Blackboard to Bedside: A Mathematical Modeling Bottom-Up Approach Toward Personalized Cancer Treatments

A Multidisciplinary Hyper-Modeling Scheme in Personalized In Silico Oncology: Coupling Cell Kinetics with Metabolism, Signaling Networks, and Biomechanics as Plug-In Component Models of a Cancer Digital Twin

The massive amount of human biological, imaging, and clinical data produced by multiple and diverse sources necessitates integrative modeling approaches able to summarize all this information into answers to specific clinical questions. In this paper, we present a hypermodeling scheme able to combine models of diverse cancer aspects regardless of their underlying method or scale. Describing tissue-scale cancer cell proliferation, biomechanical tumor growth, nutrient transport, genomic-scale aberrant cancer cell metabolism, and cell-signaling pathways that regulate the cellular response to therapy, the hypermodel integrates mutation, miRNA expression, imaging, and clinical data. The constituting hypomodels, as well as their orchestration and links, are described. Two specific cancer types, Wilms tumor (nephroblastoma) and non-small cell lung cancer, are addressed as proof-of-concept study cases. Personalized simulations of the actual anatomy of a patient have been conducted. The hypermodel has also been applied to predict tumor control after radiotherapy and the relationship between tumor proliferative activity and response to neoadjuvant chemotherapy. Our innovative hypermodel holds promise as a digital twin-based clinical decision support system and as the core of future in silico trial platforms, although additional retrospective adaptation and validation are necessary.

Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems

Theoretical and applied cancer studies that use individual-based models (IBMs) have been limited by the lack of a mathematical formulation that enables rigorous analysis of these models. However, spatial cumulant models (SCMs), which have arisen from theoretical ecology, describe population dynamics generated by a specific family of IBMs, namely spatio-temporal point processes (STPPs). SCMs are spatially resolved population models formulated by a system of differential equations that approximate the dynamics of two STPP-generated summary statistics: first-order spatial cumulants (densities), and second-order spatial cumulants (spatial covariances). We exemplify how SCMs can be used in mathematical oncology by modelling theoretical cancer cell populations comprising interacting growth factor-producing and non-producing cells. To formulate model equations, we use computational tools that enable the generation of STPPs, SCMs and mean-field population models (MFPMs) from user-defined model descriptions (Cornell et al. Nat Commun 10:4716, 2019). To calculate and compare STPP, SCM and MFPM-generated summary statistics, we develop an application-agnostic computational pipeline. Our results demonstrate that SCMs can capture STPP-generated population density dynamics, even when MFPMs fail to do so. From both MFPM and SCM equations, we derive treatment-induced death rates required to achieve non-growing cell populations. When testing these treatment strategies in STPP-generated cell populations, our results demonstrate that SCM-informed strategies outperform MFPM-informed strategies in terms of inhibiting population growths. We thus demonstrate that SCMs provide a new framework in which to study cell-cell interactions, and can be used to describe and perturb STPP-generated cell population dynamics. We, therefore, argue that SCMs can be used to increase IBMs' applicability in cancer research.

Predicting and elucidating the post-printing behavior of 3D printed cancer cells in hydrogel structures by integrating in-vitro and in-silico experiments

A key feature distinguishing 3D bioprinting from other 3D cell culture techniques is its precise control over created structures. This property allows for the high-resolution fabrication of biomimetic structures with controlled structural and mechanical properties such as porosity, permeability, and stiffness. However, analyzing post-printing cellular dynamics and optimizing their functions within the 3D fabricated environment is only possible through trial and error and replicating several experiments. This issue motivated the development of a cellular automata model for the first time to simulate post-printing cell behaviour within the 3D bioprinted construct. To improve our model, we bioprinted a 3D construct using MDA-MB-231 cell-laden hydrogel and evaluated cellular functions, including viability and proliferation in 11 days. The results showed that our model successfully simulated the 3D bioprinted structure and captured in-vitro observations. We demonstrated that in-silico model could predict and elucidate post-printing biological functions for different initial cell numbers in bioink and different bioink formulations with gelatine and alginate, without replicating several costly and time-consuming in-vitro measurements. We believe such a computational framework will substantially impact 3D bioprinting's future application. We hope this study inspires researchers to further realize how an in-silico model might be utilized to advance in-vitro 3D bioprinting research.

Mathematical modeling of cancer immunotherapy for personalized clinical translation

Encouraging advances are being made in cancer immunotherapy modeling, especially in the key areas of developing personalized treatment strategies based on individual patient parameters, predicting treatment outcomes and optimizing immunotherapy synergy when used in combination with other treatment approaches. Here we present a focused review of the most recent mathematical modeling work on cancer immunotherapy with a focus on clinical translatability. It can be seen that this field is transitioning from pure basic science to applications that can make impactful differences in patients' lives. We discuss how researchers are integrating experimental and clinical data to fully inform models so that they can be applied for clinical predictions, and present the challenges that remain to be overcome if widespread clinical adaptation is to be realized. Lastly, we discuss the most promising future applications and areas that are expected to be the focus of extensive upcoming modeling studies.

Assessing chemotherapy dosing strategies in a spatial cell culture model

Predicting patient responses to chemotherapy regimens is a major challenge in cancer treatment. Experimental model systems coupled with quantitative mathematical models to calculate optimal dose and frequency of drugs can enable improved chemotherapy regimens. Here we developed a simple approach to track two-dimensional cell colonies composed of chemo-sensitive and resistant cell populations via fluorescence microscopy and coupled this to computational model predictions. Specifically, we first developed multiple 4T1 breast cancer cell lines resistant to varying concentrations of doxorubicin, and demonstrated how heterogeneous populations expand in a two-dimensional colony. We subjected cell populations to varied dose and frequency of chemotherapy and measured colony growth. We then built a mathematical model to describe the dynamics of both chemosensitive and chemoresistant populations, where we determined which number of doses can produce the smallest tumor size based on parameters in the system. Finally, using an in vitro model we demonstrated multiple doses can decrease overall colony growth as compared to a single dose at the same total dose. In the future, this system can be adapted to optimize dosing strategies in the setting of heterogeneous cell types or patient derived cells with varied chemoresistance.

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.

Interrogating and Quantifying In Vitro Cancer Drug Pharmacodynamics via Agent-Based and Bayesian Monte Carlo Modelling

The effectiveness of chemotherapy in cancer cell regression is often limited by drug resistance, toxicity, and neoplasia heterogeneity. However, due to the significant complexities entailed by the many cancer growth processes, predicting the impact of interference and symmetry-breaking mechanisms is a difficult problem. To quantify and understand more about cancer drug pharmacodynamics, we combine in vitro with in silico cancer models. The anti-proliferative action of selected cytostatics is interrogated on human colorectal and breast adenocarcinoma cells, while an agent-based computational model is employed to reproduce experiments and shed light on the main therapeutic mechanisms of each chemotherapeutic agent. Multiple drug administration scenarios on each cancer cell line are simulated by varying the drug concentration, while a Bayesian-based method for model parameter optimisation is employed. Our proposed procedure of combining in vitro cancer drug screening with an in silico agent-based model successfully reproduces the impact of chemotherapeutic drugs in cancer growth behaviour, while the mechanisms of action of each drug are characterised through model-derived probabilities of cell apoptosis and division. We suggest that our approach could form the basis for the prospective generation of experimentally-derived and model-optimised pharmacological variables towards personalised cancer therapy.

Optimal regulation of tumour-associated neutrophils in cancer progression

In a tumour microenvironment, tumour-associated neutrophils could display two opposing differential phenotypes: anti-tumour (N1) and pro-tumour (N2) effector cells. Converting N2 to N1 neutrophils provides innovative therapies for cancer treatment. In this study, a mathematical model for N1-N2 dynamics describing the cancer survival and immune inhibition in response to TGF-β and IFN-β is considered. The effects of exogenous intervention of TGF-β inhibitor and IFN-β are examined in order to enhance N1 recruitment to combat tumour progression. Our approach employs optimal control theory to determine drug infusion protocols that could minimize tumour volume with least administration cost possible. Four optimal control scenarios corresponding to different therapeutic strategies are explored, namely, TGF-β inhibitor control only, IFN-β control only, concomitant TGF-β inhibitor and IFN-β controls, and alternating TGF-β inhibitor and IFN-β controls. For each scheme, different initial conditions are varied to depict different pathophysiological condition of a cancer patient, leading to adaptive treatment schedule. TGF-β inhibitor and IFN-β drug dosages, total drug amount, infusion times and relative cost of drug administrations are obtained under various circumstances. The control strategies achieved could guide in designing individualized therapeutic protocols.

Optimal chemotherapy counteracts cancer adaptive resistance in a cell-based, spatially-extended, evolutionary model

Most aggressive cancers are incurable due to their fast evolution of drug resistance. We model cancer growth and adaptive response in a simplified cell-based (CB) setting, assuming a genetic resistance to two chemotherapeutic drugs. We show that optimal administration protocols can steer cells resistance and turned it into a weakness for the disease. Our work extends the population-based (PB) model proposed by Orlando et al. (Physical Biology, 2012), in which a homogeneous population of cancer cells evolves according to a fitness landscape. The landscape models three types of trade-offs, differing on whether the cells are more, less, or equal effective when generalizing resistance to two drugs as opposed to specializing to a single one. The CB framework allows us to include genetic heterogeneity, spatial competition, and drugs diffusion, as well as realistic administration protocols. By calibrating our model on Orlando et al.'s assumptions, we show that dynamical protocols that alternate the two drugs minimize the cancer size at the end of (or at mid-points during) treatment. These results significantly differ from those obtained with the homogeneous model---suggesting static protocols under the pro-generalizing and neutral allocation trade-offs---highlighting the important role of spatial and genetic heterogeneities. Our work is the first attempt to search for optimal treatments in a CB setting, a step forward toward realistic clinical applications.

Quantifying ERK activity in response to inhibition of the BRAFV600E-MEK-ERK cascade using mathematical modelling

BACKGROUND

Simultaneous inhibition of multiple components of the BRAF-MEK-ERK cascade (vertical inhibition) has become a standard of care for treating BRAF-mutant melanoma. However, the molecular mechanism of how vertical inhibition synergistically suppresses intracellular ERK activity, and consequently cell proliferation, are yet to be fully elucidated.

METHODS

We develop a mechanistic mathematical model that describes how the mutant BRAF inhibitor, dabrafenib, and the MEK inhibitor, trametinib, affect BRAFV600E-MEK-ERK signalling. The model is based on a system of chemical reactions that describes cascade signalling dynamics. Using mass action kinetics, the chemical reactions are re-expressed as ordinary differential equations that are parameterised by in vitro data and solved numerically to obtain the temporal evolution of cascade component concentrations.

RESULTS

The model provides a quantitative method to compute how dabrafenib and trametinib can be used in combination to synergistically inhibit ERK activity in BRAFV600E-mutant melanoma cells. The model elucidates molecular mechanisms of vertical inhibition of the BRAFV600E-MEK-ERK cascade and delineates how elevated BRAF concentrations generate drug resistance to dabrafenib and trametinib. The computational simulations further suggest that elevated ATP levels could be a factor in drug resistance to dabrafenib.

CONCLUSIONS

The model can be used to systematically motivate which dabrafenib-trametinib dose combinations, for treating BRAFV600E-mutated melanoma, warrant experimental investigation.

Targeting Cellular DNA Damage Responses in Cancer: An In Vitro-Calibrated Agent-Based Model Simulating Monolayer and Spheroid Treatment Responses to ATR-Inhibiting Drugs

We combine a systems pharmacology approach with an agent-based modelling approach to simulate LoVo cells subjected to AZD6738, an ATR (ataxia–telangiectasia-mutated and rad3-related kinase) inhibiting anti-cancer drug that can hinder tumour proliferation by targeting cellular DNA damage responses. The agent-based model used in this study is governed by a set of empirically observable rules. By adjusting only the rules when moving between monolayer and multi-cellular tumour spheroid simulations, whilst keeping the fundamental mathematical model and parameters intact, the agent-based model is first parameterised by monolayer in vitro data and is thereafter used to simulate treatment responses in in vitro tumour spheroids subjected to dynamic drug delivery. Spheroid simulations are subsequently compared to in vivo data from xenografts in mice. The spheroid simulations are able to capture the dynamics of in vivo tumour growth and regression for approximately 8 days post-tumour injection. Translating quantitative information between in vitro and in vivo research remains a scientifically and financially challenging step in preclinical drug development processes. However, well-developed in silico tools can be used to facilitate this in vitro to in vivo translation, and in this article, we exemplify how data-driven, agent-based models can be used to bridge the gap between in vitro and in vivo research. We further highlight how agent-based models, that are currently underutilised in pharmaceutical contexts, can be used in preclinical drug development.

A mathematical framework for modelling 3D cell motility: applications to glioblastoma cell migration

The collection of 3D cell tracking data from live images of micro-tissues is a recent innovation made possible due to advances in imaging techniques. As such there is increased interest in studying cell motility in 3D in vitro model systems but a lack of rigorous methodology for analysing the resulting data sets. One such instance of the use of these in vitro models is in the study of cancerous tumours. Growing multicellular tumour spheroids in vitro allows for modelling of the tumour microenvironment and the study of tumour cell behaviours, such as migration, which improves understanding of these cells and in turn could potentially improve cancer treatments. In this paper, we present a workflow for the rigorous analysis of 3D cell tracking data, based on the persistent random walk model, but adaptable to other biologically informed mathematical models. We use statistical measures to assess the fit of the model to the motility data and to estimate model parameters and provide confidence intervals for those parameters, to allow for parametrization of the model taking correlation in the data into account. We use in silico simulations to validate the workflow in 3D before testing our method on cell tracking data taken from in vitro experiments on glioblastoma tumour cells, a brain cancer with a very poor prognosis. The presented approach is intended to be accessible to both modellers and experimentalists alike in that it provides tools for uncovering features of the data set that may suggest amendments to future experiments or modelling attempts.

Topological data analysis distinguishes parameter regimes in the Anderson-Chaplain model of angiogenesis

Angiogenesis is the process by which blood vessels form from pre-existing vessels. It plays a key role in many biological processes, including embryonic development and wound healing, and contributes to many diseases including cancer and rheumatoid arthritis. The structure of the resulting vessel networks determines their ability to deliver nutrients and remove waste products from biological tissues. Here we simulate the Anderson-Chaplain model of angiogenesis at different parameter values and quantify the vessel architectures of the resulting synthetic data. Specifically, we propose a topological data analysis (TDA) pipeline for systematic analysis of the model. TDA is a vibrant and relatively new field of computational mathematics for studying the shape of data. We compute topological and standard descriptors of model simulations generated by different parameter values. We show that TDA of model simulation data stratifies parameter space into regions with similar vessel morphology. The methodologies proposed here are widely applicable to other synthetic and experimental data including wound healing, development, and plant biology.

Towards a Reduced In Silico Model Predicting Biochemical Recurrence After Radiotherapy in Prostate Cancer

OBJECTIVE

Purposes of this work were i) to develop an in silico model of tumor response to radiotherapy, ii) to perform an exhaustive sensitivity analysis in order to iii) propose a simplified version and iv) to predict biochemical recurrence with both the comprehensive and the reduced model.

METHODS

A multiscale computational model of tumor response to radiotherapy was developed. It integrated the following radiobiological mechanisms: oxygenation, including hypoxic death; division of tumor cells; VEGF diffusion driving angiogenesis; division of healthy cells and oxygen-dependent response to irradiation, considering, cycle arrest and mitotic catastrophe. A thorough sensitivity analysis using the Morris screening method was performed on 21 prostate computational tissues. Tumor control probability (TCP) curves of the comprehensive model and 15 reduced versions were compared. Logistic regression was performed to predict biochemical recurrence after radiotherapy on 76 localized prostate cancer patients using an output of the comprehensive and the reduced models.

RESULTS

No significant difference was found between the TCP curves of the comprehensive and a simplified version which only considered oxygenation, division of tumor cells and their response to irradiation. Biochemical recurrence predictions using the comprehensive and the reduced models improved those made from pre-treatment imaging parameters (AUC = 0.81 ± 0.02 and 0.82 ± 0.02 vs. 0.75 ± 0.03, respectively).

CONCLUSION

A reduced model of tumor response to radiotherapy able to predict biochemical recurrence in prostate cancer was obtained.

SIGNIFICANCE

This reduced model may be used in the future to optimize personalized fractionation schedules.

Combining hypoxia-activated prodrugs and radiotherapy in silico: Impact of treatment scheduling and the intra-tumoural oxygen landscape

Hypoxia-activated prodrugs (HAPs) present a conceptually elegant approach to not only overcome, but better yet, exploit intra-tumoural hypoxia. Despite being successful in vitro and in vivo, HAPs are yet to achieve successful results in clinical settings. It has been hypothesised that this lack of clinical success can, in part, be explained by the insufficiently stringent clinical screening selection of determining which tumours are suitable for HAP treatments. Taking a mathematical modelling approach, we investigate how tumour properties and HAP-radiation scheduling influence treatment outcomes in simulated tumours. The following key results are demonstrated in silico: (i) HAP and ionising radiation (IR) monotherapies may attack tumours in dissimilar, and complementary, ways. (ii) HAP-IR scheduling may impact treatment efficacy. (iii) HAPs may function as IR treatment intensifiers. (iv) The spatio-temporal intra-tumoural oxygen landscape may impact HAP efficacy. Our in silico framework is based on an on-lattice, hybrid, multiscale cellular automaton spanning three spatial dimensions. The mathematical model for tumour spheroid growth is parameterised by multicellular tumour spheroid (MCTS) data.

A general mathematical framework for understanding the behavior of heterogeneous stem cell regeneration

Stem cell heterogeneity is essential for homeostasis in tissue development. This paper establishes a general mathematical framework to model the dynamics of stem cell regeneration with cell heterogeneity and random transitions of epigenetic states. The framework generalizes the classical G0 cell cycle model and incorporates the epigenetic states of individual cells represented by a continuous multidimensional variable. In the model, the kinetic rates of cell behaviors, including proliferation, differentiation, and apoptosis, are dependent on their epigenetic states, and the random transitions of epigenetic states between cell cycles are represented by an inheritance probability function that describes the conditional probability of cell state changes. Moreover, the model can be extended to include genotypic changes and describe the process of gene mutation-induced tumor development. The proposed mathematical framework provides a generalized formula that helps us to understand various dynamic processes of stem cell regeneration, including tissue development, degeneration, and abnormal growth.

Anakoinosis: Correcting Aberrant Homeostasis of Cancer Tissue-Going Beyond Apoptosis Induction

The current approach to systemic therapy for metastatic cancer is aimed predominantly at inducing apoptosis of cancer cells by blocking tumor-promoting signaling pathways or by eradicating cell compartments within the tumor. In contrast, a systems view of therapy primarily considers the communication protocols that exist at multiple levels within the tumor complex, and the role of key regulators of such systems. Such regulators may have far-reaching influence on tumor response to therapy and therefore patient survival. This implies that neoplasia may be considered as a cell non-autonomous disease. The multi-scale activity ranges from intra-tumor cell compartments, to the tumor, to the tumor-harboring organ to the organism. In contrast to molecularly targeted therapies, a systems approach that identifies the complex communications networks driving tumor growth offers the prospect of disrupting or "normalizing" such aberrant communicative behaviors and therefore attenuating tumor growth. Communicative reprogramming, a treatment strategy referred to as anakoinosis, requires novel therapeutic instruments, so-called master modifiers to deliver concerted tumor growth-attenuating action. The diversity of biological outcomes following pro-anakoinotic tumor therapy, such as differentiation, trans-differentiation, control of tumor-associated inflammation, etc. demonstrates that long-term tumor control may occur in multiple forms, inducing even continuous complete remission. Accordingly, pro-anakoinotic therapies dramatically extend the repertoire for achieving tumor control and may activate apoptosis pathways for controlling resistant metastatic tumor disease and hematologic neoplasia.

The Goldilocks Window of Personalized Chemotherapy: Getting the Immune Response Just Right

The immune system is a robust and often untapped accomplice of many standard cancer therapies. A majority of tumors exist in a state of immune tolerance where the patient's immune system has become insensitive to the cancer cells. Because of its lymphodepleting effects, chemotherapy has the potential to break this tolerance. To investigate this, we created a mathematical modeling framework of tumor-immune dynamics. Our results suggest that optimal chemotherapy scheduling must balance two opposing objectives: maximizing tumor reduction while preserving patient immune function. Successful treatment requires therapy to operate in a "Goldilocks Window" where patient immune health is not overly compromised. By keeping therapy "just right," we show that the synergistic effects of immune activation and chemotherapy can maximize tumor reduction and control. SIGNIFICANCE: To maximize the synergy between chemotherapy and antitumor immune response, lymphodepleting therapy must be balanced in a "Goldilocks Window" of optimal dosing.Graphical Abstract: http://cancerres.aacrjournals.org/content/canres/79/20/5302/F1.large.jpg.