arXiv subjects

Víctor M. Pérez-García

Publications and source records attributed to Víctor M. Pérez-García.

At least 19 recordsLinked to original sources

arXiv2025

First explore, then settle: a theoretical analysis of evolvability as a driver of adaptation

Evolvability is defined as the ability of a population to generate heritable variation to facilitate its adaptation to new environments or selection pressures. In this article, we consider evolvability as a phenotypic trait subject to evolution and discuss its implications in the adaptation of populations of asexual individuals. We explore the evolutionary dynamics of an actively proliferating population of individuals, subject to changes in their proliferative potential and their evolvability, through mathematical simulations of a stochastic individual-based model and its deterministic continuum counterpart. We find robust adaptive trajectories that rely on individuals with high evolvability rapidly exploring the phenotypic landscape and reaching the proliferative potential with the highest fitness. The strength of selection on the proliferative potential, and the cost associated with evolvability, can alter these trajectories such that, if both are sufficiently constraining, highly evolvable populations can become extinct in our individual-based model simulations. We explore the impact of this interaction at various scales, discussing its effects in undisturbed environments and also in disrupted contexts, such as cancer.

q-bio.PE↗

arXiv2025

Synergistic interplay of morphology and metabolic activity rule response to CAR-T cells in B-cell lymphomas

Cellular immunotherapies are one of the mainstream cancer treatments unveiling the power of the patient's immune system to fight tumors. CAR T-cell therapy, based on genetically engineered T cells, has demonstrated significant potential in treating hematological malignancies, including B-cell lymphomas. This treatment has complex longitudinal dynamics due to the interplay of different T-cell phenotypes (e.g. effector and memory), the expansion of the drug and the cytotoxic effect on both normal and cancerous B-cells, the exhaustion of the immune cells, the tumor immunosupressive environments, and more. Thus, the outcome of the therapy is not yet well understood leading to a variety of responses ranging from sustained complete responses, different types of partial responses, or no response at all. We developed a mechanistic model for the interaction between CAR T- and cancerous B-cells, accounting for the role of the tumor morphology and metabolic status. The simulations showed that lesions with irregular shapes and high proliferation could contribute to long term progression by potentially increasing their immunosuppressive capabilities impairing CAR T-cell efficacy. We analyzed 18F-FDG PET/CT imaging data from 63 relapsed/refractory diffuse large B-cell lymphoma receiving CAR T-cells, quantifying radiomic features including tumor sphericity and lesion aggressiveness through standardized uptake values (SUV). Statistical analyses revealed significant correlations between these metrics and progression-free survival (PFS), emphasizing that individual lesions with complex morphology and elevated metabolism play a critical role in shaping long-term treatment outcomes. We demonstrated the potential of using data-driven mathematical models in finding molecular-imaging based biomarkers to identify lymphoma patients treated with CAR T-cell therapy having higher risk of disease progression.

q-bio.PE↗

arXiv2025

Optimizing chemoradiotherapy for malignant gliomas: a validated mathematical approach

Malignant gliomas (MGs), particularly glioblastoma, are among the most aggressive brain tumors, with limited treatment options and a poor prognosis. Maximal safe resection and the so-called Stupp protocol are the standard first-line therapies. Despite combining radiotherapy and chemotherapy in an intensive manner, it provides limited survival benefits over radiation therapy alone, underscoring the need for innovative therapeutic strategies. Emerging evidence suggests that alternative dosing schedules, such as less aggressive regimens with extended intervals between consecutive treatment applications, may improve outcomes, enhancing survival, delaying the emergence of resistance, and minimizing side effects. In this study, we develop, calibrate, and validate in animal models a novel ordinary differential equation-based mathematical model, using in vivo data to describe MG dynamics under combined chemoradiotherapy. The proposed model incorporates key biological processes, including cancer cell dormancy, phenotypic switching, drug resistance through persister cells, and treatment-induced effects. Through in silico trials, we identified optimized combination treatment protocols that may outperform the standard Stupp protocol. Finally, we computationally extrapolated the results obtained from the in vivo animal model to humans, showing up to a four-fold increase in median survival with protracted administration protocols in silico. Although further experimental and clinical validation is required, our framework provides a computational foundation to optimize and personalize treatment strategies for MG and potentially other cancers with similar biological mechanisms.

q-bio.PE↗

arXiv2025

Geometric immunosuppression in CAR-T cell treatment: Insights from mathematical modeling

Chimeric antigen receptor T (CAR-T) cell therapy has emerged as a promising treatment for hematological malignancies, offering a targeted approach to cancer treatment. Understanding the complexities of CAR-T cell therapy within solid tumors poses challenges due to the intricate interactions within the tumor microenvironment. Mathematical modeling may serve as a valuable tool to unravel the dynamics of CAR-T cell therapy and improve its effectiveness in solid tumors. This study aimed to investigate the impact of spatial aspects in CAR-T therapy of solid tumors, utilizing cellular automata for modeling purposes. Our main objective was to deepen our understanding of treatment effects by analyzing scenarios with different spatial distributions and varying the initial quantities of tumor and CAR-T cells. Tumor geometry significantly influenced treatment efficacy in-silico, with notable differences observed between tumors with block-like arrangements and those with sparse cell distributions, leading to the concept of immune suppression due to geometrical effects. This research delves into the intricate relationship between spatial dynamics and the effectiveness of CAR-T therapy in solid tumors, highlighting the relevance of tumor geometry in the outcome of cellular immunotherapy treatments. Our results provide a basis for improving the efficacy of CAR-T cell treatments by combining them with other ones reducing the density of compact tumor areas and thus opening access ways for tumor killing T-cells.

q-bio.TO↗

arXiv2024

Understanding the role of B-cells in CAR T-cell therapy in leukemia through a mathematical model

Chimeric Antigen Receptor T (CAR-T) cell therapy has been proven to be successful against different leukaemias and lymphomas. This paper makes an analytical and numerical study of a mathematical model describing the competition of CAR-T, leukaemias tumor and B cells. Considering its significance in sustaining anti-CD19 CAR T-cell stimulation, we integrate a B-cell source term into the model. Through stability and bifurcation analyses, we reveal the potential for tumor eradication contingent on the continuous influx of B-cells, uncovering a transcritical bifurcation at a critical B-cell input. Additionally, we identify an almost heteroclinic cycle between equilibrium points, providing a theoretical basis for understanding disease relapse. Analyzing the oscillatory behavior of the system, we approximate the time-dependent dynamics of CAR T-cells and leukemic cells, shedding light on the impact of initial tumor burden on therapeutic outcomes. In conclusion, our study provides insights into CAR T-cell therapy dynamics for acute lymphoblastic leukemias, offering a theoretical foundation for clinical observations and suggesting avenues for future immunotherapy modeling research.

math.DS↗

arXiv2024

A mathematical model for fibrous dysplasia: The role of the flow of mutant cells

Fibrous dysplasia (FD) is a mosaic non-inheritable genetic disorder of the skeleton in which normal bone is replaced by structurally unsound fibro-osseous tissue. There is no curative treatment for FD, partly because its pathophysiology is not yet fully known. We present a simple mathematical model of the disease incorporating its basic known biology, to gain insight on the dynamics of the involved bone-cell populations, and shed light on its pathophysiology. Our mathematical models account for the dynamic evolution over time of several interacting populations of bone cells averaged over a volume of bone of sufficient size in order to obtain consistent results. We develop an analytical study of the model and study its basic properties. The existence and stability of steady states are studied, an analysis of sensitivity on the model parameters is done, and different numerical simulations provide findings in agreement with the analytical results. We discuss the model dynamics match with known facts on the disease, and how some open questions could be addressed using the model.

q-bio.TO↗

arXiv2021

Universal scaling laws rule explosive growth inhuman cancers

Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a measure of the size of the system. Here we describe the discovery of universal superlinear metabolic scaling laws in human cancers. This dependence underpins increasing tumour aggressiveness, due to evolutionary dynamics, which leads to an explosive growth as the disease progresses. We validated this dynamic using longitudinal volumetric data of different histologies from large cohorts of cancer patients. To explain our observations we put forward increasingly complex biologically-inspired mathematical models that captured the key processes governing tumor growth. Our models predicted that the emergence of superlinear allometric scaling laws is an inherently three-dimensional phenomenon. Moreover, the scaling laws thereby identified allowed us to define a set of metabolic metrics with prognostic value, thus providing added clinical utility to the base findings.

q-bio.TO↗

arXiv2020

Mathematical models of Leukaemia and its treatment: A review

Leukaemia accounts for around 3% of all cancer types diagnosed in adults, and is the most common type of cancer in children of paediatric age. There is increasing interest in the use of mathematical models in oncology to draw inferences and make predictions, providing a complementary picture to experimental biomedical models. In this paper we recapitulate the state of the art of mathematical modelling of leukaemia growth dynamics, in time and response to treatment. We intend to describe the mathematical methodologies, the biological aspects taken into account in the modelling, and the conclusions of each study. This review is intended to provide researchers in the field with solid background material, in order to achieve further breakthroughs in the promising field of mathematical biology.

q-bio.TO↗

arXiv2020

Dynamical properties of feedback signalling in B lymphopoiesis: A mathematical modelling approach

Haematopoiesis is the process of generation of blood cells. Lymphopoiesis generates lymphocytes, the cells in charge of the adaptive immune response. Disruptions of this process are associated with diseases like leukaemia, which is especially incident in children. The characteristics of self-regulation of this process make them suitable for a mathematical study. In this paper we develop mathematical models of lymphopoiesis using currently available data. We do this by drawing inspiration from existing structured models of cell lineage development and integrating them with paediatric bone marrow data, with special focus on regulatory mechanisms. A formal analysis of the models is carried out, giving steady states and their stability conditions. We use this analysis to obtain biologically relevant regions of the parameter space and to understand the dynamical behaviour of B-cell renovation. Finally, we use numerical simulations to obtain further insight into the influence of proliferation and maturation rates on the reconstitution of the cells in the B line. We conclude that a model including feedback regulation of cell proliferation represents a biologically plausible depiction for B-cell reconstitution in bone marrow. Research into haematological disorders could benefit from a precise dynamical description of B lymphopoiesis.

q-bio.TO↗

arXiv2020

CAR T cells for T-cell leukemias: Insights from mathematical models

Immunotherapy has the potential to change the way all cancer types are treated and cured. Cancer immunotherapies use elements of the patient immune system to attack tumor cells. One of the most successful types of immunotherapy is CAR-T cells. This treatment works by extracting patient's T-cells and adding to them an antigen receptor allowing tumor cells to be recognized and targeted. These new cells are called CAR-T cells and are re-infused back into the patient after expansion in-vitro. This approach has been successfully used to treat B-cell malignancies (B-cell leukemias and lymphomas). However, its application to the treatment of T-cell leukemias faces several problems. One of these is fratricide, since the CAR-T cells target both tumor and other CAR-T cells. This leads to nonlinear dynamical phenomena amenable to mathematical modeling. In this paper we construct a mathematical model describing the competition of CAR-T, tumor and normal T-cells and studied some basic properties of the model and its practical implications. Specifically, we found that the model reproduced the observed difficulties for in-vitro expansion of the therapeutic cells found in the laboratory. The mathematical model predicted that CAR-T cell expansion in the patient would be possible due to the initial presence of a large number of targets. We also show that, in the context of our mathematical approach, CAR-T cells could control tumor growth but not eradicate the disease.

q-bio.TO↗

arXiv2017

A mathematical model of low grade gliomas treated with temozolomide and its therapeutical implications

Low grade gliomas (LGGs) are infiltrative and incurable primary brain tumours with typically slow evolution. These tumours usually occur in young and otherwise healthy patients, bringing controversies in treatment planning since aggressive treatment may lead to undesirable side effects. Thus, for management decisions it would be valuable to obtain early estimates of LGG growth potential. Here we propose a simple mathematical model of LGG growth and its response to chemotherapy which allows the growth of LGGs to be described in real patients. The model predicts, and our clinical data confirms, that the speed of response to chemotherapy is related to tumour aggressiveness. Moreover, we provide a formula for the time to radiological progression, which can be possibly used as a measure of tumour aggressiveness. Finally, we suggest that the response to a few chemotherapy cycles upon diagnosis might be used to predict tumour growth and to guide therapeutical actions on the basis of the findings.

q-bio.QM↗

arXiv2014

Combined therapies of antithrombotics and antioxidants delay in silico brain tumor progression

Glioblastoma multiforme, the most frequent type of primary brain tumor, is a rapidly evolving and spatially heterogeneous high-grade astrocytoma that presents areas of necrosis, hypercellularity and microvascular hyperplasia. The aberrant vasculature leads to hypoxic areas and results in an increase of the oxidative stress selecting for more invasive tumor cell phenotypes. In our study we assay in silico different therapeutic approaches which combine antithrombotics, antioxidants and standard radiotherapy. To do so, we have developed a biocomputational model of glioblastoma multiforme that incorporates the spatio-temporal interplay among two glioma cell phenotypes corresponding to oxygenated and hypoxic cells, a necrotic core and the local vasculature whose response evolves with tumor progression. Our numerical simulations predict that suitable combinations of antithrombotics and antioxidants may diminish, in a synergetic way, oxidative stress and the subsequent hypoxic response. This novel therapeutical strategy, with potentially low or no toxicity, might reduce tumor invasion and further sensitize glioblastoma multiforme to conventional radiotherapy or other cytotoxic agents, hopefully increasing median patient overall survival time.

q-bio.QM↗

arXiv2013

Nonlinear quantum piston for the controlled generation of vortex rings and soliton trains

We propose a simple way to generate nonlinear excitations in a controllable way by managing interactions in Bose-Einstein condensates. Under the action of a quantum analogue of a classical piston the condensed atoms are pushed through the trap generating vortex rings in a fully three- dimensional condensates or soliton trains in quasi-one dimensional scenarios. The vortex rings form due to transverse instability of the shock wave train enhanced and supported by the energy transfer between waves. We elucidate in which sense the self-interactions within the atom cloud define the properties of generated vortex rings and soliton trains. Based on the quantum piston scheme we study the behavior of two component Bose-Einstein condensates and analyze how the presence of an additional superfluid influences the generation of vortex rings or solitons in the other component and vice versa. Finally, we show the dynamical emergence of skyrmions within two component systems in the immiscible regime.

cond-mat.quant-gas↗

arXiv2012

Hypoxic Cell Waves around Necrotic Cores in Glioblastoma: A Biomathematical Model and its Therapeutic Implications

Glioblastoma is a rapidly evolving high-grade astrocytoma that is distinguished pathologically from lower grade gliomas by the presence of necrosis and microvascular hiperplasia. Necrotic areas are typically surrounded by hypercellular regions known as "pseudopalisades" originated by local tumor vessel occlusions that induce collective cellular migration events. This leads to the formation of waves of tumor cells actively migrating away from central hypoxia. We present a mathematical model that incorporates the interplay among two tumor cell phenotypes, a necrotic core and the oxygen distribution. Our simulations reveal the formation of a traveling wave of tumor cells that reproduces the observed histologic patterns of pseudopalisades. Additional simulations of the model equations show that preventing the collapse of tumor microvessels leads to slower glioma invasion, a fact that might be exploited for therapeutic purposes.

q-bio.QM↗

arXiv2011

Coherent atomic soliton molecules for matter-wave switching

We discuss the dynamics of interacting dark-bright two-dimensional vector solitons in multicomponent immiscible bulk Bose-Einstein condensates. We describe matter-wave molecules without a scalar counterpart that can be seen as bound states of vector objects. We also analyze the possibility of using these structures as building blocks for the design of matter-wave switchers.

nlin.PS↗

arXiv2011

Bright Solitary Waves in Malignant Gliomas

We put forward a nonlinear wave model describing the fundamental physio-pathologic features of an aggressive type of brain tumors: glioblastomas. Our model accounts for the invasion of normal tissue by a proliferating and propagating rim of active glioma cancer cells in the tumor boundary and the subsequent formation of a necrotic core. By resorting to numerical simulations, phase space analysis and exact solutions, we prove that bright solitary tumor waves develop in such systems.

nlin.PS↗

arXiv2010

Stable multidimensional soliton stripes in two-component Bose-Einstein condensates

We discuss how to construct stable multidimensional extensions of one-dimensional dark solitons, the so-called soliton stripes, in two-species Bose-Einstein condensates in the immiscible regime. We show how using a second component to fill the core a dark soliton stripe leads to reduced instabilities while propagating in homogeneous media. We also discuss how in the presence of a trap arbitrarily long-lived dark soliton stripes can be constructed by increasing the filling of the dark stripe core. Numerical evidences of the robustness of the dark soliton stripes in collision scenarios are also provided.

cond-mat.quant-gas↗

arXiv2010

Coherent Atomic Soliton Molecules

We discuss the dynamics of interacting atomic bright solitons and dark bubbles in bulk immiscible Bose-Einstein condensates. Coherent matter-wave clusters can be constructed using dark-bright pairs with appropriate phases. In two dimensions we describe novel types of matter-wave molecules without a scalar counterpart that can be seen as bound states of vector objects.

nlin.PS↗