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]

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

Direct C–H Allylation of Unactivated Alkanes by Cooperative W/Cu Photocatalysis

Here we report a photocatalytic methodology that enables the direct allylation of strong aliphatic C–H bonds with simple allylic chlorides. The method relies on a cooperative interaction of two metal catalysts in which the decatungstate anion acts as a hydrogen-atom abstractor generating a nucleophilic carbon-centered radical that engages in an SH2′ reaction with an activated allylic π-olefin–copper complex. Because of this dual catalysis, the protocol allows for the functionalization of a range of chemical feedstocks and natural products under mild conditions in short reaction timesFinancial support from the European Research Council (ERC-CoG 863914-BECAME), Agencia Estatal de Investigación (PID2020-118237RB-I00), Xunta de Galicia (ED431C 2018/04; Centro singular de investigación de Galicia accreditation 2019-2022, ED431G 2019/03), and the European Regional Development Fund (ERDF) is gratefully acknowledgedS

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

Palladium-Catalyzed [5 + 2] Rollover Annulation of 1-Benzylpyrazoles with Alkynes: A Direct Entry to Tricyclic 2-Benzazepines

The first Pd-catalyzed [5 + 2] rollover annulation of 1-benzylpyrazoles with alkynes to assemble 10H-benzo[e]pyrazolo[1,5-a]azepines (tricyclic 2-benzazepines) has been developed. The rollover annulation implies a twofold C–H activation of aryl and heteroaryl Csp2–H bonds (C–H/C–H) of 1-benzylpyrazoles (five-atom partners) and alkynes to give the [5 + 2] annulated compounds.We acknowledge financial support from MICINN (Project PID2020-118048GB-I00 and ORFEO−CINQA Network RED2018-102387-T), the Xunta de Galicia (Project ED431C 2022/27 and Centro Singular de Investigación de Galicia Accreditation 2019−2022, ED431G 2019/03), and the European Union (European Regional Development Fund). A.S.-L. thanks MICINN for a predoctoral contract.S

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)

Los Aljezares archaeological site (Alicante, Spain) and the MIS 6/5 open-air settlement in the Iberian Peninsula

The record of open-air Middle Palaeolithic sites in the Iberian Peninsula—specifically in the Mediterranean basin—is scarce, hampering the interpretation of the landscape use strategies developed by Neanderthals in this area. In this work, we present Los Aljezares, a new Middle Palaeolithic site found in Pleistocene fluvio-lacustrine deposits in the sedimentary basin of the Vinalopó River. A U/Th age (132 ± 10 ka) from associated carbonate deposits allows us to attribute the site to the uppermost part of the Middle Pleistocene to Late Pleistocene (marine isotope stage 6/5). To date, a total of two levels of human occupation have been identified in which the density of lithic remains is low compared with cave and rock shelter sites in the region. The first results of technology and use-wear, raw material procurement and geological data indicate a settlement in Los Aljezares along a territory characterised by ephemeral channels and their associated palustrine and lacustrine zones. This palaeoenvironmental setting provided biotic and abiotic resources in a transit area between inland and coastal locations.The research has been funded through the following research projects: El pasado lejano: aproximación a la conducta y la ocupación del territorio en el paleolítico valenciano (PROMETEO/2017/060), Estudio del registro climático reciente preservado en depósitos cuaternarios: el caso de Los Aljezares (Aspe, Alicante) y su relación con los depósitos del Medio y Bajo Vinalopó (GRE17-02), Caracterización tecnológica y funcional de los elementos líticos apuntados durante el Paleolítico medio en la región central del mediterráneo ibérico (GV/2021/054) and Síntesis del Paleolítico medio y superior en Valencia y Murcia: aspectos cronológicos, paleoambientales, económicos y culturales (HAR2017-85153-P)

Tour virtual: una forma eficiente de realizar evaluaciones tempranas en aplicaciones de paciente

Tradicionalmente, los sistemas de ayuda a la decisión (Decision Support Systems, DSS) han estado dirigidos a los profesionales médicos; sin embargo también pueden ayudar a aquellos pacientes que desean tener un papel más activo en el cuidado de su salud. Además, los pacientes quieren ser tratados en el momento en que su estado de salud lo requiera, sin importar el lugar en el que se encuentren. El sistema MobiGuide proporciona un soporte personalizado y basado en evidencia clínica tanto a profesionales médicos como a pacientes en todo momento y en todo lugar. La aplicación móvil del paciente representa el punto de acceso al servicio y, por tanto, es responsable en gran medida del éxito o fracaso del sistema. En MobiGuide, se ha incorporado a los pacientes desde el comienzo en el proceso de diseño y evaluación de la aplicación para garantizar una adecuada funcionalidad y usabilidad del sistema. En este trabajo presentamos la primera evaluación realizada por los pacientes mediante un tour virtual por la Aplicación de Paciente. Los resultados son altamente positivos y útiles para mejorar la aplicación, corregir defectos y conseguir la aplicación final esperada por los pacientes

A mesoscopic simulator to uncover heterogeneity and evolutionary dynamics in tumors

Increasingly complex in silico modeling approaches offer a way to simultaneously access cancerous processes at different spatio-temporal scales. High-level models, such as those based on partial differential equations, are computationally affordable and allow large tumor sizes and long temporal windows to be studied, but miss the discrete nature of many key underlying cellular processes. Individual-based approaches provide a much more detailed description of tumors, but have difficulties when trying to handle full-sized real cancers. Thus, there exists a trade-off between the integration of macroscopic and microscopic information, now widely available, and the ability to attain clinical tumor sizes. In this paper we put forward a stochastic mesoscopic simulation framework that incorporates key cellular processes during tumor progression while keeping computational costs to a minimum. Our framework captures a physical scale that allows both the incorporation of microscopic information, tracking the spatio-temporal emergence of tumor heterogeneity and the underlying evolutionary dynamics, and the reconstruction of clinically sized tumors from high-resolution medical imaging data, with the additional benefit of low computational cost. We illustrate the functionality of our modeling approach for the case of glioblastoma, a paradigm of tumor heterogeneity that remains extremely challenging in the clinical setting.This research has been supported by grants awarded to VMPG by James S. Mc. Donnell Foundation, United States of America, 21st Century Science Initiative in Mathematical and Complex Systems Approaches for Brain Cancer (collaborative award 220020560) and Junta de Comunidades de Castilla-La Mancha, Spain (grant number SBPLY/17/180501/000154). VMPG and GFC thank the funding from Ministerio de Ciencia e Innovacion, Spain (grant number PID2019-110895RB-I00). This research has also been supported by a grant awarded to GFC and JBB by the Junta de Comunidades de Castilla-La Mancha, Spain (grant number SBPLY/19/180501/000211). AMR received support from Asociacion Pablo Ugarte (http://www.asociacionpablougarte.es). JJS received support from Universidad de Castilla-La Mancha (grant number 2020-PREDUCLM-15634). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Evaluating Human Activity and Usage Patterns of Appliances with Smart Meters

2022 IEEE International Symposium on Medical Measurements and Applications (MeMeA), 22-24 June 2022, Messina, Italy.Population ageing is becoming a key issue for most western countries, due to the challenges that it poses to the sustainability of future healthcare systems. In this context, many proposals and development are emerging trying to enhance the independent living of elderly and cognitive impaired people at their own homes. For that purpose, the massive deployment of smart meter at houses and buildings, initially focused on improving the energy management, has become a useful tool to provide the society with a variety of services and applications that can be employed for independent living. This work proposes the use of a commercial smart meter that delivers the disaggregated consumption per appliance every hour. This device has been installed on a test house during a training period of two months, in order to infer the behavior routines in the usage of the microwave. After the training, every new day can be compared to the obtained usage pattern of that appliance, in order to launch a notification when the day routine significantly differs. Similarly, since the use of the microwave is related to cooking, activities such as breakfast, lunch or dinner, may also be monitored and/or compared to a trained pattern. The proposal has been validated preliminary with experimental data coming from the aforementioned household.Agencia Estatal de InvestigaciónUniversidad de Alcal