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Juan Belmonte-Beitia

Publications and source records attributed to Juan Belmonte-Beitia.

At least 19 recordsLinked to original sources
arXiv2025

A mathematical model of CAR-T cell therapy in combination with chemotherapy for malignant gliomas

We study the dynamics and interactions between combined chemotherapy and chimeric antigen receptor (CAR-T) cells therapy and malignant gliomas (MG). MG is one of the most common primary brain tumor, with high resistance to therapy and unfavorable prognosis. Here, we develop a mathematical model that describes the application of chemo- and CAR-T cell therapies and the dynamics of sensitive and resistant populations of tumor cells. This model is a five-dimensional dynamical system with impulsive inputs corresponding to clinical administration of chemo- and immunotherapy. We provide a proof of non-negativeness of solutions of the proposed model for non-negative initial data. We demonstrate that if we apply both therapies only once, the trajectories will be attracted to an invariant surface that corresponds to the tumor carrying capacity. On the other hand, if we apply both treatments constantly, we find regions of the parameter where the tumor is eradicated. Moreover, we study applications of different combinations of the above treatments in order to find an optimal combination at the population level. To this aim, we generate a population of $10^{4}$ virtual patients with the model parameters uniformly distributed in the medically relevant ranges and perform \emph{in silico} trials with different combinations of treatments. We obtain optimal protocols for several different relations of tumor growth rates between sensitive and drug resistant cells. We demonstrate that the tumor growth rate, efficacy of chemotherapy, and tumor immunosuppression are the parameters that mostly impact survival time in \emph{in silico} trials. We believe that our results provide new theoretical insights to guide the design of clinical trials for MG therapies.

math.DS↗
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↗
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↗
arXiv2024

Modelling the role of flux density and coating on nanoparticle internalization by tumor cells under centrifugation

Nanoparticle (NP)-based applications are becoming increasingly important in the biomedical field. However, understanding the interactions of NPs with biofluids and cells is a major issue in order to develop novel approaches aimed at boosting their internalization and, therefore, their translation into the clinic. To this end, we put forward a transport mathematical model to describe the spatio-temporal dynamics of iron oxide NPs and their interaction with cells under moderate centrifugation. Our numerical simulations allowed us to quantify the relevance of the flux density as one of the unavoidable key features driving NPs interaction with the media as well as for cell internalization processes. These findings will help to increase the efficiency of cell labelling for biomedical applications.

q-bio.QM↗
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

CAR T cell therapy in B-cell acute lymphoblastic leukaemia: Insights from mathematical models

Immunotherapies use components of the patient immune system to selectively target cancer cells. The use of CAR T cells to treat B-cell malignancies --leukaemias and lymphomas-- is one of the most successful examples, with many patients experiencing long-lasting complete responses to this therapy. This treatment works by extracting the patient's T cells and adding them the CAR group, which enables them to recognize and target cells carrying the antigen CD19+, that is expressed in these haematological tumors. Here we put forward a mathematical model describing the time response of leukaemias to the injection of CAR T-cells. The model accounts for mature and progenitor B-cells, tumor cells, CAR T cells and side effects by incorporating the main biological processes involved. The model explains the early post-injection dynamics of the different compartments and the fact that the number of CAR T cells injected does not critically affect the treatment outcome. An explicit formula is found that provides the maximum CAR T cell expansion in-vivo and the severity of side effects. Our mathematical model captures other known features of the response to this immunotherapy. It also predicts that CD19+ tumor relapses could be the result of the competition between tumor and CAR T cells analogous to predator-prey dynamics. We discuss this fact on the light of available evidences and the possibility of controlling relapses by early re-challenging of the tumor with stored CAR T cells.

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

Delay effects in the response of low grade gliomas to radiotherapy: A mathematical model and its therapeutical implications

Low grade gliomas (LGGs) are a group of primary brain tumors usually encountered in young patient populations. These tumors represent a difficult challenge because many patients survive a decade or more and may be at a higher risk for treatment-related complications. Specifically, radiation therapy is known to have a relevant effect on survival but in many cases it can be deferred to avoid side effects while maintaining its beneficial effect. However, a subset of low-grade gliomas manifests more aggressive clinical behavior and requires earlier intervention. Moreover, the effectiveness of radiotherapy depends on the tumor characteristics. Recently Pallud et al., [Neuro-oncology, 14(4):1-10, 2012], studied patients with LGGs treated with radiation therapy as a first line therapy. and found the counterintuitive result that tumors with a fast response to the therapy had a worse prognosis than those responding late. In this paper we construct a mathematical model describing the basic facts of glioma progression and response to radiotherapy. The model provides also an explanation to the observations of Pallud et al. Using the model we propose radiation fractionation schemes that might be therapeutically useful by helping to evaluate the tumor malignancy while at the same time reducing the toxicity associated to the treatment.

q-bio.QM↗
arXiv2014

Effective Particle Methods for Fisher-Kolmogorov Equations: Theory and Applications to Brain Tumor Dynamics

Extended systems governed by partial differential equations can, under suitable conditions, be approximated by means of sets of ordinary differential equations for global quantities capturing the essential features of the systems dynamics. Here we obtain a small number of effective equations describing the dynamics of single-front and localized solutions of Fisher-Kolmogorov type equations. These solutions are parametrized by means of a minimal set of time-dependent quantities for which ordinary differential equations ruling their dynamics are found. A comparison of the finite dimensional equations and the dynamics of the full partial differential equation is made showing a very good quantitative agreement with the dynamics of the partial differential equation. We also discuss some implications of our findings for the understanding of the growth progression of certain types of primary brain tumors and discuss possible extensions of our results to related equations arising in different modelling scenarios.

q-bio.QM↗
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↗
arXiv2009

Bifurcation of gap solitons in periodic potentials with a sign-varying nonlinearity coefficient

We address the Gross--Pitaevskii (GP) equation with a periodic linear potential and a periodic sign-varying nonlinearity coefficient. Contrary to the claims in the previous works of Abdullaev {\em et al.} [PRE {\bf 77}, 016604 (2008)] and Smerzi & Trombettoni [PRA {\bf 68}, 023613 (2003)], we show that the intersite cubic nonlinear terms in the discrete nonlinear Schrödinger (DNLS) equation appear beyond the applicability of assumptions of the tight-binding approximation. Instead of these terms, for an even linear potential and an odd nonlinearity coefficient, the DNLS equation and other reduced equations for the semi-infinite gap have the quintic nonlinear term, which correctly describes bifurcation of gap solitons.

nlin.PS↗
arXiv2008

Localized nonlinear waves in systems with time- and space-modulated nonlinearities

Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schrödinger equations with potentials and nonlinearities depending on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly non-trivial solutions such as periodic (breathers), resonant or quasiperiodically oscillating solitons. Some implications to the field of matter-waves are also discussed.

nlin.PS↗
arXiv2008

Exact Bright and Dark Spatial Soliton Solutions in Saturable Nonlinear Media

We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schrodinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions.

nlin.SI↗
arXiv2007

Laser tweezers for atomic solitons

We describe a controllable and precise laser tweezers for Bose-Einstein condensates of ultracold atomic gases. In our configuration, a laser beam is used to locally modify the sign of the scattering length in the vicinity of a trapped BEC. The induced attractive interactions between atoms allow to extract and transport a controllable number of atoms. We analyze, through numerical simulations, the number of emitted atoms as a function of the width and intensity of the outcoupling beam. We also study different configurations of our system, as the use of moving beams. The main advantage of using the control laser beam to modify the nonlinear interactions in comparison to the usual way of inducing optical forces, i.e. through linear trapping potentials, is to improve the controllability of the outcoupled solitary wave-packet, which opens new possibilities for engineering macroscopic quantum states.

cond-mat.other↗
arXiv2006

Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities

Using Lie group theory and canonical transformations we construct explicit solutions of nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons and discuss other applications of interest to the field of nonlinear matter waves.

nlin.PS↗