches to personalize mechanism-based modeling frameworks with patient data, and then discuss how these techniques could be leveraged to improve brain cancer outcomes through patient-specific modeling and optimization of treatment strategies.

Oxygen gradients dictate angiogenesis but not barriergenesis in a 3D brain microvascular model

A variety of biophysical properties are known to regulate angiogenic sprouting, and in vitro systems can parse the individual effects of these factors in a controlled setting. Here, a three-dimensional brain microvascular model interrogates how variables including extracellular matrix composition, fluid shear stress, and radius of curvature affect angiogenic sprouting of cerebral endothelial cells. Tracking endothelial migration over several days reveals that application of fluid shear stress and enlarged vessel radius of curvature both attenuate sprouting. Computational modeling informed by oxygen consumption assays suggests that sprouting correlates to reduced oxygen concentration: both fluid shear stress and vessel geometry alter the local oxygen levels dictated by both ambient conditions and cellular respiration. Moreover, increasing cell density and consequently lowering the local oxygen levels yields significantly more sprouting. Further analysis reveals that the magnitude of oxygen concentration is not as important as its spatial concentration gradient: decreasing ambient oxygen concentration causes significantly less sprouting than applying an external oxygen gradient to the vessels. In contrast, barriergenesis is dictated by shear stress independent of local oxygen concentrations, suggesting that different mechanisms mediate angiogenesis and barrier formation and that angiogenic sprouting can occur without compromising the barrier. Overall, these results improve our understanding of how specific biophysical variables regulate the function and activation of cerebral vasculature, and identify spatial oxygen gradients as the driving factor of angiogenesis in the brain.

Synthetic 18F-FDG PET Image Generation Using a Combination of Biomathematical Modeling and Machine Learning

No previous works have attempted to combine generative adversarial network (GAN) architectures and the biomathematical modeling of positron emission tomography (PET) radiotracer uptake in tumors to generate extra training samples. Here, we developed a novel computational model to produce synthetic 18F-fluorodeoxyglucose (18F-FDG) PET images of solid tumors in different stages of progression and angiogenesis. First, a comprehensive biomathematical model is employed for creating tumor-induced angiogenesis, intravascular and extravascular fluid flow, as well as modeling of the transport phenomena and reaction processes of 18F-FDG in a tumor microenvironment. Then, a deep convolutional GAN (DCGAN) model is employed for producing synthetic PET images using 170 input images of 18F-FDG uptake in each of 10 different tumor microvascular networks. The interstitial fluid parameters and spatiotemporal distribution of 18F-FDG uptake in tumor and healthy tissues have been compared against previously published numerical and experimental studies, indicating the accuracy of the model. The structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR) of the generated PET sample and the experimental one are 0.72 and 28.53, respectively. Our results demonstrate that a combination of biomathematical modeling and GAN-based augmentation models provides a robust framework for the non-invasive and accurate generation of synthetic PET images of solid tumors in different stages.

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.

Cancer as a Model System for Testing Metabolic Scaling Theory

Biological allometries, such as the scaling of metabolism to mass, are hypothesized to result from natural selection to maximize how vascular networks fill space yet minimize internal transport distances and resistance to blood flow. Metabolic scaling theory argues two guiding principles—conservation of fluid flow and space-filling fractal distributions—describe a diversity of biological networks and predict how the geometry of these networks influences organismal metabolism. Yet, mostly absent from past efforts are studies that directly, and independently, measure metabolic rate from respiration and vascular architecture for the same organ, organism, or tissue. Lack of these measures may lead to inconsistent results and conclusions about metabolism, growth, and allometric scaling. We present simultaneous and consistent measurements of metabolic scaling exponents from clinical images of lung cancer, serving as a first-of-its-kind test of metabolic scaling theory, and identifying potential quantitative imaging biomarkers indicative of tumor growth. We analyze data for 535 clinical PET-CT scans of patients with non-small cell lung carcinoma to establish the presence of metabolic scaling between tumor metabolism and tumor volume. Furthermore, we use computer vision and mathematical modeling to examine predictions of metabolic scaling based on the branching geometry of the tumor-supplying blood vessel networks in a subset of 56 patients diagnosed with stage II-IV lung cancer. Examination of the scaling of maximum standard uptake value with metabolic tumor volume, and metabolic tumor volume with gross tumor volume, yield metabolic scaling exponents of 0.64 (0.20) and 0.70 (0.17), respectively. We compare these to the value of 0.85 (0.06) derived from the geometric scaling of the tumor-supplying vasculature. These results: (1) inform energetic models of growth and development for tumor forecasting; (2) identify imaging biomarkers in vascular geometry related to blood volume and flow; and (3) highlight unique opportunities to develop and test the metabolic scaling theory of ecology in tumors transitioning from avascular to vascular geometries.