The mathematics of cancer: integrating quantitative models

DataXflow: Synergizing data-driven modeling with best parameter fit and optimal control - An efficient data analysis for cancer research

Building data-driven models is an effective strategy for information extraction from empirical data. Adapting model parameters specifically to data with a best fitting approach encodes the relevant information into a mathematical model. Subsequently, an optimal control framework extracts the most efficient targets to steer the model into desired changes via external stimuli. The DataXflow software framework integrates three software pipelines, D2D for model fitting, a framework solving optimal control problems including external stimuli and JimenaE providing graphical user interfaces to employ the other frameworks lowering the barriers for the need of programming skills, and simultaneously automating reoccurring modeling tasks. Such tasks include equation generation from a graph and script generation allowing also to approach systems with many agents, like complex gene regulatory networks. A desired state of the model is defined, and therapeutic interventions are modeled as external stimuli. The optimal control framework purposefully exploits the model-encoded information by providing those external stimuli that effect the desired changes most efficiently. The implementation of DataXflow is available under https://github.com/MarvelousHopefull/DataXflow. We showcase its application by detecting specific drug targets for a therapy of lung cancer from measurement data to lower proliferation and increase apoptosis. By an iterative modeling process refining the topology of the model, the regulatory network of the tumor is generated from the data. An application of the optimal control framework in our example reveals the inhibition of AURKA and the activation of CDH1 as the most efficient drug target combination. DataXflow paves the way to an agile interplay between data generation and its analysis potentially accelerating cancer research by an efficient drug target identification, even in complex networks.

Deciphering oxygen distribution and hypoxia profiles in the tumor microenvironment: a data-driven mechanistic modeling approach

Objective. The distribution of hypoxia within tissues plays a critical role in tumor diagnosis and prognosis. Recognizing the significance of tumor oxygenation and hypoxia gradients, we introduce mathematical frameworks grounded in mechanistic modeling approaches for their quantitative assessment within a tumor microenvironment. By utilizing known blood vasculature, we aim to predict hypoxia levels across different tumor types.Approach. Our approach offers a computational method to measure and predict hypoxia using known blood vasculature. By formulating a reaction-diffusion model for oxygen distribution, we derive the corresponding hypoxia profile.Main results. The framework successfully replicates observed inter- and intra-tumor heterogeneity in experimentally obtained hypoxia profiles across various tumor types (breast, ovarian, pancreatic). Additionally, we propose a data-driven method to deduce partial differential equation models with spatially dependent parameters, which allows us to comprehend the variability of hypoxia profiles within tissues. The versatility of our framework lies in capturing diverse and dynamic behaviors of tumor oxygenation, as well as categorizing states of vascularization based on the dynamics of oxygen molecules, as identified by the model parameters.Significance. The proposed data-informed mechanistic method quantitatively assesses hypoxia in the tumor microenvironment by integrating diverse histopathological data and making predictions across different types of data. The framework provides valuable insights from both modeling and biological perspectives, advancing our comprehension of spatio-temporal dynamics of tumor oxygenation.

Phenotypic noise and plasticity in cancer evolution

Non-genetic alterations can produce changes in a cell's phenotype. In cancer, these phenomena can influence a cell's fitness by conferring access to heritable, beneficial phenotypes. Herein, we argue that current discussions of 'phenotypic plasticity' in cancer evolution ignore a salient feature of the original definition: namely, that it occurs in response to an environmental change. We suggest 'phenotypic noise' be used to distinguish non-genetic changes in phenotype that occur independently from the environment. We discuss the conceptual and methodological techniques used to identify these phenomena during cancer evolution. We propose that the distinction will guide efforts to define mechanisms of phenotype change, accelerate translational work to manipulate phenotypes through treatment, and, ultimately, improve patient outcomes.

A mathematical model to study low-dose metronomic scheduling for chemotherapy

Metronomic chemotherapy refers to the frequent administration of chemotherapeutic agents at a lower dose and presents an attractive alternative to conventional chemotherapy with encouraging response rates. However, the schedule of the therapy, including the dosage of the drug, is usually based on empiricism. The confounding effects of tumor-endothelial-immune interactions during metronomic administration of drugs have not yet been explored in detail, resulting in an incomplete assessment of drug dose and frequency evaluations. The present study aimed to gain a mechanistic understanding of different actions of metronomic chemotherapy using a mathematical model. We have established an analytical condition for determining the dosage and frequency of the drug depending on its clearance rate for complete tumor elimination. The model also brings forward the immune-mediated clearance of the tumor during the metronomic administration of the chemotherapeutic agent. The results from the global sensitivity analysis showed an increase in the sensitivity of drug and immune-mediated killing factors toward the tumor population during metronomic scheduling. Our results emphasize metronomic scheduling over the maximum tolerated dose (MTD) and define a model-based approach for approximating the optimal schedule of drug administration to eliminate tumors while minimizing harm to the immune cells and the patient's body.

To modulate or to skip: De-escalating PARP inhibitor maintenance therapy in ovarian cancer using adaptive therapy

Toxicity and emerging drug resistance pose important challenges in poly-adenosine ribose polymerase inhibitor (PARPi) maintenance therapy of ovarian cancer. We propose that adaptive therapy, which dynamically reduces treatment based on the tumor dynamics, might alleviate both issues. Utilizing in vitro time-lapse microscopy and stepwise model selection, we calibrate and validate a differential equation mathematical model, which we leverage to test different plausible adaptive treatment schedules. Our model indicates that adjusting the dosage, rather than skipping treatments, is more effective at reducing drug use while maintaining efficacy due to a delay in cell kill and a diminishing dose-response relationship. In vivo pilot experiments confirm this conclusion. Although our focus is toxicity mitigation, reducing drug use may also delay resistance. This study enhances our understanding of PARPi treatment scheduling and illustrates the first steps in developing adaptive therapies for new treatment settings. A record of this paper's transparent peer review process is included in the supplemental information.

From immune equilibrium to tumor ecodynamics

Objectives

There is no theory to quantitatively describe the complex tumor ecosystem. At the same time, cancer immunotherapy is considered a revolution in oncology, but the methods used to describe tumors and the criteria used to evaluate efficacy are not keeping pace. The purpose of this study is to establish a new theory for quantitatively describing the tumor ecosystem, innovating the methods of tumor characterization, and establishing new efficacy evaluation criteria for cancer immunotherapy.

Methods

Based on the mathematization of immune equilibrium theory and the establishment of immunodynamics in a previous study, the method of reverse immunodynamics was used, namely, the immune braking force was regarded as the tumor ecological force and the immune force was regarded as the tumor ecological braking force, and the concept of momentum in physics was applied to the tumor ecosystem to establish a series of tumor ecodynamic equations. These equations were used to solve the fundamental and applied problems of the complex tumor ecosystem.

Results

A series of tumor ecodynamic equations were established. The tumor ecological momentum equations and their component factors could be used to distinguish disease progression, pseudoprogression, and hyperprogression in cancer immunotherapy. On this basis, the adjusted tumor momentum equations were established to achieve the equivalence of tumor activity (including immunosuppressive activity and metabolic activity) and tumor volume, which could be used to calculate individual disease remission rate and establish new efficacy evaluation criteria (ieRECIST) for immunotherapy of solid tumor based on tumor ecodynamics. At the same time, the concept of moving cube-to-force square ratio and its expression were proposed to calculate the area under the curve of tumor ecological braking force of blood required to achieve an individual disease remission rate when the adjusted tumor ecological momentum was known.

Conclusions

A new theory termed tumor ecodynamics emphasizing both tumor activity and tumor volume is established to solve a series of basic and applied problems in the complex tumor ecosystem. It can be predicted that the future will be the era of cancer immune ecotherapy that targets the entire tumor ecosystem.

Mathematical modeling of the synergistic interplay of radiotherapy and immunotherapy in anti-cancer treatments

Introduction

While radiotherapy has long been recognized for its ability to directly ablate cancer cells through necrosis or apoptosis, radiotherapy-induced abscopal effect suggests that its impact extends beyond local tumor destruction thanks to immune response. Cellular proliferation and necrosis have been extensively studied using mathematical models that simulate tumor growth, such as Gompertz law, and the radiation effects, such as the linear-quadratic model. However, the effectiveness of radiotherapy-induced immune responses may vary among patients due to individual differences in radiation sensitivity and other factors.

Methods

We present a novel macroscopic approach designed to quantitatively analyze the intricate dynamics governing the interactions among the immune system, radiotherapy, and tumor progression. Building upon previous research demonstrating the synergistic effects of radiotherapy and immunotherapy in cancer treatment, we provide a comprehensive mathematical framework for understanding the underlying mechanisms driving these interactions.

Results

Our method leverages macroscopic observations and mathematical modeling to capture the overarching dynamics of this interplay, offering valuable insights for optimizing cancer treatment strategies. One shows that Gompertz law can describe therapy effects with two effective parameters. This result permits quantitative data analyses, which give useful indications for the disease progression and clinical decisions.

Discussion

Through validation against diverse data sets from the literature, we demonstrate the reliability and versatility of our approach in predicting the time evolution of the disease and assessing the potential efficacy of radiotherapy-immunotherapy combinations. This further supports the promising potential of the abscopal effect, suggesting that in select cases, depending on tumor size, it may confer full efficacy to radiotherapy.

The emergence of tumor-initiating cells in an advanced hypopharyngeal tumor model exhibits enhanced angiogenesis and nuclear factor erythroid 2-related factor 2 associated antioxidant effects

Hypopharyngeal cancer (HPC) is associated with the worst prognosis of all head and neck cancers and is typically identified in an advanced stage at the time of diagnosis. While oxidative stress might contribute to the onset of HPC in patients using tobacco or alcohol, the extent of this influence and the characteristics of HPC cells in advanced stage remain to be investigated. In this study, we explored whether HPC cells survived from necrotic xenograft tumors at late stage would display increased tumor resistance along with altered tolerance to oxidative stress. The remnant living HPC cells isolated from a late-stage xenograft tumor, named FaDu Ex-vivo cells showed stronger chemo- and radio-resistance, tumorigenesis, and invasiveness compared to parental FaDu cells. FaDu Ex-vivo cells also displayed increased angiogenic ability after re-transplantation to mice visualized by in vivo near infrared-II (NIR-II) fluorescence imaging modality. Moreover, FaDu Ex-vivo cells exhibited significant tumor-initiating cells (TICs) related properties accompanied by a reduction of the level of reactive oxygen species (ROS), which was associated with up-regulation of transcription factor nuclear factor erythroid 2-related factor 2 (Nrf2). Interestingly, inhibition of Nrf2 by the RNA interference and the chemical inhibitor could reduce TICs related properties of FaDu Ex-vivo cells. Oxidative stress potentially initiates HPC, but elevation of Nrf2-associated antioxidant mechanisms would be essential to mitigate this effect for promoting and sustaining the stemness of HPC at the advanced stage. Current data suggest that the antioxidant potency of advanced HPC would be a therapeutic target for the design of adjuvant treatm.

Peristromal niches protect lung cancers from targeted therapies through a combined effect of multiple molecular mediators

Targeted therapies directed against oncogenic signaling addictions, such as inhibitors of ALK in ALK+ NSCLC often induce strong and durable clinical responses. However, they are not curative in metastatic cancers, as some tumor cells persist through therapy, eventually developing resistance. Therapy sensitivity can reflect not only cell-intrinsic mechanisms but also inputs from stromal microenvironment. Yet, the contribution of tumor stroma to therapeutic responses in vivo remains poorly defined. To address this gap of knowledge, we assessed the contribution of stroma-mediated resistance to therapeutic responses to the frontline ALK inhibitor alectinib in xenograft models of ALK+ NSCLC. We found that stroma-proximal tumor cells are partially protected against cytostatic effects of alectinib. This effect is observed not only in remission, but also during relapse, indicating the strong contribution of stroma-mediated resistance to both persistence and resistance. This therapy-protective effect of the stromal niche reflects a combined action of multiple mechanisms, including growth factors and extracellular matrix components. Consequently, despite improving alectinib responses, suppression of any individual resistance mechanism was insufficient to fully overcome the protective effect of stroma. Focusing on shared collateral sensitivity of persisters offered a superior therapeutic benefit, especially when using an antibody-drug conjugate with bystander effect to limit therapeutic escape. These findings indicate that stroma-mediated resistance might be the major contributor to both residual and progressing disease and highlight the limitation of focusing on suppressing a single resistance mechanism at a time.

How mutation accumulation depends on the structure of the cell lineage tree

All the cells of a multicellular organism are the product of cell divisions that trace out a single binary tree, the so-called cell lineage tree. Because cell divisions are accompanied by replication errors, the shape of the cell lineage tree is a key determinant of how somatic evolution, which can potentially lead to cancer, proceeds. Carcinogenesis requires the accumulation of a certain number of driver mutations. By mapping the accumulation of mutations into a graph theoretical problem, we present an exact numerical method to calculate the probability of collecting a given number of mutations and show that for low mutation rates it can be approximated with a simple analytical formula, which depends only on the distribution of the lineage lengths, and is dominated by the longest lineages. Our results are crucial in understanding how natural selection can shape the cell lineage trees of multicellular organisms and curtail somatic evolution.

Second-Order Effects of Chemotherapy Pharmacodynamics and Pharmacokinetics on Tumor Regression and Cachexia

Drug dose response curves are ubiquitous in cancer biology, but these curves are often used to measure differential response in first-order effects: the effectiveness of increasing the cumulative dose delivered. In contrast, second-order effects (the variance of drug dose) are often ignored. Knowledge of second-order effects may improve the design of chemotherapy scheduling protocols, leading to improvements in tumor response without changing the total dose delivered. By considering treatment schedules with identical cumulative dose delivered, we characterize differential treatment outcomes resulting from high variance schedules (e.g. high dose, low dose) and low variance schedules (constant dose). We extend a previous framework used to quantify second-order effects, known as antifragility theory, to investigate the role of drug pharmacokinetics. Using a simple one-compartment model, we find that high variance schedules are effective for a wide range of cumulative dose values. Next, using a mouse-parameterized two-compartment model of 5-fluorouracil, we show that schedule viability depends on initial tumor volume. Finally, we illustrate the trade-off between tumor response and lean mass preservation. Mathematical modeling indicates that high variance dose schedules provide a potential path forward in mitigating the risk of chemotherapy-associated cachexia by preserving lean mass without sacrificing tumor response.

Impact of Resistance on Therapeutic Design: A Moran Model of Cancer Growth

Resistance of cancers to treatments, such as chemotherapy, largely arise due to cell mutations. These mutations allow cells to resist apoptosis and inevitably lead to recurrence and often progression to more aggressive cancer forms. Sustained-low dose therapies are being considered as an alternative over maximum tolerated dose treatments, whereby a smaller drug dosage is given over a longer period of time. However, understanding the impact that the presence of treatment-resistant clones may have on these new treatment modalities is crucial to validating them as a therapeutic avenue. In this study, a Moran process is used to capture stochastic mutations arising in cancer cells, inferring treatment resistance. The model is used to predict the probability of cancer recurrence given varying treatment modalities. The simulations predict that sustained-low dose therapies would be virtually ineffective for a cancer with a non-negligible probability of developing a sub-clone with resistance tendencies. Furthermore, calibrating the model to in vivo measurements for breast cancer treatment with Herceptin, the model suggests that standard treatment regimens are ineffective in this mouse model. Using a simple Moran model, it is possible to explore the likelihood of treatment success given a non-negligible probability of treatment resistant mutations and suggest more robust therapeutic schedules.

"Patchiness" in mechanical stiffness across a tumor as an early-stage marker for malignancy

Mechanical phenotyping of tumors, either at an individual cell level or tumor cell population level is gaining traction as a diagnostic tool. However, the extent of diagnostic and prognostic information that can be gained through these measurements is still unclear. In this work, we focus on the heterogeneity in mechanical properties of cells obtained from a single source such as a tissue or tumor as a potential novel biomarker. We believe that this heterogeneity is a conventionally overlooked source of information in mechanical phenotyping data. We use mechanics-based in-silico models of cell-cell interactions and cell population dynamics within 3D environments to probe how heterogeneity in cell mechanics drives tissue and tumor dynamics. Our simulations show that the initial heterogeneity in the mechanical properties of individual cells and the arrangement of these heterogenous sub-populations within the environment can dictate overall cell population dynamics and cause a shift towards the growth of malignant cell phenotypes within healthy tissue environments. The overall heterogeneity in the cellular mechanotype and their spatial distributions is quantified by a "patchiness" index, which is the ratio of the global to local heterogeneity in cell populations. We observe that there exists a threshold value of the patchiness index beyond which an overall healthy population of cells will show a steady shift towards a more malignant phenotype. Based on these results, we propose that the "patchiness" of a tumor or tissue sample, can be an early indicator for malignant transformation and cancer occurrence in benign tumors or healthy tissues. Additionally, we suggest that tissue patchiness, measured either by biochemical or biophysical markers, can become an important metric in predicting tissue health and disease likelihood just as landscape patchiness is an important metric in ecology.

A review of mechanistic learning in mathematical oncology

Mechanistic learning refers to the synergistic combination of mechanistic mathematical modeling and data-driven machine or deep learning. This emerging field finds increasing applications in (mathematical) oncology. This review aims to capture the current state of the field and provides a perspective on how mechanistic learning may progress in the oncology domain. We highlight the synergistic potential of mechanistic learning and point out similarities and differences between purely data-driven and mechanistic approaches concerning model complexity, data requirements, outputs generated, and interpretability of the algorithms and their results. Four categories of mechanistic learning (sequential, parallel, extrinsic, intrinsic) of mechanistic learning are presented with specific examples. We discuss a range of techniques including physics-informed neural networks, surrogate model learning, and digital twins. Example applications address complex problems predominantly from the domain of oncology research such as longitudinal tumor response predictions or time-to-event modeling. As the field of mechanistic learning advances, we aim for this review and proposed categorization framework to foster additional collaboration between the data- and knowledge-driven modeling fields. Further collaboration will help address difficult issues in oncology such as limited data availability, requirements of model transparency, and complex input data which are embraced in a mechanistic learning framework.

Fractal calculus in tumor growth simulations: The proof is in the pudding

Mathematical modeling in oncology has a long history. Recently, mathematical models and their predictions have made inroads into prospective clinical trials with encouraging results. The goal of many such modeling efforts is to make predictions, either to clinician's choice therapy or into "optimal" therapy - often for individual patients. The mathematical oncology community rightfully puts great hope into predictive modeling and mechanistic digital twins - but with this great opportunity comes great responsibility. Mathematical models need to be rigorously calibrated and validated, and their predictive performance ascertained, before conclusions about predictions into the unknown can be drawn. The recent article "Modeling tumor growth using fractal calculus: Insights into tumor dynamics" (Golmankhaneh et al., 2023), applied fractal calculus to tumor growth data. In this short commentary, I raise concerns about the study design and interpretation. In its current form, this study is poised to put cancer patients at risk if interpreted as concluded by the authors.

Order-of-Mutation Effects on Cancer Progression: Models for Myeloproliferative Neoplasm

In some patients with myeloproliferative neoplasms (MPN), two genetic mutations are often found: JAK2 V617F and one in the TET2 gene. Whether one mutation is present influences how the other subsequent mutation will affect the regulation of gene expression. In other words, when a patient carries both mutations, the order of when they first arose has been shown to influence disease progression and prognosis. We propose a nonlinear ordinary differential equation, the Moran process, and Markov chain models to explain the non-additive and non-commutative mutation effects on recent clinical observations of gene expression patterns, proportions of cells with different mutations, and ages at diagnosis of MPN. Combined, these observations are used to shape our modeling framework. Our key proposal is that bistability in gene expression provides a natural explanation for many observed order-of-mutation effects. We also propose potential experimental measurements that can be used to confirm or refute predictions of our models.

Calibration of agent based models for monophasic and biphasic tumour growth using approximate Bayesian computation

Agent-based models (ABMs) are readily used to capture the stochasticity in tumour evolution; however, these models are often challenging to validate with experimental measurements due to model complexity. The Voronoi cell-based model (VCBM) is an off-lattice agent-based model that captures individual cell shapes using a Voronoi tessellation and mimics the evolution of cancer cell proliferation and movement. Evidence suggests tumours can exhibit biphasic growth in vivo. To account for this phenomena, we extend the VCBM to capture the existence of two distinct growth phases. Prior work primarily focused on point estimation for the parameters without consideration of estimating uncertainty. In this paper, approximate Bayesian computation is employed to calibrate the model to in vivo measurements of breast, ovarian and pancreatic cancer. Our approach involves estimating the distribution of parameters that govern cancer cell proliferation and recovering outputs that match the experimental data. Our results show that the VCBM, and its biphasic extension, provides insight into tumour growth and quantifies uncertainty in the switching time between the two phases of the biphasic growth model. We find this approach enables precise estimates for the time taken for a daughter cell to become a mature cell. This allows us to propose future refinements to the model to improve accuracy, whilst also making conclusions about the differences in cancer cell characteristics.

Interplay of mutations, alternate mechanisms, and treatment breaks in leukaemia: Understanding and implications studied with stochastic models

Bcr-Abl1 kinase domain mutations are the most prevalent cause of treatment resistance in chronic myeloid leukaemia (CML). Alternate resistance pathways nevertheless exist, and cell line experiments show certain patterns in the gain, and loss, of some of these alternate adaptations. These adaptations have clinical consequences when the tumour develops mechanisms that are beneficial to its growth under treatment, but slow down its growth when not treated. The results of temporarily halting treatment in CML have not been widely discussed in the clinic and there is no robust theoretical model that could suggest when such a pause in therapy can be tolerated. We constructed a dynamic model of how mechanisms such as Bcr-Abl1 overexpression and drug transporter upregulation evolve to produce resistance in cell lines, and investigate its behaviour subject to different treatment schedules, in particular when the treatment is paused ('drug holiday'). Our study results suggest that the presence of additional resistance mechanisms creates an environment which favours mutations that are either preexisting or occur late during treatment. Importantly, the results suggest the existence of tumour drug addiction, where cancer cells become dependent on the drug for (optimal) survival, which could be exploited through a treatment holiday. All simulation code is available at https://github.com/Sandalmoth/dual-adaptation.

Engineering Heterogeneous Tumor Models for Biomedical Applications

Tumor tissue engineering holds great promise for replicating the physiological and behavioral characteristics of tumors in vitro. Advances in this field have led to new opportunities for studying the tumor microenvironment and exploring potential anti-cancer therapeutics. However, the main obstacle to the widespread adoption of tumor models is the poor understanding and insufficient reconstruction of tumor heterogeneity. In this review, the current progress of engineering heterogeneous tumor models is discussed. First, the major components of tumor heterogeneity are summarized, which encompasses various signaling pathways, cell proliferations, and spatial configurations. Then, contemporary approaches are elucidated in tumor engineering that are guided by fundamental principles of tumor biology, and the potential of a bottom-up approach in tumor engineering is highlighted. Additionally, the characterization approaches and biomedical applications of tumor models are discussed, emphasizing the significant role of engineered tumor models in scientific research and clinical trials. Lastly, the challenges of heterogeneous tumor models in promoting oncology research and tumor therapy are described and key directions for future research are provided.

Kinetics of cancer metastasis

The formation of metastases during cancer is now considered to be induced by migrating metastatic stem cells (MetSCs) in preexisting niches or niches induced by MetSCs or tumor-derived exosomes (TDEs). I propose and compare two simplest generic models describing these two scenarios. The number of tumors is predicted (i) to increase exponentially in the case of preexisting niches and (ii) to diverge during a finite time interval in the case of induced niches. The latter prediction is novel and of interest because rapid collapse in the end of a finite time interval is a well-known feature of the cancer metastasis. Two advanced models describing the two scenarios of cancer metastasis have been scrutinized as well. These models clarify the likely role of various specific factors in the metastasis. In particular, the equations derived in the framework of the advanced model with preexisting niches have been solved analytically allowing (i) to clarify the factors determining the duration of the period from the initiation of the primary tumor to the phase when the metastases start to dominate, (ii) to estimate the number of metastases in the end of this period, and (iii) to explains why the use of chemotherapy typically results in the improvement of the patient state only for a relatively short period. The equations derived in the framework of the advanced model with induced niches have no analytical solution, and their analysis merits additional attention.

Mathematical modeling predicts pathways to successful implementation of combination TRAIL-producing oncolytic virus and PAC-1 to treat granulosa cell tumors of the ovary

The development of new cancer therapies requires multiple rounds of validation from in vitro and in vivo experiments before they can be considered for clinical trials. Mathematical models assist in this preclinical phase by combining experimental data with human parameters to provide guidance about potential therapeutic regimens to bring forward into trials. However, granulosa cell tumors of the ovary lack a relevant mouse model, complexifying preclinical drug development for this rare tumor. To bridge this gap, we established a mathematical model as a framework to explore the potential of using a tumor necrosis factor-related apoptosis-inducing ligand (TRAIL)-producing oncolytic vaccinia virus in combination with the chemotherapeutic agent first procaspase activating compound (PAC-1). We have previously shown that TRAIL and PAC-1 act synergistically on granulosa tumor cells. In line with our previous results, our current model predicts that, although it is unable to stop the tumor from growing in its current form, combination oral PAC-1 with oncolytic virus (OV) provides the best result compared to monotherapies. Encouragingly, our results suggest that increases to the OV infection rate can lead to the success of this combination therapy within a year. The model developed here can continue to be improved as more data become available, allowing for regimen-tailoring via virtual clinical trials, ultimately shepherding effective regimens into trials.

Overcoming chemotherapy resistance in low-grade gliomas: A computational approach

Low-grade gliomas are primary brain tumors that arise from glial cells and are usually treated with temozolomide (TMZ) as a chemotherapeutic option. They are often incurable, but patients have a prolonged survival. One of the shortcomings of the treatment is that patients eventually develop drug resistance. Recent findings show that persisters, cells that enter a dormancy state to resist treatment, play an important role in the development of resistance to TMZ. In this study we constructed a mathematical model of low-grade glioma response to TMZ incorporating a persister population. The model was able to describe the volumetric longitudinal dynamics, observed in routine FLAIR 3D sequences, of low-grade glioma patients acquiring TMZ resistance. We used the model to explore different TMZ administration protocols, first on virtual clones of real patients and afterwards on virtual patients preserving the relationships between parameters of real patients. In silico clinical trials showed that resistance development was deferred by protocols in which individual doses are administered after rest periods, rather than the 28-days cycle standard protocol. This led to median survival gains in virtual patients of more than 15 months when using resting periods between two and three weeks and agreed with recent experimental observations in animal models. Additionally, we tested adaptive variations of these new protocols, what showed a potential reduction in toxicity, but no survival gain. Our computational results highlight the need of further clinical trials that could obtain better results from treatment with TMZ in low grade gliomas.

A multiscale model of the role of microenvironmental factors in cell segregation and heterogeneity in breast cancer development

We analyzed a quantitative multiscale model that describes the epigenetic dynamics during the growth and evolution of an avascular tumor. A gene regulatory network (GRN) formed by a set of ten genes that are believed to play an important role in breast cancer development was kinetically coupled to the microenvironmental agents: glucose, estrogens, and oxygen. The dynamics of spontaneous mutations was described by a Yule-Furry master equation whose solution represents the probability that a given cell in the tissue undergoes a certain number of mutations at a given time. We assumed that the mutation rate is modified by a spatial gradient of nutrients. The tumor mass was simulated by means of cellular automata supplemented with a set of reaction diffusion equations that described the transport of microenvironmental agents. By analyzing the epigenetic state space described by the GRN dynamics, we found three attractors that were identified with cellular epigenetic states: normal, precancer and cancer. For two-dimensional (2D) and three-dimensional (3D) tumors we calculated the spatial distribution of the following quantities: (i) number of mutations, (ii) mutation of each gene and, (iii) phenotypes. Using estrogen as the principal microenvironmental agent that regulates cell proliferation process, we obtained tumor shapes for different values of estrogen consumption and supply rates. It was found that he majority of mutations occurred in cells that were located close to the 2D tumor perimeter or close to the 3D tumor surface. Also, it was found that the occurrence of different phenotypes in the tumor are controlled by estrogen concentration levels since they can change the individual cell threshold and gene expression levels. All results were consistently observed for 2D and 3D tumors.

Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives

Keloids are fibroproliferative disorders described by excessive growth of fibrotic tissue, which also invades adjacent areas (beyond the original wound borders). Since these disorders are specific to humans (no other animal species naturally develop keloid-like tissue), experimental in vivo/in vitro research has not led to significant advances in this field. One possible approach could be to combine in vitro human models with calibrated in silico mathematical approaches (i.e., models and simulations) to generate new testable biological hypotheses related to biological mechanisms and improved treatments. Because these combined approaches do not really exist for keloid disorders, in this brief review we start by summarising the biology of these disorders, then present various types of mathematical and computational approaches used for related disorders (i.e., wound healing and solid tumours), followed by a discussion of the very few mathematical and computational models published so far to study various inflammatory and mechanical aspects of keloids. We conclude this review by discussing some open problems and mathematical opportunities offered in the context of keloid disorders by such combined in vitro/in silico approaches, and the need for multi-disciplinary research to enable clinical progress.

Mathematical modeling of radiotherapy: impact of model selection on estimating minimum radiation dose for tumor control

Introduction

Radiation therapy (RT) is one of the most common anticancer therapies. Yet, current radiation oncology practice does not adapt RT dose for individual patients, despite wide interpatient variability in radiosensitivity and accompanying treatment response. We have previously shown that mechanistic mathematical modeling of tumor volume dynamics can simulate volumetric response to RT for individual patients and estimation personalized RT dose for optimal tumor volume reduction. However, understanding the implications of the choice of the underlying RT response model is critical when calculating personalized RT dose.

Methods

In this study, we evaluate the mathematical implications and biological effects of 2 models of RT response on dose personalization: (1) cytotoxicity to cancer cells that lead to direct tumor volume reduction (DVR) and (2) radiation responses to the tumor microenvironment that lead to tumor carrying capacity reduction (CCR) and subsequent tumor shrinkage. Tumor growth was simulated as logistic growth with pre-treatment dynamics being described in the proliferation saturation index (PSI). The effect of RT was simulated according to each respective model for a standard schedule of fractionated RT with 2 Gy weekday fractions. Parameter sweeps were evaluated for the intrinsic tumor growth rate and the radiosensitivity parameter for both models to observe the qualitative impact of each model parameter. We then calculated the minimum RT dose required for locoregional tumor control (LRC) across all combinations of the full range of radiosensitvity and proliferation saturation values.

Results

Both models estimate that patients with higher radiosensitivity will require a lower RT dose to achieve LRC. However, the two models make opposite estimates on the impact of PSI on the minimum RT dose for LRC: the DVR model estimates that tumors with higher PSI values will require a higher RT dose to achieve LRC, while the CCR model estimates that higher PSI values will require a lower RT dose to achieve LRC.

Discussion

Ultimately, these results show the importance of understanding which model best describes tumor growth and treatment response in a particular setting, before using any such model to make estimates for personalized treatment recommendations.

Treatment of evolving cancers will require dynamic decision support

Cancer research has traditionally focused on developing new agents, but an underexplored question is that of the dose and frequency of existing drugs. Based on the modus operandi established in the early days of chemotherapies, most drugs are administered according to predetermined schedules that seek to deliver the maximum tolerated dose and are only adjusted for toxicity. However, we believe that the complex, evolving nature of cancer requires a more dynamic and personalized approach. Chronicling the milestones of the field, we show that the impact of schedule choice crucially depends on processes driving treatment response and failure. As such, cancer heterogeneity and evolution dictate that a one-size-fits-all solution is unlikely-instead, each patient should be mapped to the strategy that best matches their current disease characteristics and treatment objectives (i.e. their 'tumorscape'). To achieve this level of personalization, we need mathematical modeling. In this perspective, we propose a five-step 'Adaptive Dosing Adjusted for Personalized Tumorscapes (ADAPT)' paradigm to integrate data and understanding across scales and derive dynamic and personalized schedules. We conclude with promising examples of model-guided schedule personalization and a call to action to address key outstanding challenges surrounding data collection, model development, and integration.

Reuniting philosophy and science to advance cancer research

Cancers rely on multiple, heterogeneous processes at different scales, pertaining to many biomedical fields. Therefore, understanding cancer is necessarily an interdisciplinary task that requires placing specialised experimental and clinical research into a broader conceptual, theoretical, and methodological framework. Without such a framework, oncology will collect piecemeal results, with scant dialogue between the different scientific communities studying cancer. We argue that one important way forward in service of a more successful dialogue is through greater integration of applied sciences (experimental and clinical) with conceptual and theoretical approaches, informed by philosophical methods. By way of illustration, we explore six central themes: (i) the role of mutations in cancer; (ii) the clonal evolution of cancer cells; (iii) the relationship between cancer and multicellularity; (iv) the tumour microenvironment; (v) the immune system; and (vi) stem cells. In each case, we examine open questions in the scientific literature through a philosophical methodology and show the benefit of such a synergy for the scientific and medical understanding of cancer.

Mathematical analysis identifies the optimal treatment strategy for epidermal growth factor receptor-mutated non-small cell lung cancer

Introduction

In Asians, more than half of non-small cell lung cancers (NSCLC) are induced by epidermal growth factor receptor (EGFR) mutations. Although patients carrying EGFR driver mutations display a good initial response to EGFR-Tyrosine Kinase Inhibitors (EGFR-TKIs), additional mutations provoke drug resistance. Hence, predicting tumor dynamics before treatment initiation and formulating a reasonable treatment schedule is an urgent challenge.

Methods

To overcome this problem, we constructed a mathematical model based on clinical observations and investigated the optimal schedules for EGFR-TKI therapy.

Results

Based on published data on cell growth rates under different drugs, we found that using osimertinib that are efficient for secondary resistant cells as the first-line drug is beneficial in monotherapy, which is consistent with published clinical statistical data. Moreover, we identified the existence of a suitable drug-switching time; that is, changing drugs too early or too late was not helpful. Furthermore, we demonstrate that osimertinib combined with erlotinib or gefitinib as first-line treatment, has the potential for clinical application. Finally, we examined the relationship between the initial ratio of resistant cells and final cell number under different treatment conditions, and summarized it into a therapy suggestion map. By performing parameter sensitivity analysis, we identified the condition where　osimertinib-first therapy was recommended as the optimal treatment option.

Discussion

This study for the first time theoretically showed the optimal treatment strategies based on the known information in NSCLC. Our framework can be applied to other types of cancer in the future.

An adaptive information-theoretic experimental design procedure for high-to-low fidelity calibration of prostate cancer models

The use of mathematical models to make predictions about tumor growth and response to treatment has become increasingly prevalent in the clinical setting. The level of complexity within these models ranges broadly, and the calibration of more complex models requires detailed clinical data. This raises questions about the type and quantity of data that should be collected and when, in order to maximize the information gain about the model behavior while still minimizing the total amount of data used and the time until a model can be calibrated accurately. To address these questions, we propose a Bayesian information-theoretic procedure, using an adaptive score function to determine the optimal data collection times and measurement types. The novel score function introduced in this work eliminates the need for a penalization parameter used in a previous study, while yielding model predictions that are superior to those obtained using two potential pre-determined data collection protocols for two different prostate cancer model scenarios: one in which we fit a simple ODE system to synthetic data generated from a cellular automaton model using radiotherapy as the imposed treatment, and a second scenario in which a more complex ODE system is fit to clinical patient data for patients undergoing intermittent androgen suppression therapy. We also conduct a robust analysis of the calibration results, using both error and uncertainty metrics in combination to determine when additional data acquisition may be terminated.

Mathematical Modeling for the Assessment of Public Policies in the Cancer Health-Care System Implemented for the Colombian Case

The incidence of cancer has been constantly growing worldwide, placing pressure on health systems and increasing the costs associated with the treatment of cancer. In particular, low- and middle-income countries are expected to face serious challenges related to caring for the majority of the world's new cancer cases in the next 10 years. In this study, we propose a mathematical model that allows for the simulation of different strategies focused on public policies by combining spending and epidemiological indicators. In this way, strategies aimed at efficient spending management with better epidemiological indicators can be determined. For validation and calibration of the model, we use data from Colombia-which, according to the World Bank, is an upper-middle-income country. The results of the simulations using the proposed model, calibrated and validated for Colombia, indicate that the most effective strategy for reducing mortality and financial burden consists of a combination of early detection and greater efficiency of treatment in the early stages of cancer. This approach is found to present a 38% reduction in mortality rate and a 20% reduction in costs (% GDP) when compared to the baseline scenario. Hence, Colombia should prioritize comprehensive care models that focus on patient-centered care, prevention, and early detection.

A Mathematical Modelling Study of Chemotactic Dynamics in Cell Cultures: The Impact of Spatio-temporal Heterogeneity

As motivated by studies of cellular motility driven by spatiotemporal chemotactic gradients in microdevices, we develop a framework for constructing approximate analytical solutions for the location, speed and cellular densities for cell chemotaxis waves in heterogeneous fields of chemoattractant from the underlying partial differential equation models. In particular, such chemotactic waves are not in general translationally invariant travelling waves, but possess a spatial variation that evolves in time, and may even oscillate back and forth in time, according to the details of the chemotactic gradients. The analytical framework exploits the observation that unbiased cellular diffusive flux is typically small compared to chemotactic fluxes and is first developed and validated for a range of exemplar scenarios. The framework is subsequently applied to more complex models considering the chemoattractant dynamics under more general settings, potentially including those of relevance for representing pathophysiology scenarios in microdevice studies. In particular, even though solutions cannot be constructed in all cases, a wide variety of scenarios can be considered analytically, firstly providing global insight into the important mechanisms and features of cell motility in complex spatiotemporal fields of chemoattractant. Such analytical solutions also provide a means of rapid evaluation of model predictions, with the prospect of application in computationally demanding investigations relating theoretical models and experimental observation, such as Bayesian parameter estimation.

A Poisson distribution-based general model of cancer rates and a cancer risk-dependent theory of aging

This article presents a formula for modeling the lifetime incidence of cancer in humans. The formula utilizes a Poisson distribution-based "np" model to predict cancer incidence, with "n" representing the effective number of cell turnover and "p" representing the probability of single-cell transformation. The model accurately predicts the observed incidence of cancer in humans when a reduction in cell turnover due to aging is taken into account. The model also suggests that cancer development is ultimately inevitable. The article proposes a theory of aging based on this concept, called the "np" theory. According to this theory, an organism maintains its order by balancing cellular entropy through continuous proliferation. However, cellular "information entropy" in the form of accumulated DNA mutations increases irreversibly over time, restricting the total number of cells an organism can generate throughout its lifetime. When cell division slows down and fails to compensate for the increased entropy in the system, aging occurs. Essentially, aging is the phenomenon of running out of predetermined cell resources. Different species have evolved separate strategies to utilize their limited cell resources throughout their life cycle.

A Continuation Technique for Maximum Likelihood Estimators in Biological Models

Estimating model parameters is a crucial step in mathematical modelling and typically involves minimizing the disagreement between model predictions and experimental data. This calibration data can change throughout a study, particularly if modelling is performed simultaneously with the calibration experiments, or during an on-going public health crisis as in the case of the COVID-19 pandemic. Consequently, the optimal parameter set, or maximal likelihood estimator (MLE), is a function of the experimental data set. Here, we develop a numerical technique to predict the evolution of the MLE as a function of the experimental data. We show that, when considering perturbations from an initial data set, our approach is significantly more computationally efficient that re-fitting model parameters while producing acceptable model fits to the updated data. We use the continuation technique to develop an explicit functional relationship between fit model parameters and experimental data that can be used to measure the sensitivity of the MLE to experimental data. We then leverage this technique to select between model fits with similar information criteria, a priori determine the experimental measurements to which the MLE is most sensitive, and suggest additional experiment measurements that can resolve parameter uncertainty.

From Chaos to Opportunity: Decoding Cancer Heterogeneity for Enhanced Treatment Strategies

Cancer manifests as a multifaceted disease, characterized by aberrant cellular proliferation, survival, migration, and invasion. Tumors exhibit variances across diverse dimensions, encompassing genetic, epigenetic, and transcriptional realms. This heterogeneity poses significant challenges in prognosis and treatment, affording tumors advantages through an increased propensity to accumulate mutations linked to immune system evasion and drug resistance. In this review, we offer insights into tumor heterogeneity as a crucial characteristic of cancer, exploring the difficulties associated with measuring and quantifying such heterogeneity from clinical and biological perspectives. By emphasizing the critical nature of understanding tumor heterogeneity, this work contributes to raising awareness about the importance of developing effective cancer therapies that target this distinct and elusive trait of cancer.

Order-of-mutation effects on cancer progression: models for myeloproliferative neoplasm

In some patients with myeloproliferative neoplasms (MPN), two genetic mutations are often found, JAK2 V617F and one in the TET2 gene. Whether or not one mutation is present will influence how the other subsequent mutation affects the regulation of gene expression. When both mutations are present, the order of their occurrence has been shown to influence disease progression and prognosis. We propose a nonlinear ordinary differential equation (ODE), Moran process, and Markov chain models to explain the non-additive and non-commutative mutation effects on recent clinical observations of gene expression patterns, proportions of cells with different mutations, and ages at diagnosis of MPN. These observations consistently shape our modeling framework. Our key proposal is that bistability in gene expression provides a natural explanation for many observed order-of-mutation effects. We also propose potential experimental measurements that can be used to confirm or refute predictions of our models.

Modelling the Tumour Microenvironment, but What Exactly Do We Mean by "Model"?

The Oxford English Dictionary includes 17 definitions for the word "model" as a noun and another 11 as a verb. Therefore, context is necessary to understand the meaning of the word model. For instance, "model railways" refer to replicas of railways and trains at a smaller scale and a "model student" refers to an exemplary individual. In some cases, a specific context, like cancer research, may not be sufficient to provide one specific meaning for model. Even if the context is narrowed, specifically, to research related to the tumour microenvironment, "model" can be understood in a wide variety of ways, from an animal model to a mathematical expression. This paper presents a review of different "models" of the tumour microenvironment, as grouped by different definitions of the word into four categories: model organisms, in vitro models, mathematical models and computational models. Then, the frequencies of different meanings of the word "model" related to the tumour microenvironment are measured from numbers of entries in the MEDLINE database of the United States National Library of Medicine at the National Institutes of Health. The frequencies of the main components of the microenvironment and the organ-related cancers modelled are also assessed quantitatively with specific keywords. Whilst animal models, particularly xenografts and mouse models, are the most commonly used "models", the number of these entries has been slowly decreasing. Mathematical models, as well as prognostic and risk models, follow in frequency, and these have been growing in use.

Influence of electric pulse characteristics on the cellular internalization of chemotherapeutic drugs and cell survival fraction in electroporated and vasoconstricted cancer tissues using boundary element techniques

Electroporation has emerged as a suitable technique to induce the pore formation in the cell membrane of cancer tissues, facilitating the cellular internalization of chemotherapeutic drugs. An adequate selection of the electric pulse characteristics is crucial to guarantee the efficiency of this technique, minimizing the adverse effects. In the present work, the dual reciprocity boundary element method (DR-BEM) is applied for the simulation of drug transport in the extracellular and intracellular space of cancer tissues subjected to the application of controlled electric pulses, using a continuum tumour cord approach, and considering both the electro-permeabilization and vasoconstriction phenomena. The developed DR-BEM algorithm is validated with numerical and experimental results previously published, obtaining a satisfactory accuracy and convergence. Using the DR-BEM code, a study about the influence of the magnitude of electric field (E) and pulse spacing (dpulses) on the time behavior and spatial distribution of the internalized drug, as well as on the cell survival fraction, is carried out. In general, the change of drug concentration, drug exposure and cell survival fraction with the parameters E and dpulses is ruled by two important factors: the balance between the electro-permeabilization and vasoconstriction phenomena, and the relative importance of the sources of cell death (electric pulses and drug cytotoxicity); these two factors, in turn, significantly depend on the reversible and irreversible thresholds considered for the electric field.

Sequential mutations in exponentially growing populations

Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with n alterations, and how long will it take for these cells to appear. For exponentially growing populations, these questions have been tackled only in special cases so far. Here, within a multitype branching process framework, we consider a general mutational path where mutations may be advantageous, neutral or deleterious. In the biologically relevant limiting regimes of large times and small mutation rates, we derive probability distributions for the number, and arrival time, of cells with n mutations. Surprisingly, the two quantities respectively follow Mittag-Leffler and logistic distributions regardless of n or the mutations' selective effects. Our results provide a rapid method to assess how altering the fundamental division, death, and mutation rates impacts the arrival time, and number, of mutant cells. We highlight consequences for mutation rate inference in fluctuation assays.

Could Mathematics be the Key to Unlocking the Mysteries of Multiple Sclerosis?

Multiple sclerosis (MS) is an autoimmune, neurodegenerative disease that is driven by immune system-mediated demyelination of nerve axons. While diseases such as cancer, HIV, malaria and even COVID have realised notable benefits from the attention of the mathematical community, MS has received significantly less attention despite the increasing disease incidence rates, lack of curative treatment, and long-term impact on patient well-being. In this review, we highlight existing, MS-specific mathematical research and discuss the outstanding challenges and open problems that remain for mathematicians. We focus on how both non-spatial and spatial deterministic models have been used to successfully further our understanding of T cell responses and treatment in MS. We also review how agent-based models and other stochastic modelling techniques have begun to shed light on the highly stochastic and oscillatory nature of this disease. Reviewing the current mathematical work in MS, alongside the biology specific to MS immunology, it is clear that mathematical research dedicated to understanding immunotherapies in cancer or the immune responses to viral infections could be readily translatable to MS and might hold the key to unlocking some of its mysteries.

Phase I study of a novel glioblastoma radiation therapy schedule exploiting cell-state plasticity

BACKGROUND

Glioblastomas comprise heterogeneous cell populations with dynamic, bidirectional plasticity between treatment-resistant stem-like and treatment-sensitive differentiated states, with treatment influencing this process. However, current treatment protocols do not account for this plasticity. Previously, we generated a mathematical model based on preclinical experiments to describe this process and optimize a radiation therapy fractionation schedule that substantially increased survival relative to standard fractionation in a murine glioblastoma model.

METHODS

We developed statistical models to predict the survival benefit of interventions to glioblastoma patients based on the corresponding survival benefit in the mouse model used in our preclinical study. We applied our mathematical model of glioblastoma radiation response to optimize a radiation therapy fractionation schedule for patients undergoing re-irradiation for glioblastoma and developed a first-in-human trial (NCT03557372) to assess the feasibility and safety of administering our schedule.

RESULTS

Our statistical modeling predicted that the hazard ratio when comparing our novel radiation schedule with a standard schedule would be 0.74. Our mathematical modeling suggested that a practical, near-optimal schedule for re-irradiation of recurrent glioblastoma patients was 3.96 Gy × 7 (1 fraction/day) followed by 1.0 Gy × 9 (3 fractions/day). Our optimized schedule was successfully administered to 14/14 (100%) patients.

CONCLUSIONS

A novel radiation therapy schedule based on mathematical modeling of cell-state plasticity is feasible and safe to administer to glioblastoma patients.

Combining Multikinase Tyrosine Kinase Inhibitors Targeting the Vascular Endothelial Growth Factor and Cluster of Differentiation 47 Signaling Pathways Is Predicted to Increase the Efficacy of Antiangiogenic Combination Therapies

Angiogenesis is a critical step in tumor growth, development, and invasion. Nascent tumor cells secrete vascular endothelial growth factor (VEGF) that significantly remodels the tumor microenvironment through interaction with multiple receptors on vascular endothelial cells, including type 2 VEGF receptor (VEGFR2). The complex pathways initiated by VEGF binding to VEGFR2 lead to enhanced proliferation, survival, and motility of vascular endothelial cells and formation of a new vascular network, enabling tumor growth. Antiangiogenic therapies that inhibit VEGF signaling pathways were among the first drugs that targeted stroma rather than tumor cells. Despite improvements in progression-free survival and higher response rates relative to chemotherapy in some types of solid tumors, the impact on overall survival (OS) has been limited, with the majority of tumors eventually relapsing due to resistance or activation of alternate angiogenic pathways. Here, we developed a molecularly detailed computational model of endothelial cell signaling and angiogenesis-driven tumor growth to investigate combination therapies targeting different nodes of the endothelial VEGF/VEGFR2 signaling pathway. Simulations predicted a strong threshold-like behavior in extracellular signal-regulated kinases 1/2 (ERK1/2) activation relative to phosphorylated VEGFR2 levels, as continuous inhibition of at least 95% of receptors was necessary to abrogate phosphorylated ERK1/2 (pERK1/2). Combinations with mitogen-activated protein kinase/ERK kinase (MEK) and spingosine-1-phosphate inhibitors were found to be effective in overcoming the ERK1/2 activation threshold and abolishing activation of the pathway. Modeling results also identified a mechanism of resistance whereby tumor cells could reduce pERK1/2 sensitivity to inhibitors of VEGFR2 by upregulation of Raf, MEK, and sphingosine kinase 1 (SphK1), thus highlighting the need for deeper investigation of the dynamics of the crosstalk between VEGFR2 and SphK1 pathways. Inhibition of VEGFR2 phosphorylation was found to be more effective at blocking protein kinase B, also known as AKT, activation; however, to effectively abolish AKT activation, simulations identified Axl autophosphorylation or the Src kinase domain as potent targets. Simulations also supported activating cluster of differentiation 47 (CD47) on endothelial cells as an effective combination partner with tyrosine kinase inhibitors to inhibit angiogenesis signaling and tumor growth. Virtual patient simulations supported the effectiveness of CD47 agonism in combination with inhibitors of VEGFR2 and SphK1 pathways. Overall, the rule-based system model developed here provides new insights, generates novel hypothesis, and makes predictions regarding combinations that may enhance the OS with currently approved antiangiogenic therapies.

Clonal interactions in cancer: integrating quantitative models with experimental and clinical data

Tumors consist of different genotypically distinct subpopulations-or subclones-of cells. These subclones can influence neighboring clones in a process called "clonal interaction." Conventionally, research on driver mutations in cancer has focused on their cell-autonomous effects that lead to an increase in fitness of the cells containing the driver. Recently, with the advent of improved experimental and computational technologies for investigating tumor heterogeneity and clonal dynamics, new studies have shown the importance of clonal interactions in cancer initiation, progression, and metastasis. In this review we provide an overview of clonal interactions in cancer, discussing key discoveries from a diverse range of approaches to cancer biology research. We discuss common types of clonal interactions, such as cooperation and competition, its mechanisms, and the overall effect on tumorigenesis, with important implications for tumor heterogeneity, resistance to treatment, and tumor suppression. Quantitative models-in coordination with cell culture and animal model experiments-have played a vital role in investigating the nature of clonal interactions and the complex clonal dynamics they generate. We present mathematical and computational models that can be used to represent clonal interactions and provide examples of the roles they have played in identifying and quantifying the strength of clonal interactions in experimental systems. Clonal interactions have proved difficult to observe in clinical data; however, several very recent quantitative approaches enable their detection. We conclude by discussing ways in which researchers can further integrate quantitative methods with experimental and clinical data to elucidate the critical-and often surprising-roles of clonal interactions in human cancers.

Predicting regrowth of low-grade gliomas after radiotherapy

Diffuse low grade gliomas are invasive and incurable brain tumors that inevitably transform into higher grade ones. A classical treatment to delay this transition is radiotherapy (RT). Following RT, the tumor gradually shrinks during a period of typically 6 months to 4 years before regrowing. To improve the patient’s health-related quality of life and help clinicians build personalized follow-ups, one would benefit from predictions of the time during which the tumor is expected to decrease. The challenge is to provide a reliable estimate of this regrowth time shortly after RT (i.e. with few data), although patients react differently to the treatment. To this end, we analyze the tumor size dynamics from a batch of 20 high-quality longitudinal data, and propose a simple and robust analytical model, with just 4 parameters. From the study of their correlations, we build a statistical constraint that helps determine the regrowth time even for patients for which we have only a few measurements of the tumor size. We validate the procedure on the data and predict the regrowth time at the moment of the first MRI after RT, with precision of, typically, 6 months. Using virtual patients, we study whether some forecast is still possible just three months after RT. We obtain some reliable estimates of the regrowth time in 75% of the cases, in particular for all “fast-responders”. The remaining 25% represent cases where the actual regrowth time is large and can be safely estimated with another measurement a year later. These results show the feasibility of making personalized predictions of the tumor regrowth time shortly after RT.

Directional preference for glioblastoma cancer cell membrane encapsulated nanoparticle population: A probabilistic approach for cancer therapeutics

Background

Selective cancer cell recognition is the most challenging objective in the targeted delivery of anti-cancer agents. Extruded specific cancer cell membrane coated nanoparticles, exploiting the potential of homotypic binding along with certain protein-receptor interactions, have recently proven to be the method of choice for targeted delivery of anti-cancer drugs. Prediction of the selective targeting efficiency of the cancer cell membrane encapsulated nanoparticles (CCMEN) is the most critical aspect in selecting this strategy as a method of delivery.

Materials and methods

A probabilistic model based on binding scores and differential expression levels of Glioblastoma cancer cells (GCC) membrane proteins (factors and receptors) was implemented on python 3.9.1. Conditional binding efficiency (CBE) was derived for each combination of protein involved in the interactions. Selective propensities and Odds ratios in favour of cancer cells interactions were determined for all the possible combination of surface proteins for ‘k’ degree of interaction. The model was experimentally validated by two types of Test cultures.

Results

Several Glioblastoma cell surface antigens were identified from literature and databases. Those were screened based on the relevance, availability of expression levels and crystal structure in public databases. High priority eleven surface antigens were selected for probabilistic modelling. A new term, Break-even point (BEP) was defined as a characteristic of the typical cancer cell membrane encapsulated delivery agents. The model predictions lie within ±7% of the experimentally observed values for both experimental test culture types.

Conclusion

The implemented probabilistic model efficiently predicted the directional preference of the exposed nanoparticle coated with cancer cell membrane (in this case GCC membrane). This model, however, is developed and validated for glioblastoma, can be easily tailored for any type of cancer involving CCMEN as delivery agents for potential cancer immunotherapy. This probabilistic model would help in the development of future cancer immunotherapeutic with greater specificity.

Adaptive therapy for ovarian cancer: An integrated approach to PARP inhibitor scheduling

Toxicity and emerging drug resistance are important challenges in PARP inhibitor (PARPi) treatment of ovarian cancer. Recent research has shown that evolutionary-inspired treatment algorithms which adapt treatment to the tumor's treatment response (adaptive therapy) can help to mitigate both. Here, we present a first step in developing an adaptive therapy protocol for PARPi treatment by combining mathematical modelling and wet-lab experiments to characterize the cell population dynamics under different PARPi schedules. Using data from in vitro Incucyte Zoom time-lapse microscopy experiments and a step-wise model selection process we derive a calibrated and validated ordinary differential equation model, which we then use to test different plausible adaptive treatment schedules. Our model can accurately predict the in vitro treatment dynamics, even to new schedules, and suggests that treatment modifications need to be carefully timed, or one risks losing control over tumour growth, even in the absence of any resistance. This is because our model predicts that multiple rounds of cell division are required for cells to acquire sufficient DNA damage to induce apoptosis. As a result, adaptive therapy algorithms that modulate treatment but never completely withdraw it are predicted to perform better in this setting than strategies based on treatment interruptions. Pilot experiments in vivo confirm this conclusion. Overall, this study contributes to a better understanding of the impact of scheduling on treatment outcome for PARPis and showcases some of the challenges involved in developing adaptive therapies for new treatment settings.

A coupled mathematical model between bone remodeling and tumors: a study of different scenarios using Komarova's model

This paper aims to construct a general framework of coupling tumor-bone remodeling processes in order to produce plausible outcomes of the effects of tumors on the number of osteoclasts, osteoblasts, and the frequency of the bone turnover cycle. In this document, Komarova's model has been extended to include the effect of tumors on the bone remodeling processes. Thus, we explored three alternatives for coupling tumor presence into Komarova's model: first, using a "damage" parameter that depends on the tumor cell concentration. A second model follows the original structure of Komarova, including the tumor presence in those equations powered up to a new parameter, called the paracrine effect of the tumor on osteoclasts and osteoblasts; the last model is replicated from Ayati and collaborators in which the impact of the tumor is included into the paracrine parameters. Through the models, we studied their stability and considered some examples that can reproduce the tumor effects seen in clinic and experimentally. Therefore, this paper has three parts: the exposition of the three models, the results and discussion (where we explore some aspects and examples of the solution of the models), and the conclusion.

The role of acoustofluidics and microbubble dynamics for therapeutic applications and drug delivery

Targeted drug delivery is proposed to reduce the toxic effects of conventional therapeutic methods. For that purpose, nanoparticles are loaded with drugs called nanocarriers and directed toward a specific site. However, biological barriers challenge the nanocarriers to convey the drug to the target site effectively. Different targeting strategies and nanoparticle designs are used to overcome these barriers. Ultrasound is a new, safe, and non-invasive drug targeting method, especially when combined with microbubbles. Microbubbles oscillate under the effect of the ultrasound, which increases the permeability of endothelium, hence, the drug uptake to the target site. Consequently, this new technique reduces the dose of the drug and avoids its side effects. This review aims to describe the biological barriers and the targeting types with the critical features of acoustically driven microbubbles focusing on biomedical applications. The theoretical part covers the historical developments in microbubble models for different conditions: microbubbles in an incompressible and compressible medium and bubbles encapsulated by a shell. The current state and the possible future directions are discussed.

Data-driven spatio-temporal modelling of glioblastoma

Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding glioblastoma, a malignant form of brain cancer. For each approach, we summarize the scope, drawbacks and assets. We highlight the potential clinical applications of each modelling technique and discuss the connections between the mathematical models and the molecular and imaging data used to inform them. By doing so, we aim to prime cancer researchers with current and emerging computational tools for understanding tumour progression. By providing an in-depth picture of the different modelling techniques, we also aim to assist researchers who seek to build and develop their own models and the associated inference frameworks. Our article thus strikes a unique balance. On the one hand, we provide a comprehensive overview of the available modelling techniques and their applications, including key mathematical expressions. On the other hand, the content is accessible to mathematicians and biomedical scientists alike to accommodate the interdisciplinary nature of cancer research.

Beyond lymphopenia, unraveling radiation-induced leucocyte subpopulation kinetics and mechanisms through modeling approaches

Leucocyte subpopulations in both lymphoid and myeloid lineages have a significant impact on antitumor immune response. While radiation-induced lymphopenia is being studied extensively, radiation effects on lymphoid and myeloid subtypes have been relatively less addressed. Interactions between leucocyte subpopulations, their specific radiation sensitivity and the specific kinetics of each subpopulation can be modeled based on both experimental data and knowledge of physiological leucocyte depletion, production, proliferation, maturation and homeostasis. Modeling approaches of the leucocyte kinetics that may be used to unravel mechanisms underlying radiation induced-leucopenia and prediction of changes in cell counts and compositions after irradiation are presented in this review. The approaches described open up new possibilities for determining the influence of irradiation parameters both on a single-time point of acute effects and the subsequent recovery of leukocyte subpopulations. Utilization of these approaches to model kinetic data in post-radiotherapy states may be a useful tool for further development of new treatment strategies or for the combination of radiotherapy and immunotherapy.