A Mathematical Framework for Modelling the Metastatic Spread of Cancer

The development of drug resistance in metastatic tumours under chemotherapy: An evolutionary perspective

We present a mathematical model of the evolutionary dynamics of a metastatic tumour under chemotherapy, comprising non-local partial differential equations for the phenotype-structured cell populations in the primary tumour and its metastasis. These equations are coupled with a physiologically-based pharmacokinetic model of drug administration and distribution, implementing a realistic delivery schedule. The model is carefully calibrated from the literature, focusing on BRAF-mutated melanoma treated with Dabrafenib as a case study. By means of long-time asymptotic and global sensitivity analyses, as well as numerical simulations, we explore the impact of cell migration from the primary to the metastatic site, physiological aspects of the tumour tissues and drug dose on the development of chemoresistance and treatment efficacy. Our findings provide a possible explanation for empirical evidence indicating that chemotherapy may foster metastatic spread and that metastases may be less impacted by the chemotherapeutic agent.

Systematic simulation of tumor cell invasion and migration in response to time-varying rotating magnetic field

Cancer invasion and migration play a pivotal role in tumor malignancy, which is a major cause of most cancer deaths. Rotating magnetic field (RMF), one of the typical dynamic magnetic fields, can exert substantial mechanical influence on cells. However, studying the effects of RMF on cell is challenging due to its complex parameters, such as variation of magnetic field intensity and direction. Here, we developed a systematic simulation method to explore the influence of RMF on tumor invasion and migration, including a finite element method (FEM) model and a cell-based hybrid numerical model. Coupling with the data of magnetic field from FEM, the cell-based hybrid numerical model was established to simulate the tumor cell invasion and migration. This model employed partial differential equations (PDEs) and finite difference method to depict cellular activities and solve these equations in a discrete system. PDEs were used to depict cell activities, and finite difference method was used to solve the equations in discrete system. As a result, this study provides valuable insights into the potential applications of RMF in tumor treatment, and a series of in vitro experiments were performed to verify the simulation results, demonstrating the model's reliability and its capacity to predict experimental outcomes and identify pertinent factors. Furthermore, these findings shed new light on the mechanical and chemical interplay between cells and the ECM, offering new insights and providing a novel foundation for both experimental and theoretical advancements in tumor treatment by using RMF.

Mathematical modeling of brain metastases growth and response to therapies: A review

Brain metastases (BMs) are the most common intracranial tumor type and a significant health concern, affecting approximately 10% to 30% of all oncological patients. Although significant progress is being made, many aspects of the metastatic process to the brain and the growth of the resulting lesions are still not well understood. There is a need for an improved understanding of the growth dynamics and the response to treatment of these tumors. Mathematical models have been proven valuable for drawing inferences and making predictions in different fields of cancer research, but few mathematical works have considered BMs. This comprehensive review aims to establish a unified platform and contribute to fostering emerging efforts dedicated to enhancing our mathematical understanding of this intricate and challenging disease. We focus on the progress made in the initial stages of mathematical modeling research regarding BMs and the significant insights gained from such studies. We also explore the vital role of mathematical modeling in predicting treatment outcomes and enhancing the quality of clinical decision-making for patients facing BMs.

A Role of Effector CD 8 + T Cells Against Circulating Tumor Cells Cloaked with Platelets: Insights from a Mathematical Model

Cancer metastasis accounts for a majority of cancer-related deaths worldwide. Metastasis occurs when the primary tumor sheds cells into the blood and lymphatic circulation, thereby becoming circulating tumor cells (CTCs) that transverse through the circulatory system, extravasate the circulation and establish a secondary distant tumor. Accumulating evidence suggests that circulating effector CD 8 + T cells are able to recognize and attack arrested or extravasating CTCs, but this important antitumoral effect remains largely undefined. Recent studies highlighted the supporting role of activated platelets in CTCs's extravasation from the bloodstream, contributing to metastatic progression. In this work, a simple mathematical model describes how the primary tumor, CTCs, activated platelets and effector CD 8 + T cells participate in metastasis. The stability analysis reveals that for early dissemination of CTCs, effector CD 8 + T cells can present or keep secondary metastatic tumor burden at low equilibrium state. In contrast, for late dissemination of CTCs, effector CD 8 + T cells are unlikely to inhibit secondary tumor growth. Moreover, global sensitivity analysis demonstrates that the rate of the primary tumor growth, intravascular CTC proliferation, as well as the CD 8 + T cell proliferation, strongly affects the number of the secondary tumor cells. Additionally, model simulations indicate that an increase in CTC proliferation greatly contributes to tumor metastasis. Our simulations further illustrate that the higher the number of activated platelets on CTCs, the higher the probability of secondary tumor establishment. Intriguingly, from a mathematical immunology perspective, our simulations indicate that if the rate of effector CD 8 + T cell proliferation is high, then the secondary tumor formation can be considerably delayed, providing a window for adjuvant tumor control strategies. Collectively, our results suggest that the earlier the effector CD 8 + T cell response is enhanced the higher is the probability of preventing or delaying secondary tumor metastases.

Cancer cell sedimentation in 3D cultures reveals active migration regulated by self-generated gradients and adhesion sites

Cell sedimentation in 3D hydrogel cultures refers to the vertical migration of cells towards the bottom of the space. Understanding this poorly examined phenomenon may allow us to design better protocols to prevent it, as well as provide insights into the mechanobiology of cancer development. We conducted a multiscale experimental and mathematical examination of 3D cancer growth in triple negative breast cancer cells. Migration was examined in the presence and absence of Paclitaxel, in high and low adhesion environments and in the presence of fibroblasts. The observed behaviour was modeled by hypothesizing active migration due to self-generated chemotactic gradients. Our results did not reject this hypothesis, whereby migration was likely to be regulated by the MAPK and TGF-β pathways. The mathematical model enabled us to describe the experimental data in absence (normalized error<40%) and presence of Paclitaxel (normalized error<10%), suggesting inhibition of random motion and advection in the latter case. Inhibition of sedimentation in low adhesion and co-culture experiments further supported the conclusion that cells actively migrated downwards due to the presence of signals produced by cells already attached to the adhesive glass surface.

A Genuinely Hybrid, Multiscale 3D Cancer Invasion and Metastasis Modelling Framework

We introduce in this paper substantial enhancements to a previously proposed hybrid multiscale cancer invasion modelling framework to better reflect the biological reality and dynamics of cancer. These model updates contribute to a more accurate representation of cancer dynamics, they provide deeper insights and enhance our predictive capabilities. Key updates include the integration of porous medium-like diffusion for the evolution of Epithelial-like Cancer Cells and other essential cellular constituents of the system, more realistic modelling of Epithelial-Mesenchymal Transition and Mesenchymal-Epithelial Transition models with the inclusion of Transforming Growth Factor beta within the tumour microenvironment, and the introduction of Compound Poisson Process in the Stochastic Differential Equations that describe the migration behaviour of the Mesenchymal-like Cancer Cells. Another innovative feature of the model is its extension into a multi-organ metastatic framework. This framework connects various organs through a circulatory network, enabling the study of how cancer cells spread to secondary sites.

Multiscale computational modeling of aortic valve calcification

Calcific aortic valve disease (CAVD) is a common cardiovascular disease that affects millions of people worldwide. The disease is characterized by the formation of calcium nodules on the aortic valve leaflets, which can lead to stenosis and heart failure if left untreated. The pathogenesis of CAVD is still not well understood, but involves several signaling pathways, including the transforming growth factor beta (TGF β ) pathway. In this study, we developed a multiscale computational model for TGF β -stimulated CAVD. The model framework comprises cellular behavior dynamics, subcellular signaling pathways, and tissue-level diffusion fields of pertinent chemical species, where information is shared among different scales. Processes such as endothelial to mesenchymal transition (EndMT), fibrosis, and calcification are incorporated. The results indicate that the majority of myofibroblasts and osteoblast-like cells ultimately die due to lack of nutrients as they become trapped in areas with higher levels of fibrosis or calcification, and they subsequently act as sources for calcium nodules, which contribute to a polydispersed nodule size distribution. Additionally, fibrosis and calcification processes occur more frequently in regions closer to the endothelial layer where the cell activity is higher. Our results provide insights into the mechanisms of CAVD and TGF β signaling and could aid in the development of novel therapeutic approaches for CAVD and other related diseases such as cancer. More broadly, this type of modeling framework can pave the way for unraveling the complexity of biological systems by incorporating several signaling pathways in subcellular models to simulate tissue remodeling in diseases involving cellular mechanobiology.

A Model for Membrane Degradation Using a Gelatin Invadopodia Assay

One of the most crucial and lethal characteristics of solid tumors is represented by the increased ability of cancer cells to migrate and invade other organs during the so-called metastatic spread. This is allowed thanks to the production of matrix metalloproteinases (MMPs), enzymes capable of degrading a type of collagen abundant in the basal membrane separating the epithelial tissue from the connective one. In this work, we employ a synergistic experimental and mathematical modelling approach to explore the invasion process of tumor cells. A mathematical model composed of reaction-diffusion equations describing the evolution of the tumor cells density on a gelatin substrate, MMPs enzymes concentration and the degradation of the gelatin is proposed. This is completed with a calibration strategy. We perform a sensitivity analysis and explore a parameter estimation technique both on synthetic and experimental data in order to find the optimal parameters that describe the in vitro experiments. A comparison between numerical and experimental solutions ends the work.

Understanding the Interplay of CAR-NK Cells and Triple-Negative Breast Cancer: Insights from Computational Modeling

Chimeric antigen receptor (CAR)-engineered natural killer (NK) cells have recently emerged as a promising and safe alternative to CAR-T cells for targeting solid tumors. In the case of triple-negative breast cancer (TNBC), traditional cancer treatments and common immunotherapies have shown limited effectiveness. However, CAR-NK cells have been successfully employed to target epidermal growth factor receptor (EGFR) on TNBC cells, thereby enhancing the efficacy of immunotherapy. The effectiveness of CAR-NK-based immunotherapy is influenced by various factors, including the vaccination dose, vaccination pattern, and tumor immunosuppressive factors in the microenvironment. To gain insights into the dynamics and effects of CAR-NK-based immunotherapy, we propose a computational model based on experimental data and immunological theories. This model integrates an individual-based model that describes the interplay between the tumor and the immune system, along with an ordinary differential equation model that captures the variation of inflammatory cytokines. Computational results obtained from the proposed model shed light on the conditions necessary for initiating an effective anti-tumor response. Furthermore, global sensitivity analysis highlights the issue of low persistence of CAR-NK cells in vivo, which poses a significant challenge for the successful clinical application of these cells. Leveraging the model, we identify the optimal vaccination time, vaccination dose, and time interval between injections for maximizing therapeutic outcomes.

Revolutionizing anti-cancer drug discovery against breast cancer and lung cancer by modification of natural genistein: an advanced computational and drug design approach

Breast and lung cancer are two of the most lethal forms of cancer, responsible for a disproportionately high number of deaths worldwide. Both doctors and cancer patients express alarm about the rising incidence of the disease globally. Although targeted treatment has achieved enormous advancements, it is not without its drawbacks. Numerous medicines and chemotherapeutic drugs have been authorized by the FDA; nevertheless, they can be quite costly and often fall short of completely curing the condition. Therefore, this investigation has been conducted to identify a potential medication against breast and lung cancer through structural modification of genistein. Genistein is the active compound in Glycyrrhiza glabra (licorice), and it exhibits solid anticancer efficiency against various cancers, including breast cancer, lung cancer, and brain cancer. Hence, the design of its analogs with the interchange of five functional groups-COOH, NH2 and OCH3, Benzene, and NH-CH2-CH2-OH-have been employed to enhance affinities compared to primary genistein. Additionally, advanced computational studies such as PASS prediction, molecular docking, ADMET, and molecular dynamics simulation were conducted. Firstly, the PASS prediction spectrum was analyzed, revealing that the designed genistein analogs exhibit improved antineoplastic activity. In the prediction data, breast and lung cancer were selected as primary targets. Subsequently, other computational investigations were gradually conducted. The mentioned compounds have shown acceptable results for in silico ADME, AMES toxicity, and hepatotoxicity estimations, which are fundamental for their oral medication. It is noteworthy that the initial binding affinity was only -8.7 kcal/mol against the breast cancer targeted protein (PDB ID: 3HB5). However, after the modification of the functional group, when calculating the binding affinities, it becomes apparent that the binding affinities increase gradually, reaching a maximum of -11.0 and -10.0 kcal/mol. Similarly, the initial binding affinity was only -8.0 kcal/mol against lung cancer (PDB ID: 2P85), but after the addition of binding affinity, it reached -9.5 kcal/mol. Finally, a molecular dynamics simulation was conducted to study the molecular models over 100 ns and examine the stability of the docked complexes. The results indicate that the selected complexes remain highly stable throughout the 100-ns molecular dynamics simulation runs, displaying strong correlations with the binding of targeted ligands within the active site of the selected protein. It is important to further investigate and proceed to clinical or wet lab experiments to determine the practical value of the proposed compounds.

Intermetastatic and Intrametastatic Heterogeneity Shapes Adaptive Therapy Cycling Dynamics

Adaptive therapies that alternate between drug applications and drug-free vacations can exploit competition between sensitive and resistant cells to maximize the time to progression. However, optimal dosing schedules depend on the properties of metastases, which are often not directly measurable in clinical practice. Here, we proposed a framework for estimating features of metastases through tumor response dynamics during the first adaptive therapy treatment cycle. Longitudinal prostate-specific antigen (PSA) levels in 16 patients with metastatic castration-resistant prostate cancer undergoing adaptive androgen deprivation treatment were analyzed to investigate relationships between cycle dynamics and clinical variables such as Gleason score, the change in the number of metastases over a cycle, and the total number of cycles over the course of treatment. The first cycle of adaptive therapy, which consists of a response period (applying therapy until 50% PSA reduction), and a regrowth period (removing treatment until reaching initial PSA levels), delineated several features of the computational metastatic system: larger metastases had longer cycles; a higher proportion of drug-resistant cells slowed the cycles; and a faster cell turnover rate sped up drug response time and slowed regrowth time. The number of metastases did not affect cycle times, as response dynamics were dominated by the largest tumors rather than the aggregate. In addition, systems with higher intermetastasis heterogeneity responded better to continuous therapy and correlated with dynamics from patients with high or low Gleason scores. Conversely, systems with higher intrametastasis heterogeneity responded better to adaptive therapy and correlated with dynamics from patients with intermediate Gleason scores.

SIGNIFICANCE

Multiscale mathematical modeling combined with biomarker dynamics during adaptive therapy helps identify underlying features of metastatic cancer to inform treatment decisions.

Computational reactive-diffusive modeling for stratification and prognosis determination of patients with breast cancer receiving Olaparib

Mathematical models based on partial differential equations (PDEs) can be exploited to handle clinical data with space/time dimensions, e.g. tumor growth challenged by neoadjuvant therapy. A model based on simplified assessment of tumor malignancy and pharmacodynamics efficiency was exercised to discover new metrics of patient prognosis in the OLTRE trial. We tested in a 17-patients cohort affected by early-stage triple negative breast cancer (TNBC) treated with 3 weeks of olaparib, the capability of a PDEs-based reactive-diffusive model of tumor growth to efficiently predict the response to olaparib in terms of SUV_max detected at ¹⁸FDG-PET/CT scan, by using specific terms to characterize tumor diffusion and proliferation. Computations were performed with COMSOL Multiphysics. Driving parameters governing the mathematical model were selected with Pearson's correlations. Discrepancies between actual and computed SUV_max values were assessed with Student's t test and Wilcoxon rank sum test. The correlation between post-olaparib true and computed SUV_max was assessed with Pearson's r and Spearman's rho. After defining the proper mathematical assumptions, the nominal drug efficiency (ε_PD) and tumor malignancy (r_c) were computationally evaluated. The former parameter reflected the activity of olaparib on the tumor, while the latter represented the growth rate of metabolic activity as detected by SUV_max. ε_PD was found to be directly dependent on basal tumor-infiltrating lymphocytes (TILs) and Ki67% and was detectable through proper linear regression functions according to TILs values, while r_c was represented by the baseline Ki67-to-TILs ratio. Predicted post-olaparib SUV*_max did not significantly differ from original post-olaparib SUV_max in the overall, gBRCA-mutant and gBRCA-wild-type subpopulations (p > 0.05 in all cases), showing strong positive correlation (r = 0.9 and rho = 0.9, p < 0.0001 both). A model of simplified tumor dynamics was exercised to effectively produce an upfront prediction of efficacy of 3-week neoadjuvant olaparib in terms of SUV_max. Prospective evaluation in independent cohorts and correlation of these outcomes with more recognized efficacy endpoints is now warranted for model confirmation and tailoring of escalated/de-escalated therapeutic strategies for early-TNBC patients.

A computational model for the cancer field effect

Introduction

The Cancer Field Effect describes an area of pre-cancerous cells that results from continued exposure to carcinogens. Cells in the cancer field can easily develop into cancer. Removal of the main tumor mass might leave the cancer field behind, increasing risk of recurrence.

Methods

The model we propose for the cancer field effect is a hybrid cellular automaton (CA), which includes a multi-layer perceptron (MLP) to compute the effects of the carcinogens on the gene expression of the genes related to cancer development. We use carcinogen interactions that are typically associated with smoking and alcohol consumption and their effect on cancer fields of the tongue.

Results

Using simulations we support the understanding that tobacco smoking is a potent carcinogen, which can be reinforced by alcohol consumption. The effect of alcohol alone is significantly less than the effect of tobacco. We further observe that pairing tumor excision with field removal delays recurrence compared to tumor excision alone. We track cell lineages and find that, in most cases, a polyclonal field develops, where the number of distinct cell lineages decreases over time as some lineages become dominant over others. Finally, we find tumor masses rarely form via monoclonal origin.

Multiscale model of the different modes of cancer cell invasion

MOTIVATION

Mathematical models of biological processes altered in cancer are built using the knowledge of complex networks of signaling pathways, detailing the molecular regulations inside different cell types, such as tumor cells, immune and other stromal cells. If these models mainly focus on intracellular information, they often omit a description of the spatial organization among cells and their interactions, and with the tumoral microenvironment.

RESULTS

We present here a model of tumor cell invasion simulated with PhysiBoSS, a multiscale framework, which combines agent-based modeling and continuous time Markov processes applied on Boolean network models. With this model, we aim to study the different modes of cell migration and to predict means to block it by considering not only spatial information obtained from the agent-based simulation but also intracellular regulation obtained from the Boolean model.

Our multiscale model integrates the impact of gene mutations with the perturbation of the environmental conditions and allows the visualization of the results with 2D and 3D representations. The model successfully reproduces single and collective migration processes and is validated on published experiments on cell invasion. In silico experiments are suggested to search for possible targets that can block the more invasive tumoral phenotypes.

AVAILABILITY AND IMPLEMENTATION

https://github.com/sysbio-curie/Invasion_model_PhysiBoSS.

Nanoscale Prognosis of Colorectal Cancer Metastasis from AFM Image Processing of Histological Sections

Early ascertainment of metastatic tumour phases is crucial to improve cancer survival, formulate an accurate prognostic report of disease advancement, and, most importantly, quantify the metastatic progression and malignancy state of primary cancer cells with a universal numerical indexing system. This work proposes an early improvement to metastatic cancer detection with 97.7 nm spatial resolution by indexing the metastatic cancer phases from the analysis of atomic force microscopy images of human colorectal cancer histological sections. The procedure applies variograms of residuals of Gaussian filtering and theta statistics of colorectal cancer tissue image settings. This methodology elucidates the early metastatic progression at the nanoscale level by setting metastatic indexes and critical thresholds based on relatively large histological sections and categorising the malignancy state of a few suspicious cells not identified with optical image analysis. In addition, we sought to detect early tiny morphological differentiations indicating potential cell transition from epithelial cell phenotypes of low metastatic potential to those of high metastatic potential. This metastatic differentiation, which is also identified in higher moments of variograms, sets different hierarchical levels for metastatic progression dynamics.

Drug Sensitivity Testing for Cancer Therapy, Technique Analysis and Trends

The techniques and qualities of drug sensitivity testing (DST) for anticancer treatment have grown rapidly in the past two decades worldwide. Much of DST progress came from advanced systems of technical versatility (faster, highly-throughput, highly-sensitive, and smaller in tumor quantity). As the earliest drug selective system, biomedical knowledge and technical advances for DST are mutually supported. More importantly, many pharmacological controversies are resolved by these technical advances. With this technical stride, the clinical landscape of DST entered into a new phase (>500 samples per testing and extremely low quantity of tumor cells). As a forerunner of the drug selection system, DST awaits a new version that can adapt to complicated therapeutic situations and diverse tumor categories in the clinic. By upholding this goal of pathogenic and therapeutic diversity, DST could eventually cure more cancer patients by establishing high-quality drug selection systems. To smoothen DST development, there is a need to increase the understanding of cancer biology, pathology and pharmacology (cancer heterogeneity, plasticity, metastasis and drug resistance) with well-informative parameters before chemotherapy. In this article, medicinal and technical insights into DST are especially highlighted.

SMoRe ParS: A novel methodology for bridging modeling modalities and experimental data applied to 3D vascular tumor growth

Multiscale systems biology is having an increasingly powerful impact on our understanding of the interconnected molecular, cellular, and microenvironmental drivers of tumor growth and the effects of novel drugs and drug combinations for cancer therapy. Agent-based models (ABMs) that treat cells as autonomous decision-makers, each with their own intrinsic characteristics, are a natural platform for capturing intratumoral heterogeneity. Agent-based models are also useful for integrating the multiple time and spatial scales associated with vascular tumor growth and response to treatment. Despite all their benefits, the computational costs of solving agent-based models escalate and become prohibitive when simulating millions of cells, making parameter exploration and model parameterization from experimental data very challenging. Moreover, such data are typically limited, coarse-grained and may lack any spatial resolution, compounding these challenges. We address these issues by developing a first-of-its-kind method that leverages explicitly formulated surrogate models (SMs) to bridge the current computational divide between agent-based models and experimental data. In our approach, Surrogate Modeling for Reconstructing Parameter Surfaces (SMoRe ParS), we quantify the uncertainty in the relationship between agent-based model inputs and surrogate model parameters, and between surrogate model parameters and experimental data. In this way, surrogate model parameters serve as intermediaries between agent-based model input and data, making it possible to use them for calibration and uncertainty quantification of agent-based model parameters that map directly onto an experimental data set. We illustrate the functionality and novelty of Surrogate Modeling for Reconstructing Parameter Surfaces by applying it to an agent-based model of 3D vascular tumor growth, and experimental data in the form of tumor volume time-courses. Our method is broadly applicable to situations where preserving underlying mechanistic information is of interest, and where computational complexity and sparse, noisy calibration data hinder model parameterization.

Recent progress in molecular mechanisms of postoperative recurrence and metastasis of hepatocellular carcinoma

Hepatectomy is currently considered the most effective option for treating patients with early and intermediate hepatocellular carcinoma (HCC). Unfortunately, the postoperative prognosis of patients with HCC remains unsatisfactory, predominantly because of high postoperative metastasis and recurrence rates. Therefore, research on the molecular mechanisms of postoperative HCC metastasis and recurrence will help develop effective intervention measures to prevent or delay HCC metastasis and recurrence and to improve the long-term survival of HCC patients. Herein, we review the latest research progress on the molecular mechanisms underlying postoperative HCC metastasis and recurrence to lay a foundation for improving the understanding of HCC metastasis and recurrence and for developing more precise prevention and intervention strategies.

Drug Sensitivity Testing for Cancer Therapy, Key Areas

AIMS

Cancer is a high-mortality disease (9.6 million deaths in 2018 worldwide). Given various anticancer drugs, drug selection plays a key role in patient survival in clinical trials.

METHODS

Drug Sensitivity Testing (DST), one of the leading drug selective systems, was widely practiced for therapeutic promotion in the clinic. Notably, DSTs assist in drug selection that benefits drug responses against cancer from 20-22% to 30-35% over the past two decades. The relationship between drug resistance in vitro and drug treatment benefits was associated with different tumor origins and subtypes. Medical theory and underlying DST mechanisms remain poorly understood until now. The study of the clinical scenario, sustainability and financial support for mechanism and technical promotions is indispensable.

RESULTS

Despite the great technical advance, therapeutic prediction and drug selection by DST needs to be miniature, versatility and cost-effective in the clinic. Multi-parameters and automation of DST should be a future trend. Advanced biomedical knowledge and clinical approaches to translating oncologic profiles into drug selection were the main focuses of DST developments. With a great technical stride, the clinical architecture of the DST platform was entering higher levels (drug response testing at any stage of cancer patients and miniaturization of tumor samples).

DISCUSSION

The cancer biology and pharmacology for drug selection mutually benefit the clinic. New proposals to reveal more therapeutic information and drug response prediction at genetic, molecular and omics levels should be estimated overall.

CONCLUSION

By upholding this goal of non-invasive, versatility and automation, DST could save the life of several thousand annually worldwide. In this article, new insights into DST novelty and development are highlighted.

Network Analysis Identifies Phase Transitions for Tumor With Interacting Cells

Metastasis is the process by which cancer cells acquire the capability to leave the primary tumor and travel to distant sites. Recent experiments have suggested that the epithelial–mesenchymal transition can regulate invasion and metastasis. Another possible scenario is the collective motion of cells. Recent studies have also proposed a jamming–unjamming transition for epithelial cells based on physical forces. Here, we assume that there exists a short-range chemical attraction between cancer cells and employ the Brownian dynamics to simulate tumor growth. Applying the network analysis, we suggest three possible phases for a given tumor and study the transition between these phases by adjusting the attraction strength.

A two-dimensional mathematical model of tumor angiogenesis with CD147

Tumor angiogenesis is the tumor’s inherent blood supply system which is crucial for the growth of tumor. Extracellular Matrix Metallo Proteinases Inducer (EMMPRIN)/Cluster of Differentiation 147 (CD147) is found in high levels on tumor surfaces. This study focuses on these elevated levels of CD147 and the effect it has on tumor angiogenesis. The present article develops a Two-Dimensional Mathematical Model of Tumor Angiogenesis taking into account the CD147 molecule. The effects of CD147 on Tumor Angiogenesis Factors (TAFs), fibronectin and Matrix Metallo Proteinases (MMPs) are also incorporated. The results have been obtained through COMSOL Multiphysics 5.4 software. The results show that CD147 is responsible for swifter angiogenesis, calling for targeting this molecule in anti-angiogenic strategies. The present model is validated with the existing theoretical and experimental results.

Effects of Artonin E on Cell Growth Inhibition and Apoptosis Induction in Colon Cancer LoVo and HCT116 Cells

Today, colon cancer is the leading cause of cancer death. In Thailand, colon cancer is the third most common cancer in men and the second in women. Currently, the treatments for colon cancer include surgery, chemotherapy, radiation therapy, immunotherapy, hormone therapy, targeted drug therapy, and stem cell therapy. However, some treatments have side effects for cancer patients, causing unwanted symptoms. In addition, targeted therapy comes with a high cost for patients. Therefore, bioactive compounds might be a good choice for colon cancer treatment. In this study, we investigated the effect of artonin E on apoptosis induction in colon cancer LoVo and HCT116 cells. The concentration ranges of artonin E at 3, 5, 10, and 30 µg/mL in LoVo cells and 1, 1.5, 2, and 3 µg/mL in HCT116 cells were examined. The results implied that artonin E decreased cell viability and increased apoptotic cells in a dose-dependent manner. In addition, artonin E stimulated mitochondrial membrane potential (ΔΨm) changes associated with apoptosis by increasing the sub-G1 population analyzed by flow cytometry. Western blotting showed that artonin E increased the proapoptotic protein, Bax, and decreased anti-apoptotic proteins’ (Bcl-2 and Bcl-x) expression. Moreover, artonin E also increased cleaved caspase-7 and cleaved-PARP expression in both LoVo and HCT116 cells. Interestingly, artonin E induced apoptosis through p-ERK1/2, p-p38/p38, and p-c-Jun expression in both cells. Our results suggested that artonin E induced apoptosis via caspase activation associated with the MAPKs signaling pathway. Therefore, artonin E might be used as a potential anticancer drug for colon cancer in the future.

Elective Checkpoint Inhibitor Discontinuation in Metastatic Solid Tumor Patients: A Case Series

Introduction

Checkpoint inhibitor (CKI) therapy has markedly altered the survival of patients with many solid tumors. It appears clear that 10-40% of patients with a number of metastatic cancers can achieve lengthy remissions following CKI therapy. The optimal duration of treatment or whether treatment can ever be safely stopped is still controversial. Based on melanoma-derived data, we tested whether CKI treatment could safely be discontinued in patients with other solid tumors.

Methods

A retrospective analysis was performed in adults with metastatic solid tumors treated with CKI-based therapy. Patients with solid tumors who achieved complete remission on 2 sequential scans at least 3 months apart during ongoing treatment were identified from our computerized patient database. Patient data was analyzed for patient characteristics, as well as progression-free and overall survival.

Results

A total of 69 non-melanoma solid tumor patients were treated with CKI-based regimens in our clinic and 14 achieved complete remission (20.3%). Five patients were female (35.7%) and the remaining nine were male (64.3%). A 100% progression-free survival was observed for these patients. The median duration of complete remission was over 20 months from the time of elective treatment discontinuation. Median overall survival was not reached in this cohort. One patient died of no cancer-related causes.

Conclusions

Based on this retrospective case series, elective treatment discontinuation in patients who achieved complete remission appears feasible. All patients remained in a durable complete remission after treatment discontinuation. We hypothesize that appropriate selection of patients for early treatment discontinuation may decrease their economic burden related to ongoing treatment, limit potential toxicity, and improve quality of life.

Modeling codelivery of CD73 inhibitor and dendritic cell-based vaccines in cancer immunotherapy

Dendritic cells (DCs) are the dominant class of antigen-presenting cells in humans; therefore, a range of DC-based approaches have been established to promote an immune response against cancer cells. The efficacy of DC-based immunotherapeutic approaches is markedly affected by the immunosuppressive factors related to the tumor microenvironment, such as adenosine. In this paper, based on immunological theories and experimental data, a hybrid model is designed that offers some insights into the effects of DC-based immunotherapy combined with adenosine inhibition. The model combines an individual-based model for describing tumor-immune system interactions with a set of ordinary differential equations for adenosine modeling. Computational simulations of the proposed model clarify the conditions for the onset of a successful immune response against cancer cells. Global and local sensitivity analysis of the model highlights the importance of adenosine blockage for strengthening effector cells. The model is used to determine the most effective suppressive mechanism caused by adenosine, proper vaccination time, and the appropriate time interval between injections.

Multiscale modeling in disease

Multiscale computational modeling aims to connect the complex networks of effects at different length and/or time scales. For example, these networks often include intracellular molecular signaling, crosstalk, and other interactions between neighboring cell populations, and higher levels of emergent phenomena across different regions of tissues and among collections of tissues or organs interacting with each other in the whole body. Recent applications of multiscale modeling across intracellular, cellular, and/or tissue levels are highlighted here. These models incorporated the roles of biochemical and biomechanical modulation in processes that are implicated in the mechanisms of several diseases including fibrosis, joint and bone diseases, respiratory infectious diseases, and cancers.

Mechanical Pressure Driving Proteoglycan Expression in Mammographic Density: a Self-perpetuating Cycle?

Regions of high mammographic density (MD) in the breast are characterised by a proteoglycan (PG)-rich fibrous stroma, where PGs mediate aligned collagen fibrils to control tissue stiffness and hence the response to mechanical forces. Literature is accumulating to support the notion that mechanical stiffness may drive PG synthesis in the breast contributing to MD. We review emerging patterns in MD and other biological settings, of a positive feedback cycle of force promoting PG synthesis, such as in articular cartilage, due to increased pressure on weight bearing joints. Furthermore, we present evidence to suggest a pro-tumorigenic effect of increased mechanical force on epithelial cells in contexts where PG-mediated, aligned collagen fibrous tissue abounds, with implications for breast cancer development attributable to high MD. Finally, we summarise means through which this positive feedback mechanism of PG synthesis may be intercepted to reduce mechanical force within tissues and thus reduce disease burden.

Is There One Key Step in the Metastatic Cascade?

Simple Summary

To successfully metastasize, cancer cells must complete a sequence of obligatory steps called the metastatic cascade. To model the metastatic cascade, we used the framework of the Drake equation, initially created to describe the emergence of intelligent life in the Milky way, using a similar logic of a sequence of obligatory steps. Then within this framework, we used simulations on breast cancer to investigate the contribution of each step to the metastatic cascade. We show that the half-life of circulating tumor cells is one of the most important parameters in the cascade, suggesting that therapies reducing the survival of those cells in the vascular system could significantly reduce the risk of metastasis.

Abstract

The majority of cancer-related deaths are the result of metastases (i.e., dissemination and establishment of tumor cells at distant sites from the origin), which develop through a multi-step process classically termed the metastatic cascade. The respective contributions of each step to the metastatic process are well described but are also currently not completely understood. Is there, for example, a critical phase that disproportionately affects the probability of the development of metastases in individual patients? Here, we address this question using a modified Drake equation, initially formulated by the astrophysicist Frank Drake to estimate the probability of the emergence of intelligent civilizations in the Milky Way. Using simulations based on realistic parameter values obtained from the literature for breast cancer, we examine, under the linear progression hypothesis, the contribution of each component of the metastatic cascade. Simulations demonstrate that the most critical parameter governing the formation of clinical metastases is the survival duration of circulating tumor cells (CTCs).

Calibrating models of cancer invasion: parameter estimation using approximate Bayesian computation and gradient matching

We present two different methods to estimate parameters within a partial differential equation model of cancer invasion. The model describes the spatio-temporal evolution of three variables-tumour cell density, extracellular matrix density and matrix degrading enzyme concentration-in a one-dimensional tissue domain. The first method is a likelihood-free approach associated with approximate Bayesian computation; the second is a two-stage gradient matching method based on smoothing the data with a generalized additive model (GAM) and matching gradients from the GAM to those from the model. Both methods performed well on simulated data. To increase realism, additionally we tested the gradient matching scheme with simulated measurement error and found that the ability to estimate some model parameters deteriorated rapidly as measurement error increased.

The role of mechanical interactions in EMT

The detachment of cells from the boundary of an epithelial tissue and the subsequent invasion of these cells into surrounding tissues is important for cancer development and wound healing, and is strongly associated with the epithelial-mesenchymal transition (EMT). Chemical signals, such as TGF-β, produced by surrounding tissue can be uptaken by cells and induce EMT. In this work, we present a novel cell-based discrete mathematical model of mechanical cellular relaxation, cell proliferation, and cell detachment driven by chemically-dependent EMT in an epithelial tissue. A continuum description of the model is then derived in the form of a novel nonlinear free boundary problem. Using the discrete and continuum models we explore how the coupling of chemical transport and mechanical interactions influences EMT, and postulate how this could be used to help control EMT in pathological situations.

A novel 3D atomistic-continuum cancer invasion model: In silico simulations of an in vitro organotypic invasion assay

We develop a three-dimensional genuinely hybrid atomistic-continuum model that describes the invasive growth dynamics of individual cancer cells in tissue. The framework explicitly accounts for phenotypic variation by distinguishing between cancer cells of an epithelial-like and a mesenchymal-like phenotype. It also describes mutations between these cell phenotypes in the form of epithelial-mesenchymal transition (EMT) and its reverse process mesenchymal-epithelial transition (MET). The proposed model consists of a hybrid system of partial and stochastic differential equations that describe the evolution of epithelial-like and mesenchymal-like cancer cells, respectively, under the consideration of matrix-degrading enzyme concentrations and the extracellular matrix density. With the help of inverse parameter estimation and a sensitivity analysis, this three-dimensional model is then calibrated to an in vitro organotypic invasion assay experiment of oral squamous cell carcinoma cells.

Implications of immune-mediated metastatic growth on metastatic dormancy, blow-up, early detection, and treatment

Metastatic seeding of distant organs can occur in the very early stages of primary tumor development. Once seeded, these micrometastases may enter a dormant phase that can last decades. Curiously, the surgical removal of the primary tumor can stimulate the accelerated growth of distant metastases, a phenomenon known as metastatic blow-up. Recent clinical evidence has shown that the immune response can have strong tumor promoting effects. In this work, we investigate if the pro-tumor effects of the immune response can have a significant contribution to metastatic dormancy and metastatic blow-up. We develop an ordinary differential equation model of the immune-mediated theory of metastasis. We include both anti- and pro-tumor immune effects, in addition to the experimentally observed phenomenon of tumor-induced immune cell phenotypic plasticity. Using geometric singular perturbation analysis, we derive a rather simple model that captures the main processes and, at the same time, can be fully analyzed. Literature-derived parameter estimates are obtained, and model robustness is demonstrated through a time dependent sensitivity analysis. We determine conditions under which the parameterized model can successfully explain both metastatic dormancy and blow-up. The results confirm the significant active role of the immune system in the metastatic process. Numerical simulations suggest a novel measure to predict the occurrence of future metastatic blow-up in addition to new potential avenues for treatment of clinically undetectable micrometastases.

Modeling the Human Bone-Tumor Niche: Reducing and Replacing the Need for Animal Data

Bone is the most common site for cancer metastasis. Understanding the interactions within the complex, heterogeneous bone-tumor microenvironment is essential for the development of new therapeutics. Various animal models of tumor-induced bone disease are routinely used to provide valuable information on the relationship between cancer cells and the skeleton. However, new model systems exist that offer an alternative approach to the use of animals and might more accurately reveal the cellular interactions occurring within the human bone-tumor niche. This review highlights replacement models that mimic the bone microenvironment and where cancer metastases and tumor growth might be assessed alongside bone turnover. Such culture models include the use of calcified regions of animal tissue and scaffolds made from bone mineral hydroxyapatite, synthetic polymers that can be manipulated during manufacture to create structures resembling trabecular bone surfaces, gel composites that can be modified for stiffness and porosity to resemble conditions in the tumor-bone microenvironment. Possibly the most accurate model system involves the use of fresh human bone samples, which can be cultured ex vivo in the presence of human tumor cells and demonstrate similar cancer cell-bone cell interactions as described in vivo. In addition, the use of mathematical modeling and computational biology approaches provide an alternative to preliminary animal testing. The use of such models offers the capacity to mimic significant elements of the human bone-tumor environment, and complement, refine, or replace the use of preclinical models. © 2020 The Authors. JBMR Plus published by Wiley Periodicals, Inc. on behalf of American Society for Bone and Mineral Research.

A mathematical model for the immune-mediated theory of metastasis

Accumulating experimental and clinical evidence suggest that the immune response to cancer is not exclusively anti-tumor. Indeed, the pro-tumor roles of the immune system  -  as suppliers of growth and pro-angiogenic factors or defenses against cytotoxic immune attacks, for example  -  have been long appreciated, but relatively few theoretical works have considered their effects. Inspired by the recently proposed "immune-mediated" theory of metastasis, we develop a mathematical model for tumor-immune interactions at two anatomically distant sites, which includes both anti- and pro-tumor immune effects, and the experimentally observed tumor-induced phenotypic plasticity of immune cells (tumor "education" of the immune cells). Upon confrontation of our model to experimental data, we use it to evaluate the implications of the immune-mediated theory of metastasis. We find that tumor education of immune cells may explain the relatively poor performance of immunotherapies, and that many metastatic phenomena, including metastatic blow-up, dormancy, and metastasis to sites of injury, can be explained by the immune-mediated theory of metastasis. Our results suggest that further work is warranted to fully elucidate the pro-tumor effects of the immune system in metastatic cancer.