The role of the microvascular network structure on diffusion and consumption of anticancer drugs

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

Mathematical modeling of avascular tumor growth

Cancer is an extremely complex disease, both in terms of its causes and consequences to the body. Cancer cells acquire the ability to proliferate without control, invade the surrounding tissues and eventually form metastases. It is becoming increasingly clear that a description of tumors that is uniquely based on molecular biology is not enough to understand thoroughly this illness. Quantitative sciences, such as physics, mathematics and engineering, can provide a valuable contribution to this field, suggesting new ways to examine the growth of the tumor and to investigate its interaction with the neighboring environment. In this dissertation, we deal with mathematical models for avascular tumor growth. We evaluate the effects of physiological parameters on tumor development, with a particular focus on the mechanical response of the tissue. We start from tumor spheroids, an effective three-dimensional cell culture, to investigate the first stages of tumor growth. These 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. The equations of the model are derived in the framework of porous media theory, and constitutive relations for the mass transfer terms and the mechanical stress are formulated on the basis of experimental observations. The growth curves of the model are compared to the experimental data, with good agreement for the different experimental settings. A new mathematical law regulating the inhibitory effect of mechanical compression on cancer cell proliferation is also presented. Then, we perform a parametric analysis to identify the key parameters that drive the system response. We conclude this part by introducing governing equations for transport and uptake of a chemotherapeutic agent, designed to target cell proliferation. In particular, we investigate the combined effect of compressive stresses and drug action. Interestingly, we find that variation in tumor spheroid volume, due to the presence of a drug targeting cell proliferation, depends considerably on the compressive stress level of the cell aggregate. In the second part of the dissertation, we study a constitutive law describing the mechanical response of biological tissues. We introduce this relation in a biphasic model for tumor growth based on the mechanics of fluid-saturated porous media. The internal reorganization of the tissue in response to mechanical and chemical stimuli is described by enforcing the multiplicative decomposition of the deformation gradient tensor associated with the solid phase motion. In this way, we are able to distinguish the contributions of growth, rearrangement of cellular bonds, and elastic distortion, occurring during tumor evolution. Results are presented for a benchmark case and for three biological configurations. We analyze the dependence of tumor development on the mechanical environment, with particular focus on cell reorganization and its role in stress relaxation. Finally, we conclude with a summary of the results and with a discussion of possible future extensions

Mathematical modeling of avascular tumor growth

Cancer is an extremely complex disease, both in terms of its causes and consequences to the body. Cancer cells acquire the ability to proliferate without control, invade the surrounding tissues and eventually form metastases. It is becoming increasingly clear that a description of tumors that is uniquely based on molecular biology is not enough to understand thoroughly this illness. Quantitative sciences, such as physics, mathematics and engineering, can provide a valuable contribution to this field, suggesting new ways to examine the growth of the tumor and to investigate its interaction with the neighboring environment. In this dissertation, we deal with mathematical models for avascular tumor growth. We evaluate the effects of physiological parameters on tumor development, with a particular focus on the mechanical response of the tissue. We start from tumor spheroids, an effective three-dimensional cell culture, to investigate the first stages of tumor growth. These 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. The equations of the model are derived in the framework of porous media theory, and constitutive relations for the mass transfer terms and the mechanical stress are formulated on the basis of experimental observations. The growth curves of the model are compared to the experimental data, with good agreement for the different experimental settings. A new mathematical law regulating the inhibitory effect of mechanical compression on cancer cell proliferation is also presented. Then, we perform a parametric analysis to identify the key parameters that drive the system response. We conclude this part by introducing governing equations for transport and uptake of a chemotherapeutic agent, designed to target cell proliferation. In particular, we investigate the combined effect of compressive stresses and drug action. Interestingly, we find that variation in tumor spheroid volume, due to the presence of a drug targeting cell proliferation, depends considerably on the compressive stress level of the cell aggregate. In the second part of the dissertation, we study a constitutive law describing the mechanical response of biological tissues. We introduce this relation in a biphasic model for tumor growth based on the mechanics of fluid-saturated porous media. The internal reorganization of the tissue in response to mechanical and chemical stimuli is described by enforcing the multiplicative decomposition of the deformation gradient tensor associated with the solid phase motion. In this way, we are able to distinguish the contributions of growth, rearrangement of cellular bonds, and elastic distortion, occurring during tumor evolution. Results are presented for a benchmark case and for three biological configurations. We analyze the dependence of tumor development on the mechanical environment, with particular focus on cell reorganization and its role in stress relaxation. Finally, we conclude with a summary of the results and with a discussion of possible future extensions.Il cancro è una malattia estremamente complessa, sia per quanto riguarda le sue cause che per i suoi effetti sul corpo. Le cellule del cancro acquisiscono la capacità di proliferare senza controllo, invadere i tessuti vicini e infine sviluppare metastasi. Negli ultimi anni sta diventando sempre più chiaro che una descrizione dei tumori basata unicamente sulla biologia molecolare non può essere sufficiente per comprendere interamente la malattia. A questo riguardo, scienze quantitative come la Fisica, la Matematica e l'Ingegneria, possono fornire un valido contributo, suggerendo nuovi modi per esaminare la crescita di un tumore e studiare la sua interazione con l'ambiente circostante. In questa tesi ci occupiamo di modelli matematici per la crescita avascolare dei tumori. Valutiamo gli effetti dei parametri fisiologici sullo sviluppo del tumore, con un'attenzione particolare alla risposta meccanica del tessuto. Partiamo dagli sferoidi tumorali, una cultura cellulare tridimensionale, per studiare le prime fasi della crescita tumorale. Questi aggregati cellulari sono in grado di riprodurre i gradienti di nutriente e proliferazione che si ritrovano nei tumori avascolari. Inoltre, possono essere fatti crescere con un controllo molto severo delle condizioni ambientali. Le equazioni del modello sono derivate nell'ambito della teoria dei mezzi porosi dove, per chiudere il problema, definiamo opportune relazioni costitutive al fine di descrivere gli scambi di massa tra i diversi componenti del sistema e la risposta meccanica di quest'ultimo. Tali leggi sono formulate sulla base di osservazioni sperimentali. Le curve di crescita del modello sono quindi confrontate con dati sperimentali, con un buon accordo per le diverse condizioni. Presentiamo, inoltre, una nuova espressione matematica per descrivere gli effetti di inibizione della crescita da parte della compressione meccanica sulle cellule cancerose. In seguito, eseguiamo uno studio parametrico per identificare i parametri chiave che guidano la risposta del sistema. Concludiamo infine questa parte introducendo le equazioni di governo per il trasporto e il consumo di un agente chemioterapico, studiato per essere efficace sulle cellule proliferanti. In particolare, consideriamo l'effetto combinato di stress meccanici compressivi e di tale farmaco sullo sviluppo del tumore. A questo proposito, i nostri risultati indicano che una variazione di volume degli sferoidi tumorali, a causa dell'azione del farmaco, dipende sensibilmente dal livello di tensione a cui è sottoposto l'aggregato cellulare. Nella seconda parte di questa trattazione, studiamo una legge costitutiva per descrivere la risposta meccanica di tessuti biologici. Introduciamo questa relazione in un modello bifasico per la crescita tumorale basato sulla meccanica di mezzi porosi saturi. La riorganizzazione interna del tessuto in risposta a stimoli meccanici e chimici è descritta attraverso la decomposizione moltiplicativa del gradiente di deformazione associato con il moto della fase solida del sistema. In questo modo, risulta possibile distinguere i contributi di crescita, riarrangiamento dei legami cellulari e distorsione elastica che prendono luogo durante l'evoluzione del tumore. In seguito, presentiamo risultati per un caso di test e per tre configurazioni di interesse biologico. In particolare, analizziamo la dipendenza dello sviluppo del tumore dal suo ambiente meccanico, con un'attenzione particolare sulla riorganizzazione dei legami tra le cellule e il suo ruolo sul rilassamento degli stress meccanici. Infine, concludiamo la discussione con un breve riassunto dei risultati ottenuti e un resoconto dei possibili sviluppi

Investigating the Physical Effects in Bacterial Therapies for Avascular Tumors.

Tumor-targeting bacteria elicit anticancer effects by infiltrating hypoxic regions, releasing toxic agents and inducing immune responses. Although current research has largely focused on the influence of chemical and immunological aspects on the mechanisms of bacterial therapy, the impact of physical effects is still elusive. Here, we propose a mathematical model for the anti-tumor activity of bacteria in avascular tumors that takes into account the relevant chemo-mechanical effects. We consider a time-dependent administration of bacteria and analyze the impact of bacterial chemotaxis and killing rate. We show that active bacterial migration toward tumor hypoxic regions provides optimal infiltration and that high killing rates combined with high chemotactic values provide the smallest tumor volumes at the end of the treatment.We highlight the emergence of steady states in which a small population of bacteria is able to constrain tumor growth. Finally, we show that bacteria treatment works best in the case of tumors with high cellular proliferation and low oxygen consumption

The impact of vascular volume fraction and compressibility of the interstitial matrix on vascularised poroelastic tissues

No abstract available

Evaluating the influence of mechanical stress on anticancer treatments through a multiphase porous media model

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

Improving personalized tumor growth predictions using a Bayesian combination of mechanistic modeling and machine learning

Background!#!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.!##!Methods!#!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.!##!Results!#!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).!##!Conclusions!#!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

An avascular tumor growth model based on porous media mechanics and evolving natural configurations

Mechanical factors play a major role in tumor development and response to treatment. This is more evident for tumors grown in vivo, where cancer cells interact with the different components in the host tissue. Mathematical models are able to characterize the mechanical response of the tumor and can provide a deeper understanding of these interactions. In this work, we present a model for tumor growth based on porous media mechanics. We consider a biphasic system, where tumor cells and the extracellular matrix constitute a solid scaffold, filled with interstitial fluid. A nutrient is dispersed into the fluid phase, supporting the growth of the tumor. The internal reorganization of the tissue in response to external mechanical and chemical stimuli is described by enforcing the multiplicative decomposition of the deformation gradient tensor. In this way, we are able to distinguish the contributions of growth, rearrangement of cellular bonds, and elastic distortion, which occur during tumor evolution. Results are shown for three cases of biological interest, that is growth of a tumor spheroid in (i) culture medium, (ii) host tissue, and (iii) three- dimensional physiological configuration. We report the tumor growth curves for the three cases mentioned above, supplemented with the evolution of quantities of interest, such as the mechanical stresses and interstitial fluid pressures. We analyze the dependence of the tumor development on the mechanical environment, with a particular focus on cell reorganization and its role in stress relaxation. We also address the computational issues of our mathematical model, and discuss the flexibility of the employed numerical implementation. Finally, we speak of further developments, with the scope of providing a deeper understanding of cancer biophysics

On the Immunological Consequences of Conventionally Fractionated Radiotherapy.

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