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Victor M. Perez-Garcia

Publications and source records attributed to Victor M. Perez-Garcia.

At least 19 recordsLinked to original sources
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↗
arXiv2014

Extreme protraction for low grade gliomas: Theoretical proof of concept of a novel therapeutical strategy

Grade II gliomas are slowly growing primary brain tumors that affect mostly young patients and become fatal after a few years. Current clinical handling includes surgery as first line treatment. Cytotoxic therapies (radiotherapy RT or chemotherapy QT) are used initially only for patients having a bad prognosis. Therapies are administered following the 'maximum dose in minimum time' principle, what is the same schedule used for high grade brain tumors. Using mathematical models describing the growth of these tumors in response to radiotherapy, we find that a extreme protraction therapeutical strategy, i.e. enlarging substantially the time interval between RT fractions, may lead to a better tumor control. Explicit formulas are found providing the optimal spacing between doses in a very good agreement with the simulations of the full three-dimensional mathematical model approximating the tumor spatio-temporal dynamics. This idea, although breaking the well-stablished paradigm, has biological meaning since in these slowly growing tumors it may be more favourable to treat the tumor as the different tumor subpopulations move to more sensitive phases of the cell cycle.

q-bio.QM↗
arXiv2014

Waves of cells with an unstable phenotype accelerate the progression of high-grade brain tumors

In this paper we study a reduced continuous model describing the local evolution of high grade gliomas - a lethal type of primary brain tumor - through the interplay of different cellular phenotypes. We show how hypoxic events, even sporadic and/or limited in space may have a crucial role on the acceleration of the growth speed of high grade gliomas. Our modeling approach is based on two cellular phenotypes one of them being more migratory and the second one more proliferative with transitions between them being driven by the local oxygen values, assumed in this simple model to be uniform. Surprisingly even acute hypoxia events (i.e. very localized in time) leading to the appearance of migratory populations have the potential of accelerating the invasion speed of the proliferative phenotype up to speeds close to those of the migratory phenotype. The high invasion speed of the tumor persists for times much longer than the lifetime of the hypoxic event and the phenomenon is observed both when the migratory cells form a persistent wave of cells located on the invasion front and when they form a evanecent wave dissapearing after a short time by decay into the more proliferative phenotype. Our findings are obtained through numerical simulations of the model equations. We also provide a deeper mathematical analysis of some aspects of the problem such as the conditions for the existence of persistent waves of cells with a more migratory phenotype.

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↗
arXiv2010

A nonlinear quantum piston for the controlled generation of vortex rings

We propose a simple way to manage interactions in Bose-Einstein condensates to generate vortex rings in a highly controllable way. The vortex rings are generated under the action of a quantum analogue of a classical piston pushing the condensed atoms through a small aperture.

cond-mat.quant-gas↗
arXiv2009

Dissipation-induced coherent structures in Bose-Einstein condensates

We discuss how to engineer the phase and amplitude of a complex order parameter using localized dissipative perturbations. Our results are applied to generate and control various types of atomic nonlinear matter waves (solitons) by means of localized dissipative defects.

cond-mat.other↗
arXiv2008

Mapped Chebyshev pseudospectral method to study multiple scale phenomena

In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the spectral interpolation error, the new polynomial-type mapping is compared against previously proposed mappings for the study of collapse and shock wave phenomena. As a physical application, we study the dynamics of two coupled beams, described by coupled nonlinear Schrödinger equations and modeling beam propagation in an atomic coherent media, whose spatial sizes differs up to several orders of magnitude. It is demonstrated, also by numerical simulations, that the accuracy properties of the new polynomial-type mapping outperforms in orders of magnitude the ones of the other studied mapping functions.

physics.comp-ph↗
arXiv2008

Eigenvalue cut-off in the cubic-quintic nonlinear Schrodinger equation

Using theoretical arguments, we prove the numerically well-known fact that the eigenvalues of all localized stationary solutions of the cubic-quintic 2D+1 nonlinear Schrodinger equation exhibit an upper cut-off value. The existence of the cut-off is inferred using Gagliardo-Nirenberg and Holder inequalities together with Pohozaev identities. We also show that, in the limit of eigenvalues close to zero, the eigenstates of the cubic-quintic nonlinear Schrodinger equation behave similarly to those of the cubic nonlinear Schrodinger equation.

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

Collapse in coupled Nonlinear Schrodinger equations: Sufficient conditions and Applications

In this paper we study blow-up phenomena in general coupled nonlinear Schrodinger equations with different dispersion coefficients. We find sufficient conditions for blow-up and for the existence of global solutions. We discuss several applications of our results to heteronuclear multispecies Bose-Einstein condensates and to degenerate boson-fermion mixtures.

nlin.PS↗
arXiv2008

Stability of excited states of a Bose-Einstein condensate in an anharmonic trap

We analyze the stability of non-ground nonlinear states of a Bose-Einstein condensate in the mean field limit in effectively 1D (``cigar-shape'') traps for various types of confining potentials. We find that nonlinear states become, in general, more stable when switching from a harmonic potential to an anharmonic one. We discuss the relation between this fact and the specifics of the harmonic potential which has an equidistant spectrum.

nlin.PS↗
arXiv2008

Localization phenomena in Nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities: Theory and applications to Bose-Einstein condensates

We study the properties of the ground state of Nonlinear Schrödinger Equations with spatially inhomogeneous interactions and show that it experiences a strong localization on the spatial region where the interactions vanish. At the same time, tunneling to regions with positive values of the interactions is strongly supressed by the nonlinear interactions and as the number of particles is increased it saturates in the region of finite interaction values. The chemical potential has a cutoff value in these systems and thus takes values on a finite interval. The applicability of the phenomenon to Bose-Einstein condensates is discussed in detail.

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↗
arXiv2008

Supersolitons: Solitonic excitations in atomic soliton chains

We show that, by appropriately tuning physically relevant interactions in two-component nonlinear Schrodinger equations, it is possible to achieve a regime with particle-like solitonic collisions. This allows us to construct an analogue of the Newton's cradle and also to create localized collective excitations in solitary-wave chains which are quasi-integrable solitons, i.e. supersolitons. We give a physical explanation of the phenomenon, support it with a perturbative analysis, and confirm our predictions by direct simulations.

nlin.PS↗
arXiv2008

Collapse in boson-fermion mixtures with all-repulsive interactions

We describe the collapse of the bosonic component in a boson-fermion mixture due to the pressure exerted on them by a large fermionic component, leading to collapse in a system with all-repulsive interactions. We describe the phenomena early collapse and of super-slow collapse of the mixture.

nlin.PS↗
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↗