Pseudo-nullclines enable the analysis and prediction of signaling model dynamics.

A powerful method to qualitatively analyze a 2D system is the use of nullclines, curves which separate regions of the plane where the sign of the time derivatives is constant, with their intersections corresponding to steady states. As a quick way to sketch the phase portrait of the system, they can be sufficient to understand the qualitative dynamics at play without integrating the differential equations. While it cannot be extended straightforwardly for dimensions higher than 2, sometimes the phase portrait can still be projected onto a 2-dimensional subspace, with some curves becoming pseudo-nullclines. In this work, we study cell signaling models of dimension higher than 2 with behaviors such as oscillations and bistability. Pseudo-nullclines are defined and used to qualitatively analyze the dynamics involved. Our method applies when a system can be decomposed into 2 modules, mutually coupled through 2 scalar variables. At the same time, it helps track bifurcations in a quick and efficient manner, key for understanding the different behaviors. Our results are both consistent with the expected dynamics, and also lead to new responses like excitability. Further work could test the method for other regions of parameter space and determine how to extend it to three-module systems.

Clinical and angiographic assessment of the culotte technique for the treatment of complex coronary bifurcation lesions / Valoración clínica y angiográfica de la técnica de culotte para el tratamiento de lesiones complejas en bifurcaciones coronarias

Abstract Introduction: The current standard treatment for bifurcation lesions is the provisional stent technique, by implanting only one stent in the main branch; however, in certain cases, the use of more complex techniques that require double stenting should be considered. Objective: To perform a clinical and angiographic assessment of patients with true bifurcation lesions treated with the two-stent culotte technique. Materials and methods: A prospective study was done, which included patients diagnosed with significant obstructive coronary artery disease in bifurcation areas, who were candidates for angioplasty with culotte technique. The study included 44 patients with proved diagnosis of coronary bifurcation lesions; 66% of the treated bifurcation lesions compromised the anterior descending artery and the diagonal branch and 27%, the circumflex artery with the marginal branch. It was found that 68% of the cases had Medina 1,1,1 lesions and 23% had Medina 0,1,1 lesions. Six months later, it was found that 12.5% of the patients followed up by angiography had in-stent restenosis (ISR) > 50% that involved at least one of the bifurcation areas. In 9% of these patients, the ISR was at the origin of the side branch only, and in 3%, the ISR was confined to the distal segment of the main branch stent. Conclusion: The use of the culotte technique with two new-generation stents to treat complex coronary bifurcation lesions is an effective option and does not increase the risk of complications during the procedure nor the risk of the appearance of ISR.

Resumen Introducción: El tratamiento estándar actual para las lesiones en bifurcaciones es la técnica de stent provisional, implantando solo un stent en la rama principal, sin embargo, en ciertos casos, se debería considerar el uso de técnicas más complejas que requieren de doble stent. Objetivo: Realizar una evaluación clínica y angiográfica de pacientes con verdaderas lesiones en bifurcaciones tratados con la técnica culotte de doble stent. Material y métodos: Se realizó un estudio prospectivo que incluyó pacientes diagnosticados con enfermedad obstructiva significativa de arterias coronarias en bifurcaciones, quienes eran candidatos a angioplastia con la técnica culotte. El estudio incluyó 44 pacientes con un diagnóstico comprobado de lesiones coronarias en bifurcaciones; el 66% de las lesiones en bifurcaciones tratadas comprometían la arteria descendente anterior y la rama diagonal, y el 27% la arteria circunfleja con la rama marginal. Se encontró que el 68% de los casos tenían lesiones Medina 1,1,1 y el 23% tenían lesiones Medina 0,1,1. A los seis meses, se encontró que el 12,5% de los pacientes en seguimiento con angiografía presentaban reestenosis intrastent (RIS) mayor al 50%, que comprometía al menos una de las áreas de bifurcación. En el 9% de estos pacientes, la RIS se ubicaba únicamente en el origen de la rama lateral, y en el 3%, la RIS se restringió al segmento distal del stent de la rama principal. Conclusiones: El uso de la técnica culotte empleando dos stents de nueva generación es una opción efectiva para tratar las lesiones complejas en bifurcaciones coronarias, y no aumenta el riesgo de complicaciones durante el procedimiento ni el riesgo de la aparición de reestenosis intrastent.

Resonances in the response of fluidic networks inherent to the cooperation between elasticity and bifurcations.

A global response function (GRF) of an elastic network is introduced as a generalization of the response function (RF) of a rigid network, relating the average flow along the network with the pressure difference at its extremes. The GRF can be used to explore the frequency behaviour of a fluid confined in a tree-like symmetric elastic network in which vessels bifurcate into identical vessels. We study such dynamic response for elastic vessel networks containing viscous fluids. We find that the bifurcation structure, inherent to tree-like networks, qualitatively changes the dynamic response of a single elastic vessel, and gives resonances at certain frequencies. This implies that the average flow throughout the network could be enhanced if the pulsatile forcing at the network's inlet were imposed at the resonant frequencies. The resonant behaviour comes from the cooperation between the bifurcation structure and the elasticity of the network, since the GRF has no resonances either for a single elastic vessel or for a rigid network. We have found that resonances shift to high frequencies as the system becomes more rigid. We have studied two different symmetric tree-like network morphologies and found that, while many features are independent of network morphology, particular details of the response are morphology dependent. Our results could have applications to some biophysical networks, for which the morphology could be approximated to a tree-like symmetric structure and a constant pressure at the outlet. The GRF for these networks is a characteristic of the system fluid-network, being independent of the dynamic flow (or pressure) at the network's inlet. It might therefore represent a good quantity to differentiate healthy vasculatures from those with a medical condition. Our results could also be experimentally relevant in the design of networks engraved in microdevices, since the limit of the rigid case is almost impossible to attain with the materials used in microfluidics and the condition of constant pressure at the outlet is often given by the atmospheric pressure.

To Cure or Not to Cure: Consequences of Immunological Interactions in CML Treatment.

Recent clinical findings in chronic myeloid leukemia (CML) patients suggest that the number and function of immune effector cells are modulated by tyrosine kinase inhibitors (TKI) treatment. There is further evidence that the success or failure of treatment cessation at least partly depends on the patients immunological constitution. Here, we propose a general ODE model to functionally describe the interactions between immune effector cells with leukemic cells during the TKI treatment of CML. In total, we consider 20 different sub-models, which assume different functional interactions between immune effector and leukemic cells. We show that quantitative criteria, which are purely based on the quality of model fitting, are not able to identify optimal models. On the other hand, the application of qualitative criteria based on a dynamical system framework allowed us to identify nine of those models as more suitable than the others to describe clinically observed patterns and, thereby, to derive conclusion about the underlying mechanisms. Additionally, including aspects of early CML onset, we can demonstrate that certain critical parameters, such as the strength of immune response or leukemia proliferation rate, need to change during CML growth prior to diagnosis, leading to bifurcations that alter the attractor landscape. Finally, we show that the crucial parameters determining the outcome of treatment cessation are not identifiable with tumor load data only, thereby highlighting the need to measure immune cell number and function to properly derive mathematical models with predictive power.

Modeling dynamics for oncogenesis encompassing mutations and genetic instability.

Tumorigenesis has been described as a multistep process, where each step is associated with a genetic alteration, in the direction to progressively transform a normal cell and its descendants into a malignant tumour. Into this work, we propose a mathematical model for cancer onset and development, considering three populations: normal, premalignant and cancer cells. The model takes into account three hallmarks of cancer: self-sufficiency on growth signals, insensibility to anti-growth signals and evading apoptosis. By using a nonlinear expression to describe the mutation from premalignant to cancer cells, the model includes genetic instability as an enabling characteristic of tumour progression. Mathematical analysis was performed in detail. Results indicate that apoptosis and tissue repair system are the first barriers against tumour progression. One of these mechanisms must be corrupted for cancer to develop from a single mutant cell. The results also show that the presence of aggressive cancer cells opens way to survival of less adapted premalignant cells. Numerical simulations were performed with parameter values based on experimental data of breast cancer, and the necessary time taken for cancer to reach a detectable size from a single mutant cell was estimated with respect to some parameters. We find that the rates of apoptosis and mutations have a large influence on the pace of tumour progression and on the time it takes to become clinically detectable.

Histological verification of atherosclerosis due to bends and bifurcations in carotid arteries predicted by hemodynamic model.

BACKGROUND: Tortuosity and bifurcations in carotid arteries alter the blood flow, causing atherosclerosis. OBJECTIVES: The aim of the present study is to analyze the effect of variant vascular anatomy in the cervical region on development of atherosclerosis by microanatomical examination. METHODS: The effect of blood flow at anomalous bends and bifurcations was observed in right carotid arteries of a seventy year old female cadaver. Fifteen histological slides were prepared from the carotid arteries and interpreted to verify predictions of atherosclerosis. RESULTS: The model predicts atherosclerosis at bends, bifurcations and large aperture arteries. Microanatomical examination revealed presence of atherosclerosis of varying thickness at the bends and bifurcation in the right carotid arteries, as predicted. Atherosclerosis was also detected in the straight part of the wider common carotid artery. No atherosclerosis was observed in the contralateral carotid arteries. The variant carotid vascular anatomy consisting of bends, bifurcations and wider arteries revealed that the shear stress and velocity of blood flow are reduced at these anomalous sites. CONCLUSIONS: Anatomical anomalies such as bends and branching in the carotid arteries alter the irrigation pattern and generate biomechanical forces that cause turbulent flow and reduce shear stress/blood flow velocity. Decreased shear stress and velocity causes development of atherosclerosis. Histological slides established the presence of atherosclerosis at bends and bifurcations and in wider arteries.

CONTEXTO: Tortuosidade e bifurcações das artérias carótidas alteram o fluxo sanguíneo, causando aterosclerose. OBJETIVOS: O objetivo do presente estudo foi analisar o efeito de anatomia vascular variante na região cervical sobre o desenvolvimento de aterosclerose via exame microanatômico. MÉTODOS: O efeito do fluxo sanguíneo em dobras e bifurcações anômalas foi observado nas artérias carótidas do lado direito em um cadáver do sexo feminino de 70 anos de idade. Quinze lâminas histológicas foram preparadas a partir das artérias carótidas e interpretadas para confirmar as previsões de aterosclerose. RESULTADOS: O modelo prevê aterosclerose em dobras, bifurcações e artérias de grande calibre. O exame microanatômico revelou a presença de aterosclerose de densidades variáveis nas dobras e bifurcação das artérias carótidas do lado direito, conforme previsto. Aterosclerose também foi detectada na parte reta da artéria carótida comum mais larga. Não foi observada aterosclerose nas artérias carótidas contralaterais. A anatomia vascular carotídea variante consistindo de dobras, bifurcações e artérias mais largas revelou que a tensão de cisalhamento (shear stress) e a velocidade do fluxo sanguíneo são reduzidos nesses pontos anômalos. CONCLUSÕES: Anomalias anatômicas tais como dobras e ramificações das artérias carótidas alteram o padrão de irrigação e geram forças biomecânicas que causam fluxo turbulento e reduzem a tensão de cisalhamento e a velocidade do fluxo. Tensão e velocidade menores causam o desenvolvimento de aterosclerose. As lâminas histológicas estabeleceram a presença de aterosclerose nas dobras e bifurcações nas artérias mais largas.

Complex oscillatory redox dynamics with signaling potential at the edge between normal and pathological mitochondrial function.

The time-keeping properties bestowed by oscillatory behavior on functional rhythms represent an evolutionarily conserved trait in living systems. Mitochondrial networks function as timekeepers maximizing energetic output while tuning reactive oxygen species (ROS) within physiological levels compatible with signaling. In this work, we explore the potential for timekeeping functions dependent on mitochondrial dynamics with the validated two-compartment mitochondrial energetic-redox (ME-R) computational model, that takes into account (a) four main redox couples [NADH, NADPH, GSH, Trx(SH)2], (b) scavenging systems (glutathione, thioredoxin, SOD, catalase) distributed in matrix and extra-matrix compartments, and (c) transport of ROS species between them. Herein, we describe that the ME-R model can exhibit highly complex oscillatory dynamics in energetic/redox variables and ROS species, consisting of at least five frequencies with modulated amplitudes and period according to power spectral analysis. By stability analysis we describe that the extent of steady state-as against complex oscillatory behavior-was dependent upon the abundance of Mn and Cu, Zn SODs, and their interplay with ROS production in the respiratory chain. Large parametric regions corresponding to oscillatory dynamics of increasingly complex waveforms were obtained at low Cu, Zn SOD concentration as a function of Mn SOD. This oscillatory domain was greatly reduced at higher levels of Cu, Zn SOD. Interestingly, the realm of complex oscillations was located at the edge between normal and pathological mitochondrial energetic behavior, and was characterized by oxidative stress. We conclude that complex oscillatory dynamics could represent a frequency- and amplitude-modulated H2O2 signaling mechanism that arises under intense oxidative stress. By modulating SOD, cells could have evolved an adaptive compromise between relative constancy and the flexibility required under stressful redox/energetic conditions.