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In this work we address the role of the microstructural properties of a vascularised poroelastic material, characterised by the coupling between a poroelastic matrix and a viscous fluid vessels network, on its overall response in terms of pressures, velocities and stress maps. We embrace the recently developed model [1] as a theoretical starting point and present the results obtained by solving the full interplay between the microscale, represented by the intervessels’ distance, and the macroscale, representing the size of the overall tissue. We encode the influence of the vessels’ density and the poroelastic matrix compressibility in the poroe-lastic coefficients of the model, which are obtained by solving appropriate periodic cell problem at the microscale. The double poroelastic model [1] is then solved at the macroscale in the context of vascular tumours, for different values of vesssels’ walls permeability. The results clearly indicate that improving the compressibility of the matrix and decreasing the vessels’ density enhances the transvascular pressure difference and hence transport of fluid and drug within a tumour mass after a transient time. Our results suggest to combine vessel and interstitial normalization in tumors to allow for better drug delivery into the lesions.

In clinical practice, a plethora of medical examinations are conducted to assess the state of a patient's pathology producing a variety of clinical data. However, investigation of these data faces two major challenges. Firstly, we lack the knowledge of the mechanisms involved in regulating these data variables, and secondly, data collection is sparse in time since it relies on patient's clinical presentation. The former limits the predictive accuracy of clinical outcomes for any mechanistic model. The latter restrains any machine learning algorithm to accurately infer the corresponding disease dynamics.Here, we propose a novel method, based on the Bayesian coupling of mathematical modeling and machine learning, aiming at improving individualized predictions by addressing the aforementioned challenges.We evaluate the proposed method on a synthetic dataset for brain tumor growth and analyze its performance in predicting two relevant clinical outputs. The method results in improved predictions in almost all simulated patients, especially for those with a late clinical presentation (95% patients show improvements compared to standard mathematical modeling). In addition, we test the methodology in two additional settings dealing with real patient cohorts. In both cases, namely cancer growth in chronic lymphocytic leukemia and ovarian cancer, predictions show excellent agreement with reported clinical outcomes (around 60% reduction of mean squared error).We show that the combination of machine learning and mathematical modeling approaches can lead to accurate predictions of clinical outputs in the context of data sparsity and limited knowledge of disease mechanisms.

BackgroundSARS-CoV-2 has induced a worldwide pandemic and subsequent non-pharmaceutical interventions (NPIs) to control the spread of the virus. As in many countries, the SARS-CoV-2 pandemic in Germany has led to a consecutive roll-out of different NPIs. As these NPIs have (largely unknown) adverse effects, targeting them precisely and monitoring their effectiveness are essential. We developed a compartmental infection dynamics model with specific features of SARS-CoV-2 that allows daily estimation of a time-varying reproduction number and published this information openly since the beginning of April 2020. Here, we present the transmission dynamics in Germany over time to understand the effect of NPIs and allow adaptive forecasts of the epidemic progression.MethodsWe used a data-driven estimation of the evolution of the reproduction number for viral spreading in Germany as well as in all its federal states using our model. Using parameter estimates from literature and, alternatively, with parameters derived from a fit to the initial phase of COVID-19 spread in different regions of Italy, the model was optimized to fit data from the Robert Koch Institute.ResultsThe time-varying reproduction number (Rt) in Germany decreased to Rtuntil August 2020. Implications of state-specificRton other states and on national level are characterized. Retrospective evaluation of the model shows excellent agreement with the data and usage of inpatient facilities well within the healthcare limit. While short-term predictions may work for a few weeks, long-term projections are complicated by unpredictable structural changes.ConclusionsThe estimated fraction of immunized population by August 2020 warns of a renewed outbreak upon release of measures. A low detection rate prolongs the delay reaching a low case incidence number upon release, showing the importance of an effective testing-quarantine strategy. We show that real-time monitoring of transmission dynamics is important to evaluate the extent of the outbreak, short-term projections for the burden on the healthcare system, and their response to policy changes.

International audience; While many cellular mechanisms leading to chemotherapeutic resistance have been identified, there is an increasing realization that tumor-stroma interactions also play an important role. In particular, mechanical alterations are inherent to solid cancer progression and profoundly impact cell physiology. Here, we explore the influence of compressive stress on the efficacy of chemotherapeutics in pancreatic cancer spheroids. We find that increased compressive stress leads to decreased drug efficacy. Theoretical modeling and experiments suggest that mechanical stress decreases cell proliferation which in turn reduces the efficacy of chemotherapeutics that target proliferating cells. Our work highlights a mechanical form of drug resistance and suggests new strategies for therapy.

In clinical practice, a plethora of medical examinations are conducted to assess the state of a patient’s pathology producing a variety of clinical data. However, exploiting these data faces the following challenges: (C1) we lack the knowledge of the mechanisms involved in regulating these data variables, and (C2) data collection is sparse in time since it relies on patient’s clinical presentation. (C1) implies that only a small subset of the relevant variables can be modeled by virtue of mathematical modeling. This limitation allows models to be effective in analyzing the qualitative dynamics of the system, but limits their predictive accuracy. On the other hand, statistical learning methods are well-suited for quantitative reproduction of data, but they do not provide mechanistic understanding of the investigated problem. Moreover, due to (C2) any algorithm is challenged in learning the corresponding disease dynamics. Herein, we propose a novel method, based on the Bayesian coupling of mathematical modeling and machine learning (BaM3), aiming at improving individualized predictions by addressing the aforementioned challenges. As a proof of concept, we evaluate the proposed method on a synthetic dataset for brain tumor growth and analyze its performance in predicting two major clinical outputs, namely tumor burden and infiltration. The BaM3method results in improved predictions in almost all simulated patients, especially for those with a late clinical presentation. In addition, we test the proposed methodology in two settings dealing with real patient cohorts. In both cases, namely cancer growth in chronic lymphocytic leukemia and ovarian cancer, BaM3predictions show excellent agreement with reported clinical data.

Summary Emerging evidence demonstrates that radiotherapy induces immunogenic death on tumor cells that emit immunostimulating signals resulting in tumor-specific immune responses. However, the impact of tumor features and microenvironmental factors on the efficacy of radiation-induced immunity remains to be elucidated. Herein, we use a calibrated model of tumor-effector cell interactions to investigate the potential benefits and immunological consequences of radiotherapy. Simulations analysis suggests that radiotherapy success depends on the functional tumor vascularity extent and reveals that the pre-treatment tumor size is not a consistent determinant of treatment outcomes. The one-size-fits-all approach of conventionally fractionated radiotherapy is predicted to result in some overtreated patients. In addition, model simulations also suggest that an arbitrary increase in treatment duration does not necessarily result in better tumor control. This study highlights the potential benefits of tumor-immune ecosystem profiling during treatment planning to better harness the immunogenic potential of radiotherapy., Graphical Abstract, Highlights • Radiotherapy success depends on radiation-induced tumor-specific immune responses • Pre-treatment tumor size is not a consistent determinant of radiotherapy outcomes • Increase in treatment duration does not necessarily result in better tumor control • Tumor vascularity impacts antitumor efficacy of radiation-induced immune responses, Bioinformatics; Mathematical Biosciences; Cancer

We present a review of porosity and diffusion in biological tissues from different perspectives. We first introduce the topic by illustrating experimental evidence related to diffusion in porous media and review a number of state of the art experimental techniques. We then proceed by providing a revisited derivation of the equations of poroelasticity from the microstructure (via asymptotic homogenization), which is especially aimed at giving a first insight on the topic to both students and scientists who are not familiar with the subject. Results based on this kind of models have only recently been presented in the literature and could possibly complement the experiments by getting a more thorough understanding on the complex interplay between porosity and diffusion. We investigate further the matter by exploring the role of diffusion in driving growth and stresses in the context of linear elastic modeling for tumors and cellular automata. We finally conclude the chapter by (a) discussing diffusion in nonlinear, “active” materials, i.e., those which are possibly characterized by growth and remodeling, and (b) offering an overview on cutting edge research problems on diffusion for this class of complex materials.

Osteochondral defects are focal areas of damage involving articular cartilage and sub-chondral bone. Tissue engineering scaffolds are used to improve the organism regeneration ability for this kind of injury, serving as biocompatible structures for cell viability and differentiation. Since biomechanical cues such as substrate stiffness, loading conditions and fluid permeation are fundamental for successful tissue repair, understanding how these features vary in the scaffold is of primary importance. Here we present a mathematical model based on porous media mechanics for the analysis of a tissue engineering scaffold. We consider a three-layered scaffold mimicking a complete osteochondral tissue and vary the mechanical properties of the intermediate layer over a physiological range. Our results show that the interstitial fluid pressure and the vertical component of the solid effective stress depend significantly on the stiffness and permeability of the intermediate layer under mechanical loading. By properly tuning these material properties, regimes of slow or fast temporal variations of mechanical stress can be obtained in the scaffold layer of interest.

Physical phenomena in biological systems constitute an intricate framework, which develops on multiple scales and usually entails several interconnected feedbacks. Computational modeling provides the physical scientists with a set of tools for the deconvolution of such complexities. The field of application of this approach is extraordinarily large, including models for cardiovascular diseases, bone injuries, locomotion, and recently tumor progression. In this work, we present different multiphase models based upon porous media theory. We focus on two major applications, namely the growth of a solid tumor and the case of diabetic foot. The tumor model accounts for cancer cell proliferation, cell necrosis induced by the lack of nutrients, and migration of cells through an extracellular matrix. It allows also to consider the effects of cortical tensions between distinct cell species, and tumor angiogenesis. In the second part of this article, we show results for a biphasic model developed for the diabetic foot. In this case, the computational framework can predict the occurrence of high interstitial pressures and the possible appearance of ulcers. Such models, adequately extended and fed with patient-specific data, could be used in the future to stimulate novel therapeutic strategies.

Emerging evidence demonstrates that radiotherapy induces immunogenic cell death on tumor cells that emits immunostimulating signals, resulting in tumor-specific local and systemic immune responses. However, the impact of tumor features and microenvironmental factors on the efficacy of radiation-induced immunity remains to be elucidated. Herein, we propose a calibrated model of tumor-effector cell interactions to investigate the potential benefits and immunological consequences of radiotherapy. Model simulations suggest that radiotherapy success depends on the extent of functional tumor vascularity, which in turn influences the efficacy of radiation-induced immune responses. Simulation analysis revealed that tumor size at time of treatment is not a consistent determinant of radiotherapy outcomes. While small radioresistant tumors could not be eradicated by radiotherapy due to an insufficient radiation-induced antitumor immunity, poor treatment outcomes of large tumors could be attributable to an insufficient burden reduction by radiotherapy. Notably, tumors of intermediate size were more responsive due to an adequate balance between radiotherapy-induced immunostimulation and tumor shrinkage. The one-size-fits-all approach of conventionally fractionated radiotherapy was predicted to result in some overtreated patients receiving doses in excess. Model analysis also suggest that an arbitrary increase in treatment duration does not necessarily imply enhanced tumor control, because radiation-induced antitumor immunity could be mitigated after a certain number of treatment fractions. Depending on tumor features, weekend breaks during conventional radiotherapy could induce robust tumor-specific immune responses outperforming fractionation schemes daily delivered without weekend interruptions. Modeling findings highlight the potential benefits of tumor-immune ecosystem profiling during treatment planning to better harness the immunogenic potential radiotherapy and enhance tumor control.

Drug resistance is one of the leading causes of poor therapy outcomes in cancer. As several chemotherapeutics are designed to target rapidly dividing cells, the presence of a low-proliferating cell population contributes significantly to treatment resistance. Interestingly, recent studies have shown that compressive stresses acting on tumor spheroids are able to hinder cell proliferation, through a mechanism of growth inhibition. However, studies analyzing the influence of mechanical compression on therapeutic treatment efficacy have still to be performed. In this work, we start from an existing mathematical model for avascular tumors, including the description of mechanical compression. We introduce governing equations for transport and uptake of a chemotherapeutic agent, acting on cell proliferation. Then, model equations are adapted for tumor spheroids and the combined effect of compressive stresses and drug action is investigated. Interestingly, we find that the variation in tumor spheroid volume, due to the presence of a drug targeting cell proliferation, considerably depends on the compressive stress level of the cell aggregate. Our results suggest that mechanical compression of tumors may compromise the efficacy of chemotherapeutic agents. In particular, a drug dose that is effective in reducing tumor volume for stress-free conditions may not perform equally well in a mechanically compressed environment.

Nanomedicine is a recent promising setting for the advancement of current medical therapies, in particular for cancer. Nanoparticle-mediated therapies are aimed to tackle extremely complex phenomena, involving different biochemical, mechanical and biophysical factors. Computational models can contribute to medical research by helping the understanding of biological mechanisms and by providing quantitative analyses. In this work, we report on computational models that address four main issues related to the use of nanoparticles in anti-cancer therapies, namely the delivery of nanoparticles, their uptake by cells, the release of drugs from nano-platforms and nanoparticle-based therapeutics. In silico approaches constitute a valuable tool to aid clinical studies, to guide the rational design of new nanoparticle formulations and to identify the optimal strategies for existing treatments.

We investigate the impact of microvascular geometry on the transport of drugs in solid tumors, focusing on the diffusion and consumption phenomena. We embrace recent advances in the asymptotic homogenization literature starting from a double Darcy-double advection-diffusion-reaction system of partial differential equations that is obtained exploiting the sharp length separation between the intercapillary distance and the average tumor size. The geometric information on the microvascular network is encoded into effective hydraulic conductivities and diffusivities, which are numerically computed by solving periodic cell problems on appropriate microscale representative cells. The coefficients are then injected into the macroscale equations, and these are solved for an isolated, vascularized spherical tumor. We consider the effect of vascular tortuosity on the transport of anticancer molecules, focusing on Vinblastine and Doxorubicin dynamics, which are considered as a tracer and as a highly interacting molecule, respectively. The computational model is able to quantify the treatment performance through the analysis of the interstitial drug concentration and the quantity of drug metabolized in the tumor. Our results show that both drug advection and diffusion are dramatically impaired by increasing geometrical complexity of the microvasculature, leading to nonoptimal absorption and delivery of therapeutic agents. However, this effect apparently has a minor role whenever the dynamics are mostly driven by metabolic reactions in the tumor interstitium, eg, for highly interacting molecules. In the latter case, anticancer therapies that aim at regularizing the microvasculature might not play a major role, and different strategies are to be developed.

Tumor spheroids constitute an effective in vitro tool to investigate the avascular stage of tumor growth. These three-dimensional cell aggregates reproduce the nutrient and proliferation gradients found in the early stages of cancer and can be grown with a strict control of their environmental conditions. In the last years, new experimental techniques have been developed to determine the effect of mechanical stress on the growth of tumor spheroids. These studies report a reduction in cell proliferation as a function of increasingly applied stress on the surface of the spheroids. This work presents a specialization for tumor spheroid growth of a previous more general multiphase model. The equations of the model are derived in the framework of porous media theory, and constitutive relations for the mass transfer terms and the stress are formulated on the basis of experimental observations. A set of experiments is performed, investigating the growth of U-87MG spheroids both freely growing in the culture medium and subjected to an external mechanical pressure induced by a Dextran solution. The growth curves of the model are compared to the experimental data, with good agreement for both the experimental settings. A new mathematical law regulating the inhibitory effect of mechanical compression on cancer cell proliferation is presented at the end of the paper. This new law is validated against experimental data and provides better results compared to other expressions in the literature.

We investigate the impact of microvascular geometry on the transport of drugs in solid tumors, focusing on the diffusion and consumption phenomena. We embrace recent advances in the asymptotic homogenization literature starting from a double Darcy—double advection-diffusion-reaction system of partial differential equations that is obtained exploiting the sharp length separation between the intercapillary distance and the average tumor size. The geometric information on the microvascular network is encoded into effective hydraulic conductivities and diffusivities, which are numerically computed by solving periodic cell problems on appropriate microscale representative cells. The coefficients are then injected into the macroscale equations, and these are solved for an isolated, vascularized spherical tumor. We consider the effect of vascular tortuosity on the transport of anticancer molecules, focusing on Vinblastine and Doxorubicin dynamics, which are considered as a tracer and as a highly interacting molecule, respectively. The computational model is able to quantify the treatment performance through the analysis of the interstitial drug concentration and the quantity of drug metabolized in the tumor. Our results show that both drug advection and diffusion are dramatically impaired by increasing geometrical complexity of the microvasculature, leading to nonoptimal absorption and delivery of therapeutic agents. However, this effect apparently has a minor role whenever the dynamics are mostly driven by metabolic reactions in the tumor interstitium, eg, for highly interacting molecules. In the latter case, anticancer therapies that aim at regularizing the microvasculature might not play a major role, and different strategies are to be developed.