Dr. J. Héctor Morales Bárcenas






PhD in Mathematics

Rensselaer Polytechnic Institute (RPI)

Troy, New York, USA


Inverse Problems, Imaging, and

 Mathematical Modeling in Biological

and Medical Physics


Problèmes inverses, imagerie et

modélisation mathématique en biologique

et physique médicale


I am the Vicepresident for the Division of Medical Physics

of the Mexican Society of Physics (SMF) for the term 2021-2022


Lizbeth Naranjo, Bayesian Statistics (FC UNAM)

Gabriel Núñez, Bayesian Statistics (UAM-I)

Gabriel Escarela, Statistics (UAM-I)

Fabian Martínez, Bayesian and Computational Statistics (UAM-I)

Jorge Bolaños, Quantum Markov Semigroups (UAM-I)

Oscar Yáñez, Electrical and Biomedical Engineering (UAM-I)

H. M., Imaging and Inverse Problems (UAM-I).




1. Statistical and Computational Inverse Problems


Miguel Angel Moreles, Center for Mathematical Research (CIMAT), Mexico.


Gabriel Núñez, UAM Iztapalapa, Mexico.


Oscar Yáñez, UAM Iztapalapa, Mexico.


2. Mathematical Modeling in Medical Physics


Luis Alberto Medina, Institute of Physics (National University - UNAM) and National Cancer Institute (INCan), Mexico.


Iván M. Rosado Méndez, Institute of Physics (National University - UNAM).


3. Student Dissertations in Progress

Erick I. Guerrero (MSc in Applied Mathematics), ``Uncertainty Quantification in Models with Functional Response: A Bayesian Approach'', UAM Iztapalapa. Joint Supervisor Prof. Gabriel Núñez.


Viridiana Fierros (MSc in Applied Mathematics), ``Statistical Decision Theory in Tumor Characterization and Detection'', UAM Iztapalapa, Mexico. Joint Supervisor Prof. Oscar Yáñez.


Neyva D. Dimayuga (MSc in Applied Mathematics), ``Circular Data Analysis through Bayesian Inference'', UAM Iztapalapa, Mexico. Joint Supervisor Prof. Gabriel Núñez.


Fátima Fonseca Rodríguez (PhD in Mathematics), ``Inverse Problems in Elastographic Imaging", UAM Iztapalapa, Mexico. Joint Supervisor Prof. Miguel Angel Moreles.

Victor Manuel Pérez Vera (PhD in Mathematics), ``Drug Diffusion and Transport in Solid Tumors", Departamento de Ciencias Naturales y Exactas, Universidad de la Costa - CUC, Barranquilla, Colombia.


J. Montserrat López Córtes (BSc in Mathematics), ``Parametric Inference in ODEs'', UAM Iztapalapa, Mexico.


Julieta S. Águila (BSc in Physics), Intern in the Program ``Computational modeling in Medical Physics'', UAM Iztapalapa, Mexico. 


4. Past Students


"Wavelet-based Analysis in Medical Imaging", Joel Montesinos Vázquez (MSc in Applied Mathematics) Departamento de Matemáticas, UAM Iztapalapa, Aug 2020. Joint Supervisor Prof. Gabriel Núñez.

"Integral Formulation of Linear Inverse Problems", Nelsy Y. Pérez Santiz (BSc in Mathematics) Departamento de Matemáticas, UAM Iztapalapa, Feb 2020.

"ATI-SAR Imaging and Oceanographic Linear Wave Theory"Fabricio O. Pérez (PhD in Computer Sciences), CIMAT, Mexico, Feb 2020. Joint Supervisor Prof. Miguel Angel Moreles.


"Epidemic Dynamical Systems in Networks", Israel Badillo (MSc in Applied Mathematics), UAM Iztapalapa, Nov 2019.


"Adenovirus Assembly Model through the Gillespie Algorithm", Federico Porras (MSc in Applied Mathematics), UAM Iztapalapa, Nov 2019.


"Spectral Analysis of Self-excited Oscillations in Mechanical Systems", Alejandra Piña, (BSc in Mathematics), UAM Iztapalapa, Nov 2018.


"Computational Dose Estimation in Solid Tumors", Sirio Bolaños Puchet (MSc in Applied Mathematics), UAM Iztapalapa, 2017. Joint Supervisor Prof. Luis Alberto Medina.


"Bayesian Estimation in Pharmacokinetic Models", Alejandro Nieto Ramos (MSc in Applied Mathematics), UAM Iztapalapa, 2017. Joint Supervisor Prof. Gabriel Núñez.


"A Computational Model of the Attenuated Radon Transform with a Spatial-inhomogeneous Obstacle", Isabel Martínez Castañeda (MSc in Applied Mathematics), UAM Iztapalapa, 2015. Joint Supervisor Prof. Mario Medina.


"Parameter Estimation in Dynamical Systems", Federico Porras Bautista (BSc in Mathematics), UAM Iztapalapa, 2014.


"Electoral Geography: A Case Study of the State of Mexico" Marisol Hernández Sánchez (Bachelor in Sociology), UAM Azcapotzalco, 2013. Joint Supervisor Prof. Roberto J. Gutiérrez López (UAM-A).


"Tomographic Imaging with Non-ionization Radiation in Biological Tissue". Liliana Guadalupe Salvador (MSc in Applied Mathematics), CIMAT, 2012.


"Vaccination Strategies in Flu Epidemics", Victor Manuel Pérez Vera (MSc in Applied Mathematics), CIMAT, 2012.


5. Past visitors


Wonsiri Punurai, Faculty of Engineering, Department of Civil Engineering, Mahidol University, Thailand.

Shin-ichiro Shima, Graduate School of Simulation Studies, University of Hyogo, Japan.






La División de Física Médica de la Sociedad Mexicana de Física y la Universidad Autónoma de Yucatán invitan a participar en el XVI Simposio Mexicano de Física Médica que se realizará en Mérida, Yucatán en fecha por confirmar en 2020.





Vicepresidente electo de la División de Física Médica 

de la Sociedad de Mexicana de Física, 2021-2023

Miembro de la Red Temática de Investigación en Física Médica del CONACyT




My two presentations in this Summer School at IFUNAM June 10-14 2019


1. Parameter Estimation and Inverse Problems in Medical Physics. Wesnesday June 12.

2. Modeling the Dynamics of Microenvironment of Solid Tumors. Thursday June 13.




Local correspondant and participant in the


The Annual Meeting of the Unión Geofísica Mexicana (RAUGM, for its acronym in Spanish) is the most important meeting of geoscientists in México and the largest in Latin America. 

The RAUGM 2017 will be held at the Sheraton Buganvilias hotel in Puerto Vallarta, Jalisco, México from October 22 to 27, 2017.

MSG-10 | Resumen número: 0169  |  Resumen aceptado | Presentación oral 


José Héctor Morales Bárcenas

 Universidad Autónoma Metropolitana, UAM-I


MSG Modelación de sistemas geofísicos Sesión regular


In this talk we present some of the mathematical techniques that come from partial differential equations and microlocal analysis to solve inverse problems in seismic imaging. Microlocal analysis focuses on the analysis of phase and amplitudes of Fourier integral operators (FIOs) that carry the information out of underground scatterers. Those scatterers might be edges, wedges, pikes, etc., that are of the particular interest to be rightly characterized into our operators and be imaging in our inverse problem setup. This methodology turns out to be the generalization of migration methods introduced in geophysics around 1920s that, additionally, includes improvements that come from geometrical optics, WKB approximations and Fourier and Radon transforms. We illustrate the employ of microlocal analysis through an example from wave-field scattering inversion of classical wave equation in a noise and dispersive ambient.





Organizer jointly with Luz de Teresa (UNAM) and Abdón Choque (UMSH)


PRIMA 2017 Congress - Oaxaca, Mexico

The third PRIMA congress will take place in Oaxaca, Mexico from August 14th till August 18th of 2017

Title: On Microlocal Analysis and Statistical Techniques in Electromagnetic Inverse Scattering Problems







Tumor-immune dynamics

January 5 to January 9, 2015

at the 

American Institute of Mathematics, San Jose, California

organized by

Amina Eladdadi, Peter Kim, Dann Mallet, and Chae-Ok Yun


J. Hector Morales-Barcenas
Universidad Autonoma Metropolitana, Mexico City
Workshop statement





Joint Annual Meeting of the Japanese Society for Mathematical Biology and the Society for Mathematical Biology, July 28 - August 1, 2014 (JSMB/SMB 2014 Osaka)


"LAS MATEMÁTICAS son un modelo del razonamiento exacto, un reto absorbente de la mente, una experiencia estética para sus creadores y para algunos estudiantes, una desagradable experiencia para otros estudiantes, y un conducto para el despliegue egoísta del poder mental. Pero histórica, intelectual y prácticamente, las matemáticas son la creación más fina del hombre en la investigación de la naturaleza. Sus principales conceptos, sus acaparantes métodos y aún específicos teoremas se han derivado del estudio de la naturaleza; y las matemáticas son valiosas mayormente por sus contribuciones a la comprensión y domesticación del mundo físico. Estas contribuciones son numerosas." Morris Kline, Mathematics and the Physical World.


Simposio de

Difusión y Transporte

Lunes 31 de marzo en Casa Rafael Galván

Zacatecas 94, Col. Roma Norte, Del. Cuauhtémoc, México, D.F. 










Research in Mathematical Modeling


Inverse Problems and Imaging

In general, the problem of retrieving information or inferring properties of unknown quantities by indirect observations is called an Inverse ProblemIn particular, by means of radiation (probing waves) traveling across a material body or from an unknown source inside the body, we solve inverse problems; i.e., we determine or estimate physical, geometrical, or biological parameters.

With the retrieved information from probing waves, we have the ability to image the medium and/or the sources of radiation. Ultrasound, radar, sonar, X-rays, emission tomography (PET), computed tomography (CT), radioastronomy, seismology, magnetic resonance, etc., are examples of non-invasive methods that depends on the developement of mathematical algorithms to improve imaging and diagnosis (for instance, in medicine) and in several other areas of non-destructive tests in industry.

Because there are many aspects not well understood of the interaction between matter and radiation, particularly the matter related with the living organism, there is still much to do and discover in the related imaging inverse problems.

Biological Physics and Medical Physics through

Statistical and Computational Inverse Problems

Modeling guided by data. The fundamental question of how to construct mathematical models for the evolution of dynamical systems from the information contained in time series.



J'ai obtenu mon doctorat en mathématiques à Rensselaer Polytechnic Institute (RPI) aux États-Unis. Les sujets de mon intérêt sont la propagation et dispersion des ondes électromagnétiques et acoustiques, problèmes inverses et formation d'images.

Mon travail de dissertation (Ph.D.) est envisagé à la télédétection («remote sensing») et au traitement du signal à travers un milieu dispersif. En particulier, le problème a consisté de l'estimation de paramètres physiques des objets placés dans un milieu qui a dispersion dans le temps et bruit. Nous avons implémenté la technique de «radar à synthèse d'ouverture» pour former les images de la surface où sont placés les objets. Pour maximaliser la raison du signal au bruit et le raffinement des images, nous avons employé un filtre adapté (matched filter) et un filtre de Wiener, respectivement. Nous avons estimé numériquement la résolution de l'algorithme de reconstruction.

D'autre part, nous avons étudié aussi la propagation de précurseurs d'onde (champs transitoires). Aux matériaux biologiques, on a prédit l'existence de précurseurs, quand les ondes incidentes avaient une durée très courte (nanosecondes). Quand on augmente la distance de propagation, les précurseurs sont atténués plus lentement que le signal principal («carrier wave»). À fin d'améliorer la formation des images, nous prenons en considération l'atténuation caractéristique des précurseurs pour développer une théorie sur la forme optime qui doit avoir une onde transmise dans un milieu dispersif.


Car les matériaux biologiques sont dispersifs, je suis intéressé à continuer ma recherche à propos de l'imagerie médicale, puisqu'elle permet développer des algorithmes pour améliorer le traitement du signal et aussi poser et résoudre des problèmes de dispersion associés à la propagation des ondes acoustiques ou électromagnétiques.

Problèmes inverses et imagerie médical


En général, le problème de la récupération d'informations ou déduire les propriétés de quantités inconnues par des observations indirectes est appelé un problème inverse.

En particulier, nous résolvons les problèmes inverses au moyen de rayonnement (ondes de sondage) voyageant à travers un corps matériel ou d'une source inconnue, c'est à dire, nous déterminer ou d'estimer les paramètres physiques, géométriques, ou biologique.

Avec les informations récupérées à partir de sonder les ondes, nous avons la capacité à l'image du milieu et / ou les sources de rayonnement. L'échographie, radar, sonar, les rayons X, l'émission de positons (TEP), la tomodensitométrie (TDM), la radioastronomie, de la sismologie, la résonance magnétique, etc, sont des exemples de méthodes non invasives qui dépend de la Developement des algorithmes mathématiques pour améliorer l'imagerie et le diagnostic (par exemple, en médecine) et dans plusieurs autres domaines de contrôles non destructifs dans l'industrie.

Parce qu'il ya de nombreux aspects ne comprend pas bien de l'interaction entre matière et rayonnement, en particulier la question en relation avec l'organisme vivant, il reste encore beaucoup à faire et à découvrir dans les problèmes liés à l'imagerie inverses.

Modelisation de systèmes biologiques et biophysiques

Modélisation empirique. La question fondamentale de savoir comment construire des modèles mathématiques pour l'évolution des systèmes dynamiques à partir de l'information contenue dans donnée obtenu expérimentalement.



Mathematical-Related Amusements


L’étude profonde de la nature est la source la plus féconde de découvertes mathématiques. Jean Baptiste Joseph Fourier (1768–1830).


If you want to find the secrets of the universe, think in terms of energy, frequency and vibration. Nikola Tesla.

When, as a result of an experiment or numerical simulation, we have a time-dependant signal x(t) — called a time series — one of the essential task is to determine the kind of evolution that produced it.


Computations: no one believes them, except the person who made them. Measurements: everyone believes them, except the person who made them...


The well-known Gaussian law of errors teaches us that an observation error X follows a normal distribution if the error is an accumulation of a large number of small errors. R. Kubo.


Everyone believes in it because the experimentalists imagine that it is a theorem of mathematics and the mathematicians that it is an experimental fact. J.H. Poincaré, 1908.


When a new particle or new fact is discovered, I notice that all the theorisists do one of two things: they either form a group or disperse. R.P. Feynman, 1961.


A demonstration will convince a reasonable person. A proof will convince a skeptic. Mark Kac, remark during a lecture.


With four parameters I can fit an elephant, and with five I can make him wiggle his trunk. John von Neumann.


por Antonio Lazcano, Nexos septiembre 2020

por Antonio Lazcano, Reforma 15 de septiembre 2020

by Antonio Lazcano

by H. Holden Thorp, Science 367 (6483), 1169.