L'operador maximal de Hardy-Littlewood

En aquest treball donarem una introducció a la Teoria de la Diferenciació. Aquesta disciplina té el seu origen en el Teorema fonamental del Càlcul i engloba les seves generalitzacions a altres espais, com per exemple el Teorema de Diferenciació de Lebesgue, que va enunciar Lebesgue l'any 1910. Per demostrar i obtenir generalitzacions adequades d'aquest teorema, s'utilitzen els operadors maximals, dels quals el més important és el de Hardy-Littlewood, associat a boles euclidianes a l'espai, el qual utilitzarem com a eina per entendre millor els resultats i propietats que anirem obtenint al treball. Per altra banda, les propietats més importants d'aquests operadors depenen dels tipus de recobriments que tinguin associats i de les seves característiques geomètriques. En aquest treball parlarem dels 3 conceptes i de les seves connexions i obtindrem resultats avançats d'anàlisi utilitzant eines purament geomètriques

Pathophysiological role and therapeutic potential of extracellular vesicles in cancer

Extracellular vesicles (EVs) are nanosized lipid bilayer vesicles that are endogenously generated through various biogenesis pathways within most cellular entities. Subsequently, they are released into the extracellular milieu to facilitate intercellular communication. They are composed of diverse bioactive molecules with important roles in physiological and pathological states. Over the past few decades, the therapeutic potential of EVs has garnered significant interest in the drug delivery field. However, deepened understanding of EV biology and further technological advances are needed to bridge the gap between research and clinical translation. In this thesis, we address these challenges and investigate EVs as novel biomedical agents. EVs are crucial components of physiological processes and disease development. Sensitive visualisation techniques are needed to better understand their function as therapeutic agents. In paper I, a bioluminescent labelling system was developed to track EVs in vitro and in vivo. The system uses genetic modifications to enable the encapsulation of sensitive luciferase-variants in EVs. The system was used in vivo to enable highly sensitive detection of EV distribution pattern. Exogenously administered EVs were found to rapidly distribute within different organs, with a preference for the spleen, lung, and liver. In addition to endogenously engineered EVs for in vivo tracking, exogenously engineered EVs can be utilised as promising drug delivery platforms. However, cargo loading is often insufficient, requiring improved EV loading approaches. In paper II, we developed an optimised cargo loading method using electroporation. An optimised protocol was designed to load EVs with doxorubicin, which increased cargo loading, EV recovery, and drug potency by 190-fold over free doxorubicin. Owing to their potential to cross biological barriers, transport bioactive cargo, and targetability, EVs can be exploited as delivery vehicles for targeting of therapeutics. EVs were used as delivery vectors in paper III by coating their surfaces with an Fc domain-specific antibodybinding moiety. These Fc-EVs were then decorated with various IgG antibodies and targeted to cells of interest. In vitro and in vivo antibody targeting studies showed the broad potential of this technology for cancer therapy. The platform efficiently targeted EVs to cancer cells, including HER2 and PD-L1 positive cells. As proof of concept, Fc-EVs with PD-L1 antibody accumulate in tumour tissue and, when loaded with doxorubicin, reduce tumour burden, and increase survival in melanoma-bearing mice. Despite significant EV engineering advances, we have a limited understanding of the biology of tumour-derived extracellular vesicles (tEVs). In paper IV, we investigated the role of in vitrogenerated melanoma-derived EVs as indirect communicators in tumour-induced haematopoiesis dysregulation. The tEVs, which contain high levels of angiogenic factors like VEGF, osteopontin, and tissue factor, were found to cause splenomegaly, extramedullary haematopoiesis, expansion of splenic immature erythroid progenitors, reduced bone marrow cellularity, medullary expansion of granulocytic myeloid suppressor cells, and anaemia in syngeneic mice. These findings suggest that tEVs dysregulate haematopoiesis during the immune escape phase of cancer immunoediting, making them potential targets for overcoming immune evasion and restoring normal haematopoiesis. To summarise, the tools generated in this thesis, including the ability to detect EVs in vivo, effective cargo loading, display antibody binding moieties on EV surfaces for targeting, and understanding the pathophysiological role of tEVs, contribute to the advancement of EVs for biomedical purposes, and clinical translation down the line

Electrophysiological mechanisms underlying T wave pseudonormalisation on stress ECGs in hypertrophic cardiomyopathy

Background: Pseudonormal T waves may be detected on stress electrocardiograms (ECGs) in hypertrophic cardiomyopathy (HCM). Either myocardial ischaemia or purely exercise-induced changes have been hypothesised to contribute to this phenomenon, but the precise electrophysiological mechanisms remain unknown. Methods: Computational models of human HCM ventricles (n = 20) with apical and asymmetric septal hypertrophy phenotypes with variable severities of repolarisation impairment were used to investigate the effects of acute myocardial ischaemia on ECGs with T wave inversions at baseline. Virtual 12-lead ECGs were derived from a total of 520 biventricular simulations, for cases with regionally ischaemic K+ accumulation in hypertrophied segments, global exercise-induced serum K+ increases, and/or increased pacing frequency, to analyse effects on ECG biomarkers including ST segments, T wave amplitudes, and QT intervals. Results: Regional ischaemic K+ accumulation had a greater impact on T wave pseudonormalisation than exercise-induced serum K+ increases, due to larger reductions in repolarisation gradients. Increases in serum K+ and pacing rate partially corrected T waves in some anatomical and electrophysiological phenotypes. T wave morphology was more sensitive than ST segment elevation to regional K+ increases, suggesting that T wave pseudonormalisation may sometimes be an early, or the only, ECG feature of myocardial ischaemia in HCM. Conclusions: Ischaemia-induced T wave pseudonormalisation can occur on stress ECG testing in HCM before significant ST segment changes. Some anatomical and electrophysiological phenotypes may enable T wave pseudonormalisation due to exercise-induced increased serum K+ and pacing rate. Consideration of dynamic T wave abnormalities could improve the detection of myocardial ischaemia in HCM

Ventricular anatomical complexity and sex differences impact predictions from electrophysiological computational models

The aim of this work was to analyze the influence of sex hormones and anatomical details (trabeculations and false tendons) on the electrophysiology of healthy human hearts. Additionally, sex- and anatomy-dependent effects of ventricular tachycardia (VT) inducibility are presented. To this end, four anatomically normal, human, biventricular geometries (two male, two female), with identifiable trabeculations, were obtained from high-resolution, ex-vivo MRI and represented by detailed and smoothed geometrical models (with and without the trabeculations). Additionally one model was augmented by a scar. The electrophysiology finite element model (FEM) simulations were carried out, using O’Hara-Rudy human myocyte model with sex phenotypes of Yang and Clancy. A systematic comparison between detailed vs smooth anatomies, male vs female normal hearts was carried out. The heart with a myocardial infarction was subjected to a programmed stimulus protocol to identify the effects of sex and anatomical detail on ventricular tachycardia inducibility. All female hearts presented QT-interval prolongation however the prolongation interval in comparison to the male phenotypes was anatomy-dependent and was not correlated to the size of the heart. Detailed geometries showed QRS fractionation and increased T-wave magnitude in comparison to the corresponding smoothed geometries. A variety of sustained VTs were obtained in the detailed and smoothed male geometries at different pacing locations, which provide evidence of the geometry-dependent differences regarding the prediction of the locations of reentry channels. In the female phenotype, sustained VTs were induced in both detailed and smooth geometries with RV apex pacing, however no consistent reentry channels were identified. Anatomical and physiological cardiac features play an important role defining risk in cardiac disease. These are often excluded from cardiac electrophysiology simulations. The assumption that the cardiac endocardium is smooth may produce inaccurate predictions towards the location of reentry channels in in-silico tachycardia inducibility studiesJA-S, FS, GH and MV are supported by the European Union’s Horizon 2020 research and innovation programme under grant agreements No 675451 (Compbiomed project phase 1) and No 823712 (CompBioMed project, phase 2) and project No 777204 (SilicoFCM project). Part of the simulation computing hours were provided by the CompBioMed project phase 1. JA-S was awarded computation time from Red Espanola de Supercomputacion (RES). (Activity IDs: FI-2018-2-0049 and BCV-2019-2-0014) JA-S is funded by a Ramon y Cajal fellowship (RYC-2017-22532), Ministerio de Ciencia e Innovacion, Spain; and by Plan Estatal de Investigacion Cientifica y Tecnica y de Innovacion 2017-2020 from the Ministerio de Ciencia e Innovacion y Universidades (PID2019-104356RBC41/AEI/10.13039/501100011033): meHeart ME PID2019-104356RB-C44. CB is funded by the Torres Quevedo Program (PTQ2018-010290), Ministerio de Ciencia e Innovacion, Spain. MV, GH and CB are funded by the Spanish Neotec project EXP - 00123159/SNEO-20191113 Generador de corazones virtuales. LKGM was funded by Fundacion Carolina-BBVA. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. There was no additional external funding received for this study.Peer Reviewed"Article signat per 11 autors/es: Pablo Gonzalez-Martin,Federica Sacco,Constantine Butakoff,Ruben Doste,Carlos Bederian,Lilian K. Gutierrez Espinosa de los Monteros,Guillaume Houzeaux,Paul A. Iaizzo,Tinen L. Iles,Mariano Vazquez,Jazmin Aguado-Sierra"Postprint (published version

Mechanisms of ischaemia-induced arrhythmias in hypertrophic cardiomyopathy: a large-scale computational study

Aims: Lethal arrhythmias in hypertrophic cardiomyopathy (HCM) are widely attributed to myocardial ischaemia and fibrosis. How these factors modulate arrhythmic risk remains largely unknown, especially as invasive mapping protocols are not routinely used in these patients. By leveraging multiscale digital twin technologies, we aim to investigate ischaemic mechanisms of increased arrhythmic risk in HCM. Methods and results: Computational models of human HCM cardiomyocytes, tissue, and ventricles were used to simulate outcomes of Phase 1A acute myocardial ischaemia. Cellular response predictions were validated with patch-clamp studies of human HCM cardiomyocytes (n = 12 cells, N = 5 patients). Ventricular simulations were informed by typical distributions of subendocardial/transmural ischaemia as analysed in perfusion scans (N = 28 patients). S1-S2 pacing protocols were used to quantify arrhythmic risk for scenarios in which regions of septal obstructive hypertrophy were affected by (i) ischaemia, (ii) ischaemia and impaired repolarization, and (iii) ischaemia, impaired repolarization, and diffuse fibrosis. HCM cardiomyocytes exhibited enhanced action potential and abnormal effective refractory period shortening to ischaemic insults. Analysis of ∼75 000 re-entry induction cases revealed that the abnormal HCM cellular response enabled establishment of arrhythmia at milder ischaemia than otherwise possible in healthy myocardium, due to larger refractoriness gradients that promoted conduction block. Arrhythmias were more easily sustained in transmural than subendocardial ischaemia. Mechanisms of ischaemia–fibrosis interaction were strongly electrophysiology dependent. Fibrosis enabled asymmetric re-entry patterns and break-up into sustained ventricular tachycardia. Conclusion: HCM ventricles exhibited an increased risk to non-sustained and sustained re-entry, largely dominated by an impaired cellular response and deleterious interactions with the diffuse fibrotic substrate

Effects of ranolazine on the arrhythmic substrate in hypertrophic cardiomyopathy

Introduction: Hypertrophic cardiomyopathy (HCM) is a leading cause of lethal arrhythmias in the young. Although the arrhythmic substrate has been hypothesised to be amenable to late Na+ block with ranolazine, the specific mechanisms are not fully understood. Therefore, this study aimed to investigate the substrate mechanisms of safety and antiarrhythmic efficacy of ranolazine in HCM. Methods: Computational models of human tissue and ventricles were used to simulate the electrophysiological behaviour of diseased HCM myocardium for variable degrees of repolarisation impairment, validated against in vitro and clinical recordings. S1-S2 pacing protocols were used to quantify arrhythmic risk in scenarios of (i) untreated HCM-remodelled myocardium and (ii) myocardium treated with 3µM, 6µM and 10µM ranolazine, for variable repolarisation heterogeneity sizes and pacing rates. ECGs were derived from biventricular simulations to identify ECG biomarkers linked to antiarrhythmic effects. Results: 10µM ranolazine given to models manifesting ventricular tachycardia (VT) at baseline led to a 40% reduction in number of VT episodes on pooled analysis of >40,000 re-entry inducibility simulations. Antiarrhythmic efficacy and safety were dependent on the degree of repolarisation impairment, with optimal benefit in models with maximum JTc interval <370 ms. Ranolazine increased risk of VT only in models with severe-extreme repolarisation impairment. Conclusion: Ranolazine efficacy and safety may be critically dependent upon the degree of repolarisation impairment in HCM. For moderate repolarisation impairment, reductions in refractoriness heterogeneity by ranolazine may prevent conduction blocks and re-entry. With severe-extreme disease substrates, reductions of the refractory period can increase re-entry sustainability

Training machine learning models with synthetic data improves the prediction of ventricular origin in outflow tract ventricular arrhythmias

In order to determine the site of origin (SOO) in outflow tract ventricular arrhythmias (OTVAs) before an ablation procedure, several algorithms based on manual identification of electrocardiogram (ECG) features, have been developed. However, the reported accuracy decreases when tested with different datasets. Machine learning algorithms can automatize the process and improve generalization, but their performance is hampered by the lack of large enough OTVA databases. We propose the use of detailed electrophysiological simulations of OTVAs to train a machine learning classification model to predict the ventricular origin of the SOO of ectopic beats. We generated a synthetic database of 12-lead ECGs (2,496 signals) by running multiple simulations from the most typical OTVA SOO in 16 patient-specific geometries. Two types of input data were considered in the classification, raw and feature ECG signals. From the simulated raw 12-lead ECG, we analyzed the contribution of each lead in the predictions, keeping the best ones for the training process. For feature-based analysis, we used entropy-based methods to rank the obtained features. A cross-validation process was included to evaluate the machine learning model. Following, two clinical OTVA databases from different hospitals, including ECGs from 365 patients, were used as test-sets to assess the generalization of the proposed approach. The results show that V2 was the best lead for classification. Prediction of the SOO in OTVA, using both raw signals or features for classification, presented high accuracy values (>0.96). Generalization of the network trained on simulated data was good for both patient datasets (accuracy of 0.86 and 0.84, respectively) and presented better values than using exclusively real ECGs for classification (accuracy of 0.84 and 0.76 for each dataset). The use of simulated ECG data for training machine learning-based classification algorithms is critical to obtain good SOO predictions in OTVA compared to real data alone. The fast implementation and generalization of the proposed methodology may contribute towards its application to a clinical routine.Copyright © 2022 Doste, Lozano, Jimenez-Perez, Mont, Berruezo, Penela, Camara and Sebastian