A mathematical model of tumor growth and its response to single irradiation

Impact of stroma remodeling on forces experienced by cancer cells and stromal cells within a pancreatic tumor tissue

Remodeling (re-engineering) of a tumor's stroma has been shown to improve the efficacy of anti-tumor therapies, without destroying the stroma. Even though it still remains unclear which stromal component/-s and what characteristics hinder the reach of nanoparticles deep into cancer cells, we hypothesis that mechanisms behind stroma's resistance to the penetration of nanoparticles rely heavily on extrinsic mechanical forces on stromal cells and cancer cells. Our hypothesis has been formulated on the basis of our previous study which has shown that changes in extracellular matrix (ECM) stiffness with tumor growth influence stresses exerted on fibroblasts and cancer cells, and that malignant cancer cells generate higher stresses on their stroma. This study attempts to establish a distinct identification of the components' remodeling on the distribution and magnitude of stress within a tumor tissue which ultimately will impact the resistance of stroma to treatment. In this study, our objective is to construct a three-dimensional in silico model of a pancreas tumor tissue consisting of cancer cells, stromal cells, and ECM to determine how stromal remodeling alters the stresses distribution and magnitude within the pancreas tumor tissue. Our results show that changes in mechanical properties of ECM significantly alter the magnitude and distribution of stresses within the pancreas tumor tissue. Our results revealed that these stresses are more sensitive to ECM properties as we see the stresses reaching to a maximum of 22,000 Pa for softer ECM with Young's modulus of 250 Pa. The stress distribution and magnitude within the pancreas tumor tissue does not show high sensitivity to the changes in mechanical properties of stromal cells surrounding stiffer cancer cells (PANC-1 with Young's modulus of 2400 Pa). However, softer cancer cells (MIA-PaCa-2 with (Young's modulus of 500 Pa) increase the stresses experienced by stiffer stromal cells and for stiffer ECM. By providing a unique platform to dissect and quantify the impact of individual stromal components on the stress distribution within a tumor tissue, this study serves as an important first step in understanding of which stromal components are vital for an efficient remodeling. This knowledge will be leveraged to overcome a tumor's resistance against the penetration of nanoparticles on a per-patient basis.

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.

New insights into targeted therapy of glioblastoma using smart nanoparticles

In recent times, the intersection of nanotechnology and biomedical research has given rise to nanobiomedicine, a captivating realm that holds immense promise for revolutionizing diagnostic and therapeutic approaches in the field of cancer. This innovative fusion of biology, medicine, and nanotechnology aims to create diagnostic and therapeutic agents with enhanced safety and efficacy, particularly in the realm of theranostics for various malignancies. Diverse inorganic, organic, and hybrid organic-inorganic nanoparticles, each possessing unique properties, have been introduced into this domain. This review seeks to highlight the latest strides in targeted glioblastoma therapy by focusing on the application of inorganic smart nanoparticles. Beyond exploring the general role of nanotechnology in medical applications, this review delves into groundbreaking strategies for glioblastoma treatment, showcasing the potential of smart nanoparticles through in vitro studies, in vivo investigations, and ongoing clinical trials.

Modeling Physical Forces Experienced by Cancer and Stromal Cells Within Different Organ-Specific Tumor Tissue

Mechanical force exerted on cancer cells by their microenvironment have been reported to drive cells toward invasive phenotypes by altering cells' motility, proliferation, and apoptosis. These mechanical forces include compressive, tensile, hydrostatic, and shear forces. The importance of forces is then hypothesized to be an alteration of cancer cells' and their microenvironment's biophysical properties as the indicator of a tumor's malignancy state. Our objective is to investigate and quantify the correlation between a tumor's malignancy state and forces experienced by the cancer cells and components of the microenvironment. In this study, we have developed a multicomponent, three-dimensional model of tumor tissue consisting of a cancer cell surrounded by fibroblasts and extracellular matrix (ECM). Our results on three different organs including breast, kidney, and pancreas show that: A) the stresses within tumor tissue are impacted by the organ specific ECM's biophysical properties, B) more invasive cancer cells experience higher stresses, C) in pancreas which has a softer ECM (Young modulus of 1.0 kPa) and stiffer cancer cells (Young modulus of 2.4 kPa and 1.7 kPa) than breast and kidney, cancer cells experienced significantly higher stresses, D) cancer cells in contact with ECM experienced higher stresses compared to cells surrounded by fibroblasts but the area of tumor stroma experiencing high stresses has a maximum length of 40 μm when the cancer cell is surrounded by fibroblasts and 12 μm for when the cancer cell is in vicinity of ECM. This study serves as an important first step in understanding of how the stresses experienced by cancer cells, fibroblasts, and ECM are associated with malignancy states of cancer cells in different organs. The quantification of forces exerted on cancer cells by different organ-specific ECM and at different stages of malignancy will help, first to develop theranostic strategies, second to predict accurately which tumors will become highly malignant, and third to establish accurate criteria controlling the progression of cancer cells malignancy. Furthermore, our in silico model of tumor tissue can yield critical, useful information for guiding ex vivo or in vitro experiments, narrowing down variables to be investigated, understanding what factors could be impacting cancer treatments or even biomarkers to be looking for.

An AI-based approach for modeling the synergy between radiotherapy and immunotherapy

Personalized, ultra-fractionated stereotactic adaptive radiotherapy (PULSAR) is designed to administer tumoricidal doses in a pulsed mode with extended intervals, spanning weeks or months. This approach leverages longer intervals to adapt the treatment plan based on tumor changes and enhance immune-modulated effects. In this investigation, we seek to elucidate the potential synergy between combined PULSAR and PD-L1 blockade immunotherapy using experimental data from a Lewis Lung Carcinoma (LLC) syngeneic murine cancer model. Employing a long short-term memory (LSTM) recurrent neural network (RNN) model, we simulated the treatment response by treating irradiation and anti-PD-L1 as external stimuli occurring in a temporal sequence. Our findings demonstrate that: (1) The model can simulate tumor growth by integrating various parameters such as timing and dose, and (2) The model provides mechanistic interpretations of a "causal relationship" in combined treatment, offering a completely novel perspective. The model can be utilized for in-silico modeling, facilitating exploration of innovative treatment combinations to optimize therapeutic outcomes. Advanced modeling techniques, coupled with additional efforts in biomarker identification, may deepen our understanding of the biological mechanisms underlying the combined treatment.

A Mathematical Model of Stroma-Supported Allometric Tumor Growth

Mounting empirical research suggests that the stroma, or interface between healthy and cancerous tissue, is a critical determinate of cancer invasion. At the same time, a cancer cell's location and potential to proliferate can influence its sensitivity to cancer treatments. In this paper, we use ordinary differential equations to develop spatially structured models for solid tumors wherein the growth of tumor components is coordinated. The model tumors feature two components, a proliferating peripheral growth region, which potentially includes a mix of cancerous and noncancerous stroma cells, and a solid tumor core. Mathematical and numerical analysis are used to investigate how coordinated expansion of the tumor growth region and core can influence overall growth dynamics in a variety of tumor types. Model assumptions, which are motivated by empirical and in silico solid tumor research, are evaluated through comparison to tumor volume data and existing models of tumor growth.

Simulating tumor volume dynamics in response to radiotherapy: Implications of model selection

From the beginning of the usage of radiotherapy (RT) for cancer treatment, mathematical modeling has been integral to understanding radiobiology and for designing treatment approaches and schedules. There has been extensive modeling of response to RT with the inclusion of various degrees of biological complexity. In this study, we compare three models of tumor volume dynamics: (1) exponential growth with RT directly reducing tumor volume, (2) logistic growth with direct tumor volume reduction, and (3) logistic growth with RT reducing the tumor carrying capacity with the objective of understanding the implications of model selection and informing the process of model calibration and parameterization. For all three models, we: examined the rates of change in tumor volume during and RT treatment course; performed parameter sensitivity and identifiability analyses; and investigated the impact of the parameter sensitivity on the tumor volume trajectories. In examining the tumor volume dynamics trends, we coined a new metric - the point of maximum reduction of tumor volume (MRV) - to quantify the magnitude and timing of the expected largest impact of RT during a treatment course. We found distinct timing differences in MRV, dependent on model selection. The parameter identifiability and sensitivity analyses revealed the interdependence of the different model parameters and that it is only possible to independently identify tumor growth and radiation response parameters if the underlying tumor growth rate is sufficiently large. Ultimately, the results of these analyses help us to better understand the implications of model selection while simultaneously generating falsifiable hypotheses about MRV timing that can be tested on longitudinal measurements of tumor volume from pre-clinical or clinical data with high acquisition frequency. Although, our study only compares three particular models, the results demonstrate that caution is necessary in selecting models of response to RT, given the artifacts imposed by each model.

Modeling tumor growth using fractal calculus: Insights into tumor dynamics

Important concepts like fractal calculus and fractal analysis, the sum of squared residuals, and Aikaike's information criterion must be thoroughly understood in order to correctly fit cancer-related data using the proposed models. The fractal growth models employed in this work are classified in three main categories: Sigmoidal growth models (Logistic, Gompertz, and Richards models), Power Law growth model, and Exponential growth models (Exponential and Exponential-Lineal models)". We fitted the data, computed the sum of squared residuals, and determined Aikaike's information criteria using Matlab and the web tool WebPlotDigitizer. In addition, the research investigates "double-size cancer" in the fractal temporal dimension with respect to various mathematical models.

Robust Control of Repeated Drug Administration with Variable Doses Based on Uncertain Mathematical Model

The aim of this paper was to design a repeated drug administration strategy to reach and maintain the requested drug concentration in the body. Conservative designs require an exact knowledge of pharmacokinetic parameters, which is considered an unrealistic demand. The problem is usually resolved using the trial-and-error open-loop approach; yet, this can be considered insufficient due to the parametric uncertainties as the dosing strategy may induce an undesired behavior of the drug concentrations. Therefore, the presented approach is rather based on the paradigms of system and control theory. An algorithm was designed that computes the required doses to be administered based on the blood samples. Since repeated drug dosing is essentially a discrete time process, the entire design considers the discrete time domain. We have also presented the idea of applying this methodology for the stabilization of an unstable model, for instance, a model of tumor growth. The simulation experiments demonstrated that all variants of the proposed control algorithm can reach and maintain the desired drug concentration robustly, i.e., despite the presence of parametric uncertainties, in a way that is superior to that of the traditional open-loop approach. It was shown that the closed-loop control with the integral controller and stabilizing state feedback is robust against large parametric uncertainties.

Mathematical model combined with microdosimetric kinetic model for tumor volume calculation in stereotactic body radiation therapy

We proposed a new mathematical model that combines an ordinary differential equation (ODE) and microdosimetric kinetic model (MKM) to predict the tumor-cell lethal effect of Stereotactic body radiation therapy (SBRT) applied to non-small cell lung cancer (NSCLC). The tumor growth volume was calculated by the ODE in the multi-component mathematical model (MCM) for the cell lines NSCLC A549 and NCI-H460 (H460). The prescription doses 48 Gy/4 fr and 54 Gy/3 fr were used in the SBRT, and the effect of the SBRT on tumor cells was evaluated by the MKM. We also evaluated the effects of (1) linear quadratic model (LQM) and the MKM, (2) varying the ratio of active and quiescent tumors for the total tumor volume, and (3) the length of the dose-delivery time per fractionated dose (tinter) on the initial tumor volume. We used the ratio of the tumor volume at 1 day after the end of irradiation to the tumor volume before irradiation to define the radiation effectiveness value (REV). The combination of MKM and MCM significantly reduced REV at 48 Gy/4 fr compared to the combination of LQM and MCM. The ratio of active tumors and the prolonging of tinter affected the decrease in the REV for A549 and H460 cells. We evaluated the tumor volume considering a large fractionated dose and the dose-delivery time by combining the MKM with a mathematical model of tumor growth using an ODE in lung SBRT for NSCLC A549 and H460 cells.

Investigating the Influence of Growth Arrest Mechanisms on Tumour Responses to Radiotherapy

Cancer is a heterogeneous disease and tumours of the same type can differ greatly at the genetic and phenotypic levels. Understanding how these differences impact sensitivity to treatment is an essential step towards patient-specific treatment design. In this paper, we investigate how two different mechanisms for growth control may affect tumour cell responses to fractionated radiotherapy (RT) by extending an existing ordinary differential equation model of tumour growth. In the absence of treatment, this model distinguishes between growth arrest due to nutrient insufficiency and competition for space and exhibits three growth regimes: nutrient limited, space limited (SL) and bistable (BS), where both mechanisms for growth arrest coexist. We study the effect of RT for tumours in each regime, finding that tumours in the SL regime typically respond best to RT, while tumours in the BS regime typically respond worst to RT. For tumours in each regime, we also identify the biological processes that may explain positive and negative treatment outcomes and the dosing regimen which maximises the reduction in tumour burden.

Model-based assessment of combination therapies - ranking of radiosensitizing agents in oncology

BACKGROUND

To increase the chances of finding efficacious anticancer drugs, improve development times and reduce costs, it is of interest to rank test compounds based on their potential for human use as early as possible in the drug development process. In this paper, we present a method for ranking radiosensitizers using preclinical data.

METHODS

We used data from three xenograft mice studies to calibrate a model that accounts for radiation treatment combined with radiosensitizers. A nonlinear mixed effects approach was utilized where between-subject variability and inter-study variability were considered. Using the calibrated model, we ranked three different Ataxia telangiectasia-mutated inhibitors in terms of anticancer activity. The ranking was based on the Tumor Static Exposure (TSE) concept and primarily illustrated through TSE-curves.

RESULTS

The model described data well and the predicted number of eradicated tumors was in good agreement with experimental data. The efficacy of the radiosensitizers was evaluated for the median individual and the 95% population percentile. Simulations predicted that a total dose of 220 Gy (5 radiation sessions a week for 6 weeks) was required for 95% of tumors to be eradicated when radiation was given alone. When radiation was combined with doses that achieved at least 8 [Formula: see text] of each radiosensitizer in mouse blood, it was predicted that the radiation dose could be decreased to 50, 65, and 100 Gy, respectively, while maintaining 95% eradication.

CONCLUSIONS

A simulation-based method for calculating TSE-curves was developed, which provides more accurate predictions of tumor eradication than earlier, analytically derived, TSE-curves. The tool we present can potentially be used for radiosensitizer selection before proceeding to subsequent phases of the drug discovery and development process.

A Mathematical Model for Predicting Patient Responses to Combined Radiotherapy with CTLA-4 Immune Checkpoint Inhibitors

The purpose of this study was to develop a cell-cell interaction model that could predict a tumor's response to radiotherapy (RT) combined with CTLA-4 immune checkpoint inhibition (ICI) in patients with hepatocellular carcinoma (HCC). The previously developed model was extended by adding a new term representing tremelimumab, an inhibitor of CTLA-4. The distribution of the new immune activation term was derived from the results of a clinical trial for tremelimumab monotherapy (NCT01008358). The proposed model successfully reproduced longitudinal tumor diameter changes in HCC patients treated with tremelimumab (complete response = 0%, partial response = 17.6%, stable disease = 58.8%, and progressive disease = 23.6%). For the non-irradiated tumor control group, adding ICI to RT increased the clinical benefit rate from 8% to 32%. The simulation predicts that it is beneficial to start CTLA-4 blockade before RT in terms of treatment sequences. We developed a mathematical model that can predict the response of patients to the combined CTLA-4 blockade with radiation therapy. We anticipate that the developed model will be helpful for designing clinical trials with the ultimate aim of maximizing the efficacy of ICI-RT combination therapy.

Multicomponent mathematical model for tumor volume calculation with setup error using single-isocenter stereotactic radiotherapy for multiple brain metastases

We evaluated the tumor residual volumes considering six degrees-of-freedom (6DoF) patient setup errors in stereotactic radiotherapy (SRT) with multicomponent mathematical model using single-isocenter irradiation for brain metastases. Simulated spherical gross tumor volumes (GTVs) with 1.0 (GTV 1), 2.0 (GTV 2), and 3.0 (GTV 3)-cm diameters were used. The distance between the GTV center and isocenter (d) was set at 0-10 cm. The GTV was simultaneously translated within 0-1.0 mm (T) and rotated within 0°-1.0° (R) in the three axis directions using affine transformation. We optimized the tumor growth model parameters using measurements of non-small cell lung cancer cell lines' (A549 and NCI-H460) growth. We calculated the GTV residual volume at the irradiation's end using the physical dose to the GTV when the GTV size, d, and 6DoF setup error varied. The d-values that satisfy tolerance values (10%, 35%, and 50%) of the GTV residual volume rate based on the pre-irradiation GTV volume were determined. The larger the tolerance value set for both cell lines, the longer the distance to satisfy the tolerance value. In GTV residual volume evaluations based on the multicomponent mathematical model on SRT with single-isocenter irradiation, the smaller the GTV size and the larger the distance and 6DoF setup error, the shorter the distance that satisfies the tolerance value might need to be.

Exploration of anticancer potential of Lantadenes from weed Lantana camara: Synthesis, in silico, in vitro and in vivo studies

Naturally occurring pentacyclic triterpenoids and their semisynthetic analogues have engrossed increasing attention for their anticancer potential and exhibiting promising role in discovery of new anticancer agents. Present study include the semi synthetic modifications of Lantadenes from the weed Lantana carama and their structures delineation by FT-IR, ¹H-NMR, ¹³C-NMR & mass spectroscopy. All the compounds were scrutinized for in vitro cytotoxicity, ligand receptor interaction and in vivo anticancer studies. Most of the novel analogues displayed potent antiproliferative activity against A375 & A431 cancer cell lines and found superior to parent Lantadenes. In particular, 3β-(4-Methoxybenzoyloxy)-22β-senecioyloxy-olean-12-en-28-oic acid was found to be most suitable compound, with IC₅₀ value of 3.027 μM aganist A375 cell line having least docking score (-69.40 kcal/mol). Promising anticancer potential of the lead was further indicated by significant reduction in tumor volume and burden in two stage carcinoma model. These findings suggests that the Lantadene derivatives may hold promising potential for the intervention of skin cancers.

Tumor heterogeneity: preclinical models, emerging technologies, and future applications

Heterogeneity describes the differences among cancer cells within and between tumors. It refers to cancer cells describing variations in morphology, transcriptional profiles, metabolism, and metastatic potential. More recently, the field has included the characterization of the tumor immune microenvironment and the depiction of the dynamics underlying the cellular interactions promoting the tumor ecosystem evolution. Heterogeneity has been found in most tumors representing one of the most challenging behaviors in cancer ecosystems. As one of the critical factors impairing the long-term efficacy of solid tumor therapy, heterogeneity leads to tumor resistance, more aggressive metastasizing, and recurrence. We review the role of the main models and the emerging single-cell and spatial genomic technologies in our understanding of tumor heterogeneity, its contribution to lethal cancer outcomes, and the physiological challenges to consider in designing cancer therapies. We highlight how tumor cells dynamically evolve because of the interactions within the tumor immune microenvironment and how to leverage this to unleash immune recognition through immunotherapy. A multidisciplinary approach grounded in novel bioinformatic and computational tools will allow reaching the integrated, multilayered knowledge of tumor heterogeneity required to implement personalized, more efficient therapies urgently required for cancer patients.

Patient-Derived Multiple Myeloma 3D Models for Personalized Medicine-Are We There Yet?

Despite the wide variety of existing therapies, multiple myeloma (MM) remains a disease with dismal prognosis. Choosing the right treatment for each patient remains one of the major challenges. A new approach being explored is the use of ex vivo models for personalized medicine. Two-dimensional culture or animal models often fail to predict clinical outcomes. Three-dimensional ex vivo models using patients' bone marrow (BM) cells may better reproduce the complexity and heterogeneity of the BM microenvironment. Here, we review the strengths and limitations of currently existing patient-derived ex vivo three-dimensional MM models. We analyze their biochemical and biophysical properties, molecular and cellular characteristics, as well as their potential for drug testing and identification of disease biomarkers. Furthermore, we discuss the remaining challenges and give some insight on how to achieve a more biomimetic and accurate MM BM model. Overall, there is still a need for standardized culture methods and refined readout techniques. Including both myeloma and other cells of the BM microenvironment in a simple and reproducible three-dimensional scaffold is the key to faithfully mapping and examining the relationship between these players in MM. This will allow a patient-personalized profile, providing a powerful tool for clinical and research applications.

Multiscale modeling of collective cell migration elucidates the mechanism underlying tumor-stromal interactions in different spatiotemporal scales

Metastasis is the pathogenic spread of cancer cells from a primary tumor to a secondary site which happens at the late stages of cancer. It is caused by a variety of biological, chemical, and physical processes, such as molecular interactions, intercellular communications, and tissue-level activities. Complex interactions of cancer cells with their microenvironment components such as cancer associated fibroblasts (CAFs) and extracellular matrix (ECM) cause them to adopt an invasive phenotype that promotes tumor growth and migration. This paper presents a multiscale model for integrating a wide range of time and space interactions at the molecular, cellular, and tissue levels in a three-dimensional domain. The modeling procedure starts with presenting nonlinear dynamics of cancer cells and CAFs using ordinary differential equations based on TGFβ, CXCL12, and LIF signaling pathways. Unknown kinetic parameters in these models are estimated using hybrid unscented Kalman filter and the models are validated using experimental data. Then, the principal role of CAFs on metastasis is revealed by spatial-temporal modeling of circulating signals throughout the TME. At this stage, the model has evolved into a coupled ODE-PDE system that is capable of determining cancer cells' status in one of the quiescent, proliferating or migratory conditions due to certain metastasis factors and ECM characteristics. At the tissue level, we consider a force-based framework to model the cancer cell proliferation and migration as the final step towards cancer cell metastasis. The ability of the multiscale model to depict cancer cells' behavior in different levels of modeling is confirmed by comparing its outputs with the results of RT PCR and wound scratch assay techniques. Performance evaluation of the model indicates that the proposed multiscale model can pave the way for improving the efficiency of therapeutic methods in metastasis prevention.

3D brain slice classification and feature extraction using Deformable Hierarchical Heuristic Model

Brain tumors are the most frequently occurring and severe type of cancer, with a life expectancy of only a few months in most advanced stages. As a result, planning the best course of therapy is critical to improve a patient's ability to fight cancer and their quality of life. Various imaging modalities, such as computed tomography (CT), magnetic resonance imaging (MRI) and ultrasound imaging, are commonly employed to assess a brain tumor. This research proposes a novel technique for extracting and classifying tumor features in 3D brain slice images. After input images are processed for noise removal, resizing, and smoothening, features of brain tumor are extracted using Volume of Interest (VOI). The extracted features are then classified using the Deformable Hierarchical Heuristic Model-Deep Deconvolutional Residual Network (DHHM-DDRN) based on surfaces, curves, and geometric patterns. Experimental results show that proposed approach obtained an accuracy of 95%, DSC of 83%, precision of 80%, recall of 85%, and F1 score of 55% for classifying brain cancer features.

Nanomedicine for Glioblastoma: Progress and Future Prospects

Glioblastoma is the most aggressive form of brain tumor, accounting for the highest mortality and morbidity rates. Current treatment for patients with glioblastoma includes maximal safe tumor resection followed by radiation therapy with concomitant temozolomide (TMZ) chemotherapy. The addition of TMZ to the conformal radiation therapy has improved the median survival time only from 12 months to 16 months in patients with glioblastoma. Despite these aggressive treatment strategies, patients' prognosis remains poor. This therapeutic failure is primarily attributed to the blood-brain barrier (BBB) that restricts the transport of TMZ from reaching the tumor site. In recent years, nanomedicine has gained considerable attention among researchers and shown promising developments in clinical applications, including the diagnosis, prognosis, and treatment of glioblastoma tumors. This review sheds light on the morphological and physiological complexity of the BBB. It also explains the development of nanomedicine strategies to enhance the permeability of drug molecules across the BBB.

A reinforcement learning approach for finding optimal policy of adaptive radiation therapy considering uncertain tumor biological response

Recent studies have shown that a tumor's biological response to radiation varies over time and has a dynamic nature. Dynamic biological features of tumor cells underscore the importance of using fractionation and adapting the treatment plan to tumor volume changes in radiation therapy treatment. Adaptive radiation therapy (ART) is an iterative process to adjust the dose of radiation in response to potential changes during the treatment. One of the key challenges in ART is how to determine the optimal timing of adaptations corresponding to tumor response to radiation. This paper aims to develop an automated treatment planning framework incorporating the biological uncertainties to find the optimal adaptation points to achieve a more effective treatment plan. First, a dynamic tumor-response model is proposed to predict weekly tumor volume regression during the period of radiation therapy treatment based on biological factors. Second, a Reinforcement Learning (RL) framework is developed to find the optimal adaptation points for ART considering the uncertainty in biological factors with the goal of achieving maximum final tumor control while minimizing or maintaining the toxicity level of the organs at risk (OARs) per the decision-maker's preference. Third, a beamlet intensity optimization model is solved using the predicted tumor volume at each adaptation point. The performance of the proposed RT treatment planning framework is tested using a clinical non-small cell lung cancer (NSCLC) case. The results are compared with the conventional fractionation schedule (i.e., equal dose fractionation) as a reference plan. The results show that the proposed approach performed well in achieving a robust optimal ART treatment plan under high uncertainty in the biological parameters. The ART plan outperformed the reference plan by increasing the mean biological effective dose (BED) value of the tumor by 2.01%, while maintaining the OAR BED within +0.5% and reducing the variability, in terms of the interquartile range (IQR) of tumor BED, by 25%.

Exposure-response modeling improves selection of radiation and radiosensitizer combinations

A central question in drug discovery is how to select drug candidates from a large number of available compounds. This analysis presents a model-based approach for comparing and ranking combinations of radiation and radiosensitizers. The approach is quantitative and based on the previously-derived Tumor Static Exposure (TSE) concept. Combinations of radiation and radiosensitizers are evaluated based on their ability to induce tumor regression relative to toxicity and other potential costs. The approach is presented in the form of a case study where the objective is to find the most promising candidate out of three radiosensitizing agents. Data from a xenograft study is described using a nonlinear mixed-effects modeling approach and a previously-published tumor model for radiation and radiosensitizing agents. First, the most promising candidate is chosen under the assumption that all compounds are equally toxic. The impact of toxicity in compound selection is then illustrated by assuming that one compound is more toxic than the others, leading to a different choice of candidate.

A Voxel Model to Decipher the Role of Molecular Communication in the Growth of Glioblastoma Multiforme

Glioblastoma Multiforme (GBM), the most malignant human tumour, can be defined by the evolution of growing bio-nanomachine networks within an interplay between self-renewal (Grow) and invasion (Go) potential of mutually exclusive phenotypes of transmitter and receiver cells. Herein, we present a mathematical model for the growth of GBM tumour driven by molecule-mediated inter-cellular communication between two populations of evolutionary bio-nanomachines representing the Glioma Stem Cells (GSCs) and Glioma Cells (GCs). The contribution of each subpopulation to tumour growth is quantified by a voxel model representing the end to end inter-cellular communication models for GSCs and progressively evolving invasiveness levels of glioma cells within a network of diverse cell configurations. Mutual information, information propagation speed and the impact of cell numbers and phenotypes on the communication output and GBM growth are studied by using analysis from information theory. The numerical simulations show that the progression of GBM is directly related to higher mutual information and higher input information flow of molecules between the GSCs and GCs, resulting in an increased tumour growth rate. These fundamental findings contribute to deciphering the mechanisms of tumour growth and are expected to provide new knowledge towards the development of future bio-nanomachine-based therapeutic approaches for GBM.

WAM to SeeSaw model for cancer therapy - overcoming LQM difficulties

PURPOSE

The assessment of biological effects caused by radiation exposure has been currently carried out with the linear-quadratic (LQ) model as an extension of the linear non-threshold (LNT) model. In this study, we suggest a new mathematical model named as SeaSaw (SS) model, which describes proliferation and cell death effects by taking account of Bergonie-Tribondeau's law in terms of a differential equation in time. We show how this model overcomes the long-standing difficulties of the LQ model.

MATERIALS AND METHODS

We construct the SS model as an extended Wack-A-Mole (WAM) model by using a differential equation with respect to time in order to express the dynamics of the proliferation effect. A large number of accumulated data of such parameters as α and β in the LQ based models provide us with valuable pieces of information on the corresponding parameter b 1 and the maximum volume V m of the SS model. The dose rate b 1 and the notion of active cell can explain the present data without introduction of β, which is obtained by comparing the SS model with not only the cancer therapy data but also with in vitro experimental data. Numerical calculations are presented to grasp the global features of the SS model.

RESULTS

The SS model predicts the time dependence of the number of active- and inactive-cells. The SS model clarifies how the effect of radiation depends on the cancer stage at the starting time in the treatment. Further, the time dependence of the tumor volume is calculated by changing individual dose strength, which results in the change of the irradiation duration for the same effect. We can consider continuous irradiation in the SS model with interesting outcome on the time dependence of the tumor volume for various dose rates. Especially by choosing the value of the dose rate to be balanced with the total growth rate, the tumor volume is kept constant.

CONCLUSIONS

The SS model gives a simple equation to study the situation of clinical radiation therapy and risk estimation of radiation. The radiation parameter extracted from the cancer therapy is close to the value obtained from animal experiment in vitro and in vivo. We expect the SS model leads us to a unified description of radiation therapy and protection and provides a great development in cancer-therapy clinical-planning.

Tumor ablation due to inhomogeneous anisotropic diffusion in generic three-dimensional topologies

In recent decades computer-aided technologies have become prevalent in medicine, however, cancer drugs are often only tested on in vitro cell lines from biopsies. We derive a full three-dimensional model of inhomogeneous -anisotropic diffusion in a tumor region coupled to a binary population model, which simulates in vivo scenarios faster than traditional cell-line tests. The diffusion tensors are acquired using diffusion tensor magnetic resonance imaging from a patient diagnosed with glioblastoma multiform. Then we numerically simulate the full model with finite element methods and produce drug concentration heat maps, apoptosis hotspots, and dose-response curves. Finally, predictions are made about optimal injection locations and volumes, which are presented in a form that can be employed by doctors and oncologists.

Radial basis function-generated finite difference scheme for simulating the brain cancer growth model under radiotherapy in various types of computational domains

BACKGROUND AND OBJECTIVES

We extend the original mathematical model, i.e., Swanson's reaction-diffusion equation to the surfaces with no boundary, and we find a new numerical method based on a meshless approach for solving numerically Swanson's reaction-diffusion model in the square and on the sphere.

METHODS

To solve numerically the Swanson's reaction-diffusion model and its extension version, a collocation meshless technique, namely radial basis function-generated finite difference (RBF-FD) scheme is employed for approximating the spatial variables in the square domain and on the sphere, respectively. Also, to approximate the time variable of the studied models, a first-order semi-implicit backward Euler scheme is used. The resulting fully discrete scheme is a linear system of algebraic equations per time step that is solved via the biconjugate gradient stabilized (BiCGSTAB) iterative algorithm with a zero-fill incomplete lower-upper (ILU) preconditioner.

RESULTS

The numerical simulations show the growth of untreated and treated brain tumors with radiotherapy using estimated and clinical data (given from magnetic resonance imaging (MRI) scans of patients). Moreover, the results reported here can be used for improving the treatment strategies of the invasive brain tumor.

CONCLUSIONS

Using the developed numerical scheme in this paper, we can simulate the behavior of the invasive form of brain tumor response to radiotherapy. Also, we can see the effects of radiation response on the brain tumor cell concentration of individual patients. The proposed meshless technique, which is applied for solving numerically the studied model, does not depend on any background mesh or triangulation for approximation in comparison with mesh-dependent methods. Moreover, we apply this technique to the sphere via any set of distributed points easily.

Parameter estimation and treatment optimization in a stochastic model for immunotherapy of cancer

Adoptive Cell Transfer therapy of cancer is currently in full development and mathematical modeling is playing a critical role in this area. We study a stochastic model developed by Baar et al. (2015) for modeling immunotherapy against melanoma skin cancer. First, we estimate the parameters of the deterministic limit of the model based on biological data of tumor growth in mice. A Nonlinear Mixed Effects Model is estimated by the Stochastic Approximation Expectation Maximization algorithm. With the estimated parameters, we return to the stochastic model and calculate the probability of complete T cells exhaustion. We show that for some relevant parameter values, an early relapse is due to stochastic fluctuations (complete T cells exhaustion) with a non negligible probability. Then, focusing on the relapse related to the T cell exhaustion, we propose to optimize the treatment plan (treatment doses and restimulation times) by minimizing the T cell exhaustion probability in the parameter estimation ranges.

Optimization of irradiation interval for fractionated stereotactic radiosurgery by a cellular automata model with reoxygenation effects

The current study aims to determine the optimal irradiation interval of fractionated stereotactic radiosurgery (SRS) by using an improved cellular automata (CA) model. The tumor growth process was simulated by considering the amount of oxygen and the density of blood vessels, which supplied oxygen and nutrient required for cell growth. Cancer cells died by the mitotic death process due to radiation, which was quantified by the LQ-model, or the apoptosis due to the lack of nutrients. The radiation caused increased permeation of plasma protein through the blood vessel or the breakdown of the vasculature. Consequently, these changes lead to a change in radiation sensitivity of cancer cells and tumor growth rate after irradiation. The optimal model parameters were determined with experimental data of the rat tumor volume. The tumor control probability (TCP) was defined as the ratio of the number of histories in which all cancer cells died after the irradiation to the total number of the histories per simulation. The optimal irradiation interval was defined as the irradiation interval that TCP was the maximum. For one fractionation treatment, the ratio of hypoxic cells to the total number of cancer cells kept decreasing until day 16th after irradiation; whereas the number of surviving cancer cells begun increasing immediately after irradiation. This intricate relationship between the hypoxia (or reoxygenation) and the number of cancer cells lead to an optimal irradiation interval for the second irradiation. The optimal irradiation interval for two-fraction SRS was six days. The optimum intervals for the first-second irradiations and the second-third irradiations were five and two days, respectively, for three fraction SRS. For 4 and 5-fraction treatments, the optimum first-interval was five days, which was similar to three fraction treatment. The remaining intervals should be one day. We showed that the improved CA model could be used to optimize the irradiation interval by explicitly including the reoxygenation after irradiation in the model.

Modeling long-term tumor growth and kill after combinations of radiation and radiosensitizing agents

PURPOSE

Radiation therapy, whether given alone or in combination with chemical agents, is one of the cornerstones of oncology. We develop a quantitative model that describes tumor growth during and after treatment with radiation and radiosensitizing agents. The model also describes long-term treatment effects including tumor regrowth and eradication.

METHODS

We challenge the model with data from a xenograft study using a clinically relevant administration schedule and use a mixed-effects approach for model-fitting. We use the calibrated model to predict exposure combinations that result in tumor eradication using Tumor Static Exposure (TSE).

RESULTS

The model is able to adequately describe data from all treatment groups, with the parameter estimates taking biologically reasonable values. Using TSE, we predict the total radiation dose necessary for tumor eradication to be 110 Gy, which is reduced to 80 or 30 Gy with co-administration of 25 or 100 mg kg^-1 of a radiosensitizer. TSE is also explored via a heat map of different growth and shrinkage rates. Finally, we discuss the translational potential of the model and TSE concept to humans.

CONCLUSIONS

The new model is capable of describing different tumor dynamics including tumor eradication and tumor regrowth with different rates, and can be calibrated using data from standard xenograft experiments. TSE and related concepts can be used to predict tumor shrinkage and eradication, and have the potential to guide new experiments and support translations from animals to humans.

Simulation analysis for tumor radiotherapy based on three-component mathematical models

OBJECTIVE

To setup a three-component tumor growth mathematical model and discuss its basic application in tumor fractional radiotherapy with computer simulation.

METHOD

First, our three-component tumor growth model extended from the classical Gompertz tumor model was formulated and applied to a fractional radiotherapy with a series of proper parameters. With the computer simulation of our model, the impact of some parameters such as fractional dose, amount of quiescent tumor cells, and α/β value to the effect of radiotherapy was also analyzed, respectively.

RESULTS

With several optimal technologies, the model could run stably and output a series of convergent results. The simulation results showed that the fractional radiotherapy dose could impact the effect of radiotherapy significantly, while the amount of quiescent tumor cells and α/β value did that to a certain extent.

CONCLUSIONS

Supported with some proper parameters, our model can simulate and analyze the tumor radiotherapy program as well as give some theoretical instruction to radiotherapy personalized optimization.

A structural methodology for modeling immune-tumor interactions including pro- and anti-tumor factors for clinical applications

The immune system turns out to have both stimulatory and inhibitory factors influencing on tumor growth. In recent years, the pro-tumor role of immunity factors such as regulatory T cells and TGF-β cytokines has specially been considered in mathematical modeling of tumor-immune interactions. This paper presents a novel structural methodology for reviewing these models and classifies them into five subgroups on the basis of immune factors included. By using our experimental data due to immunotherapy experimentation in mice, these five modeling groups are evaluated and scored. The results show that a model with a small number of variables and coefficients performs efficiently in predicting the tumor-immune system interactions. Though immunology theorems suggest to employ a larger number of variables and coefficients, more complicated models are here shown to be inefficient due to redundant parallel pathways. So, these models are trapped in local minima and restricted in prediction capability. This paper investigates the mathematical models that were previously developed and proposes variables and pathways that are essential for modeling tumor-immune. Using these variables and pathways, a minimal structure for modeling tumor-immune interactions is proposed for future studies.

Advances in Glioblastoma Multiforme Treatment: New Models for Nanoparticle Therapy

The most lethal form of brain cancer, glioblastoma multiforme, is characterized by rapid growth and invasion facilitated by cell migration and degradation of the extracellular matrix. Despite technological advances in surgery and radio-chemotherapy, glioblastoma remains largely resistant to treatment. New approaches to study glioblastoma and to design optimized therapies are greatly needed. One such approach harnesses computational modeling to support the design and delivery of glioblastoma treatment. In this paper, we critically summarize current glioblastoma therapy, with a focus on emerging nanomedicine and therapies that capitalize on cell-specific signaling in glioblastoma. We follow this summary by discussing computational modeling approaches focused on optimizing these emerging nanotherapeutics for brain cancer. We conclude by illustrating how mathematical analysis can be used to compare the delivery of a high potential anticancer molecule, delphinidin, in both free and nanoparticle loaded forms across the blood-brain barrier for glioblastoma.

Radiation and PD-(L)1 treatment combinations: immune response and dose optimization via a predictive systems model

BACKGROUND

Numerous oncology combination therapies involving modulators of the cancer immune cycle are being developed, yet quantitative simulation models predictive of outcome are lacking. We here present a model-based analysis of tumor size dynamics and immune markers, which integrates experimental data from multiple studies and provides a validated simulation framework predictive of biomarkers and anti-tumor response rates, for untested dosing sequences and schedules of combined radiation (RT) and anti PD-(L)1 therapies.

METHODS

A quantitative systems pharmacology model, which includes key elements of the cancer immunity cycle and the tumor microenvironment, tumor growth, as well as dose-exposure-target modulation features, was developed to reproduce experimental data of CT26 tumor size dynamics upon administration of RT and/or a pharmacological IO treatment such as an anti-PD-L1 agent. Variability in individual tumor size dynamics was taken into account using a mixed-effects model at the level of tumor-infiltrating T cell influx.

RESULTS

The model allowed for a detailed quantitative understanding of the synergistic kinetic effects underlying immune cell interactions as linked to tumor size modulation, under these treatments. The model showed that the ability of T cells to infiltrate tumor tissue is a primary determinant of variability in individual tumor size dynamics and tumor response. The model was further used as an in silico evaluation tool to quantitatively predict, prospectively, untested treatment combination schedules and sequences. We demonstrate that anti-PD-L1 administration prior to, or concurrently with RT reveal further synergistic effects, which, according to the model, may materialize due to more favorable dynamics between RT-induced immuno-modulation and reduced immuno-suppression of T cells through anti-PD-L1.

CONCLUSIONS

This study provides quantitative mechanistic explanations of the links between RT and anti-tumor immune responses, and describes how optimized combinations and schedules of immunomodulation and radiation may tip the immune balance in favor of the host, sufficiently to lead to tumor shrinkage or rejection.

Model-Based Evaluation of Radiation and Radiosensitizing Agents in Oncology

Radiotherapy is one of the major therapy forms in oncology, and combination therapies involving radiation and chemical compounds can yield highly effective tumor eradication. In this paper, we develop a tumor growth inhibition model for combination therapy with radiation and radiosensitizing agents. Moreover, we extend previous analyses of drug combinations by introducing the tumor static exposure (TSE) curve. The TSE curve for radiation and radiosensitizer visualizes exposure combinations sufficient for tumor regression. The model and TSE analysis are then tested on xenograft data. The calibrated model indicates that the highest dose of combination therapy increases the time until tumor regrowth 10-fold. The TSE curve shows that with an average radiosensitizer concentration of 1.0 μg/mL the radiation dose can be decreased from 2.2 Gy to 0.7 Gy. Finally, we successfully predict the effect of a clinically relevant treatment schedule, which contributes to validating both the model and the TSE concept.

Untangling the model muddle: Empirical tumour growth in Tasmanian devil facial tumour disease

A pressing and unresolved topic in cancer research is how tumours grow in the absence of treatment. Despite advances in cancer biology, therapeutic and diagnostic technologies, there is limited knowledge regarding the fundamental growth and developmental patterns in solid tumours. In this ten year study, we estimated growth curves in Tasmanian devil facial tumours, a clonal transmissible cancer, in males and females with two different karyotypes (diploid, tetraploid) and facial locations (mucosal, dermal), using established differential equation models and model selection. Logistic growth was the most parsimonious model for diploid, tetraploid and mucosal tumours, with less model certainty for dermal tumours. Estimates of daily proportional tumour growth rate per day (95% Bayesian CIs) varied with ploidy and location [diploid 0.016 (0.014–0.020), tetraploid 0.026 (0.020–0.033), mucosal 0.013 (0.011–0.015), dermal 0.020 (0.016–0.024)]. Final tumour size (cm³) also varied, particularly the upper credible interval owing to host mortality as tumours approached maximum volume [diploid 364 (136–2,475), tetraploid 172 (100–305), dermal 226 (134–471)]. To our knowledge, these are the first empirical estimates of tumour growth in the absence of treatment in a wild population. Through this animal-cancer system our findings may enhance understanding of how tumour properties interact with growth dynamics in other types of cancer.