Mechanistic characterization of oscillatory patterns in unperturbed tumor growth dynamics: The interplay between cancer cells and components of tumor microenvironment.

Mathematical modeling of unperturbed and perturbed tumor growth dynamics (TGD) in preclinical experiments provides an opportunity to establish translational frameworks. The most commonly used unperturbed tumor growth models (i.e. linear, exponential, Gompertz and Simeoni) describe a monotonic increase and although they capture the mean trend of the data reasonably well, systematic model misspecifications can be identified. This represents an opportunity to investigate possible underlying mechanisms controlling tumor growth dynamics through a mathematical framework. The overall goal of this work is to develop a data-driven semi-mechanistic model describing non-monotonic tumor growth in untreated mice. For this purpose, longitudinal tumor volume profiles from different tumor types and cell lines were pooled together and analyzed using the population approach. After characterizing the oscillatory patterns (oscillator half-periods between 8-11 days) and confirming that they were systematically observed across the different preclinical experiments available (p<10-9), a tumor growth model was built including the interplay between resources (i.e. oxygen or nutrients), angiogenesis and cancer cells. The new structure, in addition to improving the model diagnostic compared to the previously used tumor growth models (i.e. AIC reduction of 71.48 and absence of autocorrelation in the residuals (p>0.05)), allows the evaluation of the different oncologic treatments in a mechanistic way. Drug effects can potentially, be included in relevant processes taking place during tumor growth. In brief, the new model, in addition to describing non-monotonic tumor growth and the interaction between biological factors of the tumor microenvironment, can be used to explore different drug scenarios in monotherapy or combination during preclinical drug development.

Association of left atrium voltage amplitude and distribution with the risk of atrial fibrillation recurrence and evolution after pulmonary vein isolation: An ultrahigh-density mapping study.

INTRODUCTION: Ultrahigh-density-voltage mapping (uHDV M) is a new tool that can add new insights into the pathophysiology of atrial fibrillation (AF). The aim of this study was to evaluate the performance of uHDV M in predicting postablation AF recurrence (AFR). METHODS AND RESULTS: We included 98 consecutive patients undergoing pulmonary vein isolation for AF (40.8% persistent) using an uHDV M system and followed for 1 year. The left atrium (LA) mean voltage (Vm ) and the Vslope (slope of the voltage histogram calculated by linear interpolation, with the relative frequency on the vertical axis and the bipolar potential on the horizontal axis) were calculated from 12 567 ± 5486 points per map. Patients with AFR (N = 29) had lower Vm and higher Vslope as compared with patients without AFR (N = 69). Receiver operating characteristic curves identified Vm as the strongest predictor of AFR, with a higher incidence of AFR in patients with Vm 0.758 mV (57.6%) or lower than patients with Vm higher than 0.758 mV (15.4%; P < .0001). Among patients with Vm  higher than 0.758 mV, patients with Vslope 0.637 or higher exhibited higher (P = .043) AFR incidence (31.3%) than patients with Vslope lower than 0.637 (10.2%). This classification showed incremental predictive value over relevant covariables. Vm values were lower and Vslope values were higher in patients that progressed from paroxysmal to persistent AF. Patients with Vslope 0.637 or higher had a 14.2% incidence of postablation atypical atrial flutter, whereas patients with Vslope lower than 0.637 did not present this outcome. CONCLUSIONS: The risk of AFR, atrial flutter, and progression from paroxysmal to persistent AF can be detected by quantitative analysis of LA uHDV M identifying diverse patterns of atrial substrate alterations.

Shock-induced termination of reentrant cardiac arrhythmias: comparing monophasic and biphasic shock protocols.

In this article, we compare quantitatively the efficiency of three different protocols commonly used in commercial defibrillators. These are based on monophasic and both symmetric and asymmetric biphasic shocks. A numerical one-dimensional model of cardiac tissue using the bidomain formulation is used in order to test the different protocols. In particular, we performed a total of 4.8 × 10(6) simulations by varying shock waveform, shock energy, initial conditions, and heterogeneity in internal electrical conductivity. Whenever the shock successfully removed the reentrant dynamics in the tissue, we classified the mechanism. The analysis of the numerical data shows that biphasic shocks are significantly more efficient (by about 25%) than the corresponding monophasic ones. We determine that the increase in efficiency of the biphasic shocks can be explained by the higher proportion of newly excited tissue through the mechanism of direct activation.

Bleb geometry and morphology after Preserflo Microshunt surgery: Risk factors for surgical failure.

PURPOSE: To investigate the possible risk factors for treatment failure in patients who had undergone Preserflo Microshunt (PMS) implantation, using anterior-segment optical coherence tomography (AS-OCT) to analyze the internal structures of the bleb. METHODS: The PMS blebs of 54 patients were evaluated with AS-OCT. A mathematical model was used to calculate the total filtering surface of the episcleral fluid cavity (EFC) and the hydraulic conductivity (HC) of the bleb wall. Complete and qualified success were defined as IOP between 6 and 17 mmHg with or without glaucoma medication. The relation between baseline characteristics and probability of bleb success was analyzed by bivariate and multivariate logistic regression. The main outcome measures were mean bleb wall thickness (BWT), reflectivity (BWR), HC, mean horizontal and vertical diameter and total filtering surface (TFS) of the EFC. RESULTS: Blebs from 74% patients were considered as complete success and 26% as failure. BWR and BWT increased linearly up to the first year in both groups. BWR was higher in the group failure (p = 0.02) and BWT in the group success (p<0.001). EFC was wider and shorter in the success group (p = 0.009, p = 0.03). Higher TFS showed a negative correlation with IOP (r = -0.4, p = 0.002). Higher baseline IOP was associated with success of PMS by multivariate analysis (p = 0.01). Mean HC, 0.034 ± 0.008 (µL/min)/mm2/mmHg, was negatively correlated with bleb surface (r = -0.5, p<0.0001) and wall´s thickness (r = -0.3, p = 0.01). CONCLUSIONS: AS-OCT revealed that successful PMS blebs could show either thick hyporreflective walls or wide filtering surfaces with thin capsules. A higher baseline IOP increased the probability of surgical success.

Cardiac dynamics: a simplified model for action potential propagation.

This paper analyzes a new semiphysiological ionic model, used recently to study reexitations and reentry in cardiac tissue [I.R. Cantalapiedra et al, PRE 82 011907 (2010)]. The aim of the model is to reproduce action potencial morphologies and restitution curves obtained, either from experimental data, or from more complex electrophysiological models. The model divides all ion currents into four groups according to their function, thus resulting into fast-slow and inward-outward currents. We show that this simplified model is flexible enough as to accurately capture the electrical properties of cardiac myocytes, having the advantage of being less computational demanding than detailed electrophysiological models. Under some conditions, it has been shown to be amenable to mathematical analysis. The model reproduces the action potential (AP) change with stimulation rate observed both experimentally and in realistic models of healthy human and guinea pig myocytes (TNNP and LRd models, respectively). When simulated in a cable it also gives the right dependence of the conduction velocity (CV) with stimulation rate. Besides reproducing correctly these restitution properties, it also gives a good fit for the morphology of the AP, including the notch typical of phase 1. Finally, we perform simulations in a realistic geometric model of the rabbit's ventricles, finding a good qualitative agreement in AP propagation and the ECG. Thus, this simplified model represents an alternative to more complex models when studying instabilities in wave propagation.

Etiology-Specific Remodeling in Ventricular Tissue of Heart Failure Patients and Its Implications for Computational Modeling of Electrical Conduction.

With an estimated 64.3 million cases worldwide, heart failure (HF) imposes an enormous burden on healthcare systems. Sudden death from arrhythmia is the major cause of mortality in HF patients. Computational modeling of the failing heart provides insights into mechanisms of arrhythmogenesis, risk stratification of patients, and clinical treatment. However, the lack of a clinically informed approach to model cardiac tissues in HF hinders progress in developing patient-specific strategies. Here, we provide a microscopy-based foundation for modeling conduction in HF tissues. We acquired 2D images of left ventricular tissues from HF patients (n = 16) and donors (n = 5). The composition and heterogeneity of fibrosis were quantified at a sub-micrometer resolution over an area of 1 mm2. From the images, we constructed computational bidomain models of tissue electrophysiology. We computed local upstroke velocities of the membrane voltage and anisotropic conduction velocities (CV). The non-myocyte volume fraction was higher in HF than donors (39.68 ± 14.23 vs. 22.09 ± 2.72%, p < 0.01), and higher in ischemic (IC) than nonischemic (NIC) cardiomyopathy (47.2 ± 16.18 vs. 32.16 ± 6.55%, p < 0.05). The heterogeneity of fibrosis within each subject was highest for IC (27.1 ± 6.03%) and lowest for donors (7.47 ± 1.37%) with NIC (15.69 ± 5.76%) in between. K-means clustering of this heterogeneity discriminated IC and NIC with an accuracy of 81.25%. The heterogeneity in CV increased from donor to NIC to IC tissues. CV decreased with increasing fibrosis for longitudinal (R 2 = 0.28, p < 0.05) and transverse conduction (R 2 = 0.46, p < 0.01). The tilt angle of the CV vectors increased 2.1° for longitudinal and 0.91° for transverse conduction per 1% increase in fibrosis. Our study suggests that conduction fundamentally differs in the two etiologies due to the characteristics of fibrosis. Our study highlights the importance of the etiology-specific modeling of HF tissues and integration of medical history into electrophysiology models for personalized risk stratification and treatment planning.

Cardiac computational modelling.

Cardiovascular diseases currently have a major social and economic impact, constituting one of the leading causes of mortality and morbidity. Personalized computational models of the heart are demonstrating their usefulness both to help understand the mechanisms underlying cardiac disease, and to optimize their treatment and predict the patient's response. Within this framework, the Spanish Research Network for Cardiac Computational Modelling (VHeart-SN) has been launched. The general objective of the VHeart-SN network is the development of an integrated, modular and multiscale multiphysical computational model of the heart. This general objective is addressed through the following specific objectives: a) to integrate the different numerical methods and models taking into account the specificity of patients; b) to assist in advancing knowledge of the mechanisms associated with cardiac and vascular diseases; and c) to support the application of different personalized therapies. This article presents the current state of cardiac computational modelling and different scientific works conducted by the members of the network to gain greater understanding of the characteristics and usefulness of these models.

Evaluation of the Ultrastructural and In Vitro Flow Properties of the PRESERFLO MicroShunt.

Purpose: To measure the in vitro flow properties of the PRESERFLO implant for comparison with the theoretical resistance to flow. Methods: The PRESERFLO was designed to control the flow of aqueous humor according to the Hagen-Poiseuille (HP) equation. Scanning electron microscopy (SEM) was performed to analyze the ultrastructure, and flow measurements were carried out using a gravity-flow setup. Results: SEM images of the PRESERFLO showed luminal diameters of 67.73 × 65.95 µm and 63.66 × 70.54 µm. The total diameter was 337.2 µm, and the wall was 154 µm wide. The theoretical calculation of the resistance to flow (R) for an aqueous humor (AH) viscosity of 0.7185 centipoises (cP) was 1.3 mm Hg/(µL/min). Hence, assuming a constant AH flow of 2 µL/min, the pressure differential across the device (ΔP) was estimated to be 2.6 mm Hg. The gravity-flow experiment allowed us to measure the experimental resistance to flow, which was RE = 1.301 mm Hg/(µL/min), in agreement with the theoretical resistance to flow R given by the HP equation. Conclusions: The experimental and theoretical flow testing showed that the pressure drop across this device would not be large enough to avoid hypotony unless the resistance to outflow of the sub-Tenon space was sufficient to control the intraocular pressure in the early postoperative period. Translational Relevance: The fluid properties of glaucoma subconjunctival drainage devices determine their specific bleb-forming capacity and ability to avoid hypotony and therefore their safety and efficacy profile.

Continuous intraocular pressure monitoring in patients with obstructive sleep apnea syndrome using a contact lens sensor.

PURPOSE: To analyse nocturnal intraocular pressure (IOP) fluctuations in patients with obstructive sleep apnea syndrome (OSAS) using a contact lens sensor (CLS) and to identify associations between the OSAS parameters determined by polysomnographic study (PSG) and IOP changes. METHOD: Prospective, observational study. Twenty participants suspected of having OSAS were recruited. During PSG study, IOP was monitored using a CLS placed in the eye of the patient. The patients were classified according to the apnea-hypopnea index (AHI) in two categories, severe (>30) or mild/moderate (<30) OSAS. We evaluated several parameters determined by the IOP curves, including nocturnal elevations (acrophase) and plateau times in acrophase (PTs) defined by mathematical and visual methods. RESULTS: The IOP curves exhibited a nocturnal acrophase followed by PTs of varying extents at which the IOP remained higher than daytime measurement with small variations. We found significant differences in the length of the PTs in patients with severe OSAS compared to those with mild/moderate disease (P = 0.032/P = 0.028). We found a positive correlation between PTs and OSAS severity measured by the total number of apneic events (r = 0.681/0.751 P = 0.004/0.001) and AHI (r = 0.674/0.710, P = 0.004/0.002). Respiratory-related arousal and oxygen saturation also were associated significantly with the IOP PT length. CONCLUSIONS: Periods of nocturnal IOP elevation lasted longer in severe OSAS patients than those with mild/moderate OSAS and correlate with the severity of the disease. The length of the nocturnal PT is also associated to respiratory parameters altered in patients with OSAS.

Extended Bidomain Modeling of Defibrillation: Quantifying Virtual Electrode Strengths in Fibrotic Myocardium.

Defibrillation is a well-established therapy for atrial and ventricular arrhythmia. Here, we shed light on defibrillation in the fibrotic heart. Using the extended bidomain model of electrical conduction in cardiac tissue, we assessed the influence of fibrosis on the strength of virtual electrodes caused by extracellular electrical current. We created one-dimensional models of rabbit ventricular tissue with a central patch of fibrosis. The fibrosis was incorporated by altering volume fractions for extracellular, myocyte and fibroblast domains. In our prior work, we calculated these volume fractions from microscopic images at the infarct border zone of rabbit hearts. An average and a large degree of fibrosis were modeled. We simulated defibrillation by application of an extracellular current for a short duration (5 ms). We explored the effects of myocyte-fibroblast coupling, intra-fibroblast conductivity and patch length on the strength of the virtual electrodes present at the borders of the normal and fibrotic tissue. We discriminated between effects on myocyte and fibroblast membranes at both borders of the patch. Similarly, we studied defibrillation in two-dimensional models of fibrotic tissue. Square and disk-like patches of fibrotic tissue were embedded in control tissue. We quantified the influence of the geometry and fibrosis composition on virtual electrode strength. We compared the results obtained with a square and disk shape of the fibrotic patch with results from the one-dimensional simulations. Both, one- and two-dimensional simulations indicate that extracellular current application causes virtual electrodes at boundaries of fibrotic patches. A higher degree of fibrosis and larger patch size were associated with an increased strength of the virtual electrodes. Also, patch geometry affected the strength of the virtual electrodes. Our simulations suggest that increased fibroblast-myocyte coupling and intra-fibroblast conductivity reduce virtual electrode strength. However, experimental data to constrain these modeling parameters are limited and thus pinpointing the magnitude of the reduction will require further understanding of electrical coupling of fibroblasts in native cardiac tissues. We propose that the findings from our computational studies are important for development of patient-specific protocols for internal defibrillators.

Combination of Circulating Type I Collagen-Related Biomarkers Is Associated With Atrial Fibrillation.

BACKGROUND: A combination of circulating biomarkers associated with excessive myocardial collagen type-I cross-linking or CCL+ (i.e., decreased carboxy-terminal telopeptide of collagen type-I to matrix metalloproteinase-1 ratio) and with excessive myocardial collagen type-I deposition or CD+ (i.e., increased carboxy-terminal propeptide of procollagen type-I) has been described in heart failure (HF) patients and associates with poor outcomes. OBJECTIVES: The purpose of this study was to investigate whether the CCL+CD+ combination of biomarkers associates with atrial fibrillation (AF). METHODS: Biomarkers were analyzed in serum samples from 242 HF patients (study 1) and 150 patients referred for AF ablation (study 2). Patients were classified into 3 groups (CCL-CD-, CCL+CD- or CCL-CD+, and CCL+CD+) in accordance to biomarker threshold values. Left atrial electroanatomic high-density mapping was performed in 71 patients from study 2. RESULTS: In study 1, 53.7% patients had AF at baseline and 19.6% developed AF (median follow-up 5.5 years). Adjusted odds and hazard ratios associated with baseline and new-onset AF, respectively, were both ≥3.3 (p ≤ 0.050) in CCL+CD+ patients compared with CCL-CD- patients, with nonsignificant changes in the other group. In study 2, 29.3% patients had AF recurrence during 1-year post-ablation. The adjusted hazard ratio for AF recurrence was 3.4 (p = 0.008) in CCL+CD+ patients compared with CCL-CD- patients, with nonsignificant changes in the other group. The CCL+CD+ combination added incremental predictive value over relevant covariables. CCL+CD+ patients exhibited lower left atrial voltage than the remaining patients (p = 0.005). CONCLUSIONS: A combination of circulating biomarkers reflecting excessive myocardial collagen type-I cross-linking and deposition is associated with higher AF prevalence, incidence, and recurrence after ablation.

Modeling of anisotropic properties of double quantum rings by the terahertz laser field.

The rendering of different shapes of just a single sample of a concentric double quantum ring is demonstrated realizable with a terahertz laser field, that in turn, allows the manipulation of electronic and optical properties of a sample. It is shown that by changing the intensity or frequency of laser field, one can come to a new set of degenerated levels in double quantum rings and switch the charge distribution between the rings. In addition, depending on the direction of an additional static electric field, the linear and quadratic quantum confined Stark effects are observed. The absorption spectrum shifts and the additive absorption coefficient variations affected by laser and electric fields are discussed. Finally, anisotropic electronic and optical properties of isotropic concentric double quantum rings are modeled with the help of terahertz laser field.

Modeling the effector - regulatory T cell cross-regulation reveals the intrinsic character of relapses in Multiple Sclerosis.

BACKGROUND: The relapsing-remitting dynamics is a hallmark of autoimmune diseases such as Multiple Sclerosis (MS). Although current understanding of both cellular and molecular mechanisms involved in the pathogenesis of autoimmune diseases is significant, how their activity generates this prototypical dynamics is not understood yet. In order to gain insight about the mechanisms that drive these relapsing-remitting dynamics, we developed a computational model using such biological knowledge. We hypothesized that the relapsing dynamics in autoimmunity can arise through the failure in the mechanisms controlling cross-regulation between regulatory and effector T cells with the interplay of stochastic events (e.g. failure in central tolerance, activation by pathogens) that are able to trigger the immune system. RESULTS: The model represents five concepts: central tolerance (T-cell generation by the thymus), T-cell activation, T-cell memory, cross-regulation (negative feedback) between regulatory and effector T-cells and tissue damage. We enriched the model with reversible and irreversible tissue damage, which aims to provide a comprehensible link between autoimmune activity and clinical relapses and active lesions in the magnetic resonances studies in patients with Multiple Sclerosis. Our analysis shows that the weakness in this negative feedback between effector and regulatory T-cells, allows the immune system to generate the characteristic relapsing-remitting dynamics of autoimmune diseases, without the need of additional environmental triggers. The simulations show that the timing at which relapses appear is highly unpredictable. We also introduced targeted perturbations into the model that mimicked immunotherapies that modulate effector and regulatory populations. The effects of such therapies happened to be highly dependent on the timing and/or dose, and on the underlying dynamic of the immune system. CONCLUSION: The relapsing dynamic in MS derives from the emergent properties of the immune system operating in a pathological state, a fact that has implications for predicting disease course and developing new therapies for MS.

Phase-2 reentry in cardiac tissue: role of the slow calcium pulse.

Phase-2 re-entry is thought to underlie many causes of idiopathic ventricular arrhythmias as, for instance, those occurring in Brugada syndrome. In this paper, we study under which circumstances a region of depolarized tissue can re-excite adjacent regions that exhibit shorter action potential duration (APD), eventually inducing reentry. For this purpose, we use a simplified ionic model that reproduces well the ventricular action potential. With the help of this model, we analyze the conditions that lead to very short action potentials (APs), as well as possible mechanisms for re-excitation in a cable. We then study the induction of re-entrant waves (spiral waves) in simulations of AP propagation in the heart ventricles. We show that re-excitation takes place via a slow pulse produced by calcium current that propagates into the region of short APs until it encounters excitable tissue. We calculate analytically the speed of the slow pulse, and also give an estimate of the minimal tissue size necessary for allowing reexcitation to take place.

Pinning control of spatiotemporal chaos in the LCLV device.

We study the feasibility of transferring data in an optical device by using a limited number of parallel channels. By applying a spatially localized correcting term to the evolution of a liquid crystal light valve in its spatio temporal chaotic regime, we are able to restore the dynamics to a specified target pattern. The system is controlled in a finite time. The number and position of pinning points needed to attain control is also investigated.