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

Lie point symmetries for generalised Fisher's equations describing tumour dynamics

A huge variety of phenomena are governed by ordinary differential equations (ODEs) and partial differential equations (PDEs). However, there is no general method to solve them. Obtaining solutions for differential equations is one of the greatest problem for both applied mathematics and physics. Multiple integration methods have been developed to the day to solve particular types of differential equations, specially those focused on physical or biological phenomena. In this work, we review several applications of the Lie method to obtain solutions of reaction-diffusion equations describing cell dynamics and tumour invasion.We would like to acknowledge group FQM-201 from Junta de Andalucia. We also would like to acknowledge Profs. Rita Tracina and Mariano Torrisi from the University of Catania (Italy) and Victor M. Perez Garcia from the University of Castilla-La Mancha (Spain) for discussions. This work was partially supported by the Fundacion Espanola para la Ciencia y la Tecnologia [UCA PR214], the Asociacion Pablo Ugarte (APU, Spain) and Inversion Territorial Integrada de la Provincia de Cadiz [ITI-0038-2019]

Herramienta de análisis de contenido en libros de texto: ecuaciones de primer grado

En este artículo se realiza un análisis de contenido de diferentes libros de texto de la educación secundaria obligatoria, centrándose en los temas de la resolución de ecuaciones de primer grado. Para ello, se realiza un diseño de investigación basado en los sistemas de categorías, que permitirá estudiar el contenido de dichos libros de texto. Finalmente, se investigan diferentes libros de texto, que son de 2o y 3er curso de secundaria y, a su vez, de tres editoriales diferentes

Mathematical Modeling of Leukemia Chemotherapy in Bone Marrow

Acute Lymphoblastic Leukemia (ALL) accounts for the 80% of leukemias when coming down to pediatric ages. Survival of these patients has increased by a considerable amount in recent years. However, around 15-20% of treatments are unsuccessful. For this reason, it is definitely required to come up with new strategies to study and select which patients are at higher risk of relapse. Thus the importance to monitor the amount of leukemic cells to predict relapses in the first treatment phase. In this work we develop a mathematical model describing the behavior of ALL, examining the evolution of a leukemic clone when treatment is applied. In the study of this model it can be observed how the risk of relapse is connected with the response in the first treatment phase. This model is able to simulate cell dynamics without treatment, representing a virtual patient bone marrow behavior. Furthermore, several parameters are related to treatment dynamics, therefore proposing a basis for future works regarding childhood ALL survival improvement.Comment: 20 pages and a supplementary information documen

A Mathematical Description of the Bone Marrow Dynamics during CAR T-Cell Therapy in B-Cell Childhood Acute Lymphoblastic Leukemia

Chimeric Antigen Receptor (CAR) T-cell therapy has demonstrated high rates of response in recurrent B-cell Acute Lymphoblastic Leukemia in children and young adults. Despite this success, a fraction of patients' experience relapse after treatment. Relapse is often preceded by recovery of healthy B cells, which suggests loss or dysfunction of CAR T-cells in bone marrow. This site is harder to access, and thus is not monitored as frequently as peripheral blood. Understanding the interplay between B cells, leukemic cells, and CAR T-cells in bone marrow is paramount in ascertaining the causes of lack of response. In this paper, we put forward a mathematical model representing the interaction between constantly renewing B cells, CAR T-cells, and leukemic cells in the bone marrow. Our model accounts for the maturation dynamics of B cells and incorporates effector and memory CAR T-cells. The model provides a plausible description of the dynamics of the various cellular compartments in bone marrow after CAR T infusion. After exploration of the parameter space, we found that the dynamics of CAR T product and disease were independent of the dose injected, initial B-cell load, and leukemia burden. We also show theoretically the importance of CAR T product attributes in determining therapy outcome, and have studied a variety of possible response scenarios, including second dosage schemes. We conclude by setting out ideas for the refinement of the model.This work was partially supported by the Fundacion Espanola para la Ciencia y la Tecnologia (UCA PR214), the Asociacion Pablo Ugarte (APU, Spain), Junta de Comunidades de Castilla-La Mancha (SBPLY/17/180501/000154), Ministry of Science and Technology, Spain (PID2019110895RB-I00), and Inversion Territorial Integrada de la Provincia de Cadiz (ITI-0038-2019)

Overcoming chemotherapy resistance in low-grade gliomas: A computational approach.

Low-grade gliomas are primary brain tumors that arise from glial cells and are usually treated with temozolomide (TMZ) as a chemotherapeutic option. They are often incurable, but patients have a prolonged survival. One of the shortcomings of the treatment is that patients eventually develop drug resistance. Recent findings show that persisters, cells that enter a dormancy state to resist treatment, play an important role in the development of resistance to TMZ. In this study we constructed a mathematical model of low-grade glioma response to TMZ incorporating a persister population. The model was able to describe the volumetric longitudinal dynamics, observed in routine FLAIR 3D sequences, of low-grade glioma patients acquiring TMZ resistance. We used the model to explore different TMZ administration protocols, first on virtual clones of real patients and afterwards on virtual patients preserving the relationships between parameters of real patients. In silico clinical trials showed that resistance development was deferred by protocols in which individual doses are administered after rest periods, rather than the 28-days cycle standard protocol. This led to median survival gains in virtual patients of more than 15 months when using resting periods between two and three weeks and agreed with recent experimental observations in animal models. Additionally, we tested adaptive variations of these new protocols, what showed a potential reduction in toxicity, but no survival gain. Our computational results highlight the need of further clinical trials that could obtain better results from treatment with TMZ in low grade gliomas

High-Dimensional Analysis of Single-Cell Flow Cytometry Data Predicts Relapse in Childhood Acute Lymphoblastic Leukaemia

B-cell Acute Lymphoblastic Leukaemia is one of the most common cancers in childhood, with 20% of patients eventually relapsing. Flow cytometry is routinely used for diagnosis and follow-up, but it currently does not provide prognostic value at diagnosis. The volume and the high-dimensional character of this data makes it ideal for its exploitation by means of Artificial Intelligence methods. We collected flow cytometry data from 56 patients from two hospitals. We analysed differences in intensity of marker expression in order to predict relapse at the moment of diagnosis. We finally correlated this data with biomolecular information, constructing a classifier based on CD38 expression. Artificial intelligence methods may help in unveiling information that is hidden in high-dimensional oncological data. Flow cytometry studies of haematological malignancies provide quantitative data with the potential to be used for the construction of response biomarkers. Many computational methods from the bioinformatics toolbox can be applied to these data, but they have not been exploited in their full potential in leukaemias, specifically for the case of childhood B-cell Acute Lymphoblastic Leukaemia. In this paper, we analysed flow cytometry data that were obtained at diagnosis from 56 paediatric B-cell Acute Lymphoblastic Leukaemia patients from two local institutions. Our aim was to assess the prognostic potential of immunophenotypical marker expression intensity. We constructed classifiers that are based on the Fisher's Ratio to quantify differences between patients with relapsing and non-relapsing disease. We also correlated this with genetic information. The main result that arises from the data was the association between subexpression of marker CD38 and the probability of relapse

The relapsed acute lymphoblastic leukemia network (ReALLNet): a multidisciplinary project from the spanish society of pediatric hematology and oncology (SEHOP)

Acute lymphoblastic leukemia (ALL) is the most common pediatric cancer, with survival rates exceeding 85%. However, 15% of patients will relapse; consequently, their survival rates decrease to below 50%. Therefore, several research and innovation studies are focusing on pediatric relapsed or refractory ALL (R/R ALL). Driven by this context and following the European strategic plan to implement precision medicine equitably, the Relapsed ALL Network (ReALLNet) was launched under the umbrella of SEHOP in 2021, aiming to connect bedside patient care with expert groups in R/R ALL in an interdisciplinary and multicentric network. To achieve this objective, a board consisting of experts in diagnosis, management, preclinical research, and clinical trials has been established. The requirements of treatment centers have been evaluated, and the available oncogenomic and functional study resources have been assessed and organized. A shipping platform has been developed to process samples requiring study derivation, and an integrated diagnostic committee has been established to report results. These biological data, as well as patient outcomes, are collected in a national registry. Additionally, samples from all patients are stored in a biobank. This comprehensive repository of data and samples is expected to foster an environment where preclinical researchers and data scientists can seek to meet the complex needs of this challenging population. This proof of concept aims to demonstrate that a network-based organization, such as that embodied by ReALLNet, provides the ideal niche for the equitable and efficient implementation of “what's next” in the management of children with R/R ALL

Modelos matemáticos en cáncer, hematopoyesis y análisis de datos en leucemia

En esta tesis se exploran métodos y modelos matemáticos como herramientas para descifrar interrogantes acerca de la dinámica tumoral y la recaída. Nos centramos en la leucemia, cáncer de las células blancas sanguíneas que se desarrolla en la médula ósea. Los tumores asociados a la leucemia, así como los tumores cerebrales, son la primera causa de fallecimiento por cáncer en niños y jóvenes adultos. Se examinan múltiples modelos matemáticos, basados en ecuaciones diferenciales ordinarias o parciales, dada su capacidad para describir dinámicas tumorales, especialmente la de la leucemia, el cáncer más frecuente en la infancia. Se desarrolla un modelo que describe la dinámica de los linfocitos B sanos, células blancas causantes de la leucemia linfoblástica aguda B, una de las más comunes en la edad pediátrica. Se consideran datos de citometría de flujo de pacientes, no sólo para describir el desarrollo de las células B, sino también para caracterizar biomarcadores capaces de predecir factores asociados a la recaída en el cáncer. Para ello, se analizan las diferencias en la intensidad de marcadores de superficie celular, tanto con técnicas de "machine learning", como con métodos topológicos, para así describir características de forma que predigan la recaída en pacientes con leucemia. Para finalizar, se recurre al método clásico de Lie para obtener soluciones de ecuaciones que describen de manera general la dinámica tumoral. Este estudio ha sido el resultado del esfuerzo colaborativo entre profesionales clínicos, hematólogos, inmunólogos y matemáticos. Esta investigación multidisciplinar tiene como objetivo el de entender las características tumorales, para así mejorar la clasificación de factores de riesgo y, por lo tanto, los protocolos terapéuticos asociados

Epsilon

Título, resumen y palabras clave en español e inglésResumen basado en el de la publicaciónSe realiza un análisis de contenido de diferentes libros de texto de la Educación Secundaria Obligatoria, centrándose en los temas de la resolución de ecuaciones de primer grado. Para ello, se realiza un diseño de investigación basado en los sistemas de categorías, que permitirá estudiar el contenido de dichos libros de texto. Finalmente, se investigan diferentes libros de texto, que son de 2º y 3º curso de secundaria y, a su vez, de tres editoriales diferentes.ES