Integration of detailed modules in a core model of body fluid homeostasis and blood pressure regulation

Modeling patient-specific desaturation patterns in sleep apnea

OBJECTIVE

The physiological mechanisms involved in cardio-respiratory responses to sleep apnea events are not yet fully elucidated. A model-based approach is proposed to analyse the acute desaturation response to obstructive apneas.

METHODS

An integrated model of cardio-respiratory interactions was proposed and parameters were identified, using an evolutionary algorithm, on a database composed of 107 obstructive apneas acquired from 10 patients (HYPNOS clinical study). Unsupervised clustering was applied to the identified parameters in order to characterize the phenotype of each response to obstructive apneas.

RESULTS

A close match was observed between simulated oxygen saturation (SaO2) and experimental SaO2 in all identifications (median RMSE = 1.3892%). Two clusters of parameters, associated with different dynamics related to sleep apnea and periodic breathing were obtained.

CONCLUSION AND SIGNIFICANCE

The proposed patient and event-specific model-based analysis provides understanding on specific desaturation patterns, consequent to apnea events, with potential applications for personalized diagnosis and treatment.

A Computer Model of Oxygen Dynamics in the Cortex of the Rat Kidney at the Cell-Tissue Level

The renal cortex drives renal function. Hypoxia/reoxygenation are primary factors in ischemia-reperfusion (IR) injuries, but renal oxygenation per se is complex and awaits full elucidation. Few mathematical models address this issue: none captures cortical tissue heterogeneity. Using agent-based modeling, we develop the first model of cortical oxygenation at the cell-tissue level (RCM), based on first principles and careful bibliographical analysis. Entirely parameterized with Rat data, RCM is a morphometrically equivalent 2D-slice of cortical tissue, featuring peritubular capillaries (PTC), tubules and interstitium. It implements hemoglobin/O2 binding-release, oxygen diffusion, and consumption, as well as capillary and tubular flows. Inputs are renal blood flow RBF and PO2 feeds; output is average tissue PO2 (tPO2). After verification and sensitivity analysis, RCM was validated at steady-state (tPO2 37.7 ± 2.2 vs. 36.9 ± 6 mmHg) and under transients (ischemic oxygen half-time: 4.5 ± 2.5 vs. 2.3 ± 0.5 s in situ). Simulations confirm that PO2 is largely independent of RBF, except at low values. They suggest that, at least in the proximal tubule, the luminal flow dominantly contributes to oxygen delivery, while the contribution of capillaries increases under partial ischemia. Before addressing IR-induced injuries, upcoming developments include ATP production, adaptation to minutes-hours scale, and segmental and regional specification.

Recursive model identification for the analysis of the autonomic response to exercise testing in Brugada syndrome

This paper proposes the integration and analysis of a closed-loop model of the baroreflex and cardiovascular systems, focused on a time-varying estimation of the autonomic modulation of heart rate in Brugada syndrome (BS), during exercise and subsequent recovery. Patient-specific models of 44 BS patients at different levels of risk (symptomatic and asymptomatic) were identified through a recursive evolutionary algorithm. After parameter identification, a close match between experimental and simulated signals (mean error = 0.81%) was observed. The model-based estimation of vagal and sympathetic contributions were consistent with physiological knowledge, enabling to observe the expected autonomic changes induced by exercise testing. In particular, symptomatic patients presented a significantly higher parasympathetic activity during exercise, and an autonomic imbalance was observed in these patients at peak effort and during post-exercise recovery. A higher vagal modulation during exercise, as well as an increasing parasympathetic activity at peak effort and a decreasing vagal contribution during post-exercise recovery could be related with symptoms and, thus, with a worse prognosis in BS. This work proposes the first evaluation of the sympathetic and parasympathetic responses to exercise testing in patients suffering from BS, through the recursive identification of computational models; highlighting important trends of clinical relevance that provide new insights into the underlying autonomic mechanisms regulating the cardiovascular system in BS. The joint analysis of the extracted autonomic parameters and classic electrophysiological markers could improve BS risk stratification.

Model-based analysis of the autonomic response to head-up tilt testing in Brugada syndrome

The etiology of Brugada syndrome (BS) is complex and multifactorial, making risk stratification in this population a major challenge. Since changes in the autonomic modulation of these patients are commonly related to arrhythmic events, we analyze in this work whether the response to head-up tilt (HUT) testing on this population may provide useful, complementary information for risk stratification. In order to perform this analysis, a coupled physiological model integrating the cardiac electrical activity, the cardiovascular system and the baroreceptors reflex control of the autonomic function, in response to HUT is proposed. A sensitivity analysis was performed, based on a screening method, evidencing the influence of cardiovascular parameters on blood pressure and of baroreflex regulation on heart rate. The most sensitive parameters have been identified on a set of 20 subjects (8 controls and 12 BS patients), so as to assess subject-specific model parameters. According to the results, controls showed an increased sympathetic modulation after tilting, as well as a reduced left ventricular contractility was observed in symptomatic, with respect to asymptomatic BS patients. These results provide new insights regarding the autonomic mechanisms regulating the cardiovascular system in BS which might be used as a complementary source of information, along with classical electrophysiological parameters, for BS risk stratification.

Recursive Model Identification for the Evaluation of Baroreflex Sensitivity

A method for the recursive identification of physiological models of the cardiovascular baroreflex is proposed and applied to the time-varying analysis of vagal and sympathetic activities. The proposed method was evaluated with data from five newborn lambs, which were acquired during injection of vasodilator and vasoconstrictors and the results show a close match between experimental and simulated signals. The model-based estimation of vagal and sympathetic contributions were consistent with physiological knowledge and the obtained estimators of vagal and sympathetic activities were compared to traditional markers associated with baroreflex sensitivity. High correlations were observed between traditional markers and model-based indices.

Efficient Integration of Coupled Electrical-Chemical Systems in Multiscale Neuronal Simulations

Multiscale modeling and simulations in neuroscience is gaining scientific attention due to its growing importance and unexplored capabilities. For instance, it can help to acquire better understanding of biological phenomena that have important features at multiple scales of time and space. This includes synaptic plasticity, memory formation and modulation, homeostasis. There are several ways to organize multiscale simulations depending on the scientific problem and the system to be modeled. One of the possibilities is to simulate different components of a multiscale system simultaneously and exchange data when required. The latter may become a challenging task for several reasons. First, the components of a multiscale system usually span different spatial and temporal scales, such that rigorous analysis of possible coupling solutions is required. Then, the components can be defined by different mathematical formalisms. For certain classes of problems a number of coupling mechanisms have been proposed and successfully used. However, a strict mathematical theory is missing in many cases. Recent work in the field has not so far investigated artifacts that may arise during coupled integration of different approximation methods. Moreover, in neuroscience, the coupling of widely used numerical fixed step size solvers may lead to unexpected inefficiency. In this paper we address the question of possible numerical artifacts that can arise during the integration of a coupled system. We develop an efficient strategy to couple the components comprising a multiscale test problem in neuroscience. We introduce an efficient coupling method based on the second-order backward differentiation formula (BDF2) numerical approximation. The method uses an adaptive step size integration with an error estimation proposed by Skelboe (2000). The method shows a significant advantage over conventional fixed step size solvers used in neuroscience for similar problems. We explore different coupling strategies that define the organization of computations between system components. We study the importance of an appropriate approximation of exchanged variables during the simulation. The analysis shows a substantial impact of these aspects on the solution accuracy in the application to our multiscale neuroscientific test problem. We believe that the ideas presented in the paper may essentially contribute to the development of a robust and efficient framework for multiscale brain modeling and simulations in neuroscience.

Recursive identification of an arterial baroreflex model for the evaluation of cardiovascular autonomic modulation

The evaluation of the time-varying vagal and sympathetic contributions to heart rate remains a challenging task because the observability of the baroreflex is generally limited and the time-varying properties are difficult to take into account, especially in non-stationnary conditions. The objective is to propose a model-based approach to estimate the autonomic modulation during a pharmacological challenge. A recursive parameter identification method is proposed and applied to a mathematical model of the baroreflex, in order to estimate the time-varying vagal and sympathetic contributions to heart rate modulation during autonomic maneuvers. The model-based method was evaluated with data from five newborn lambs, which were acquired during injection of vasodilator and vasoconstrictor drugs, on normal conditions and under beta-blockers, so as to quantify the effect of the pharmacological sympathetic blockade on the estimated parameters. After parameter identification, results show a close match between experimental and simulated signals for the five lambs, as the mean relative root mean squared error is equal to 0.0026 (± 0.003). The error, between simulated and experimental signals, is significantly reduced compared to a batch identification of parameters. The model-based estimation of vagal and sympathetic contributions were consistent with physiological knowledge and, as expected, it was possible to observe an alteration of the sympathetic response under beta-blockers. The simulated vagal modulation illustrates a response similar to traditional heart rate variability markers during the pharmacological maneuver. The model-based method, proposed in the paper, highlights the advantages of using a recursive identification method for the estimation of vagal and sympathetic modulation.

Implementation of a model of bodily fluids regulation

The classic model of blood pressure regulation by Guyton et al. (Annu Rev Physiol 34:13–46, 1972a; Ann Biomed Eng 1:254–281, 1972b) set a new standard for quantitative exploration of physiological function and led to important new insights, some of which still remain the focus of debate, such as whether the kidney plays the primary role in the genesis of hypertension (Montani et al. in Exp Physiol 24:41–54, 2009a; Exp Physiol 94:382–388, 2009b; Osborn et al. in Exp Physiol 94:389–396, 2009a; Exp Physiol 94:388–389, 2009b). Key to the success of this model was the fact that the authors made the computer code (in FORTRAN) freely available and eventually provided a convivial user interface for exploration of model behavior on early microcomputers (Montani et al. in Int J Bio-med Comput 24:41–54, 1989). Ikeda et al. (Ann Biomed Eng 7:135–166, 1979) developed an offshoot of the Guyton model targeting especially the regulation of body fluids and acid–base balance; their model provides extended renal and respiratory functions and would be a good basis for further extensions. In the interest of providing a simple, useable version of Ikeda et al.’s model and to facilitate further such extensions, we present a practical implementation of the model of Ikeda et al. (Ann Biomed Eng 7:135–166, 1979), using the ODE solver Berkeley Madonna.

Sensitivity analysis and parameter estimation of a coronary circulation model for triple-vessel disease

Mathematical models of the coronary circulation have been shown to provide useful information for the analysis of intracoronary blood flow and pressure measurements acquired during coronary artery bypass graft (CABG) surgery. Although some efforts towards the patient-specific estimation of model parameters have been presented in this context, they are based on simplifying hypotheses about the collateral circulation and do not take advantage of the whole set of data acquired during CABG. In order to overcome these limitations, this paper presents an exhaustive parameter sensitivity analysis and a multiobjective patient-specific parameter estimation method, applied to a model of the coronary circulation of patients with triple vessel disease. The results of the sensitivity analysis highlighted the importance of capillary and collateral development. On the other hand, the estimation method was applied to intraoperative clinical data from ten patients obtained during CABG, which permitted to assess patient-specific collateral vessel situations. These approaches provide new insights regarding the heterogeneous configuration of the collateral circulation.

A model-based approach to investigating the pathophysiological mechanisms of hypertension and response to antihypertensive therapies: extending the Guyton model

Reproducibly differential responses to different classes of antihypertensive agents are observed among hypertensive patients and may be due to interindividual differences in hypertension pathology. Computational models provide a tool for investigating the impact of underlying disease mechanisms on the response to antihypertensive therapies with different mechanisms of action. We present the development, calibration, validation, and application of an extension of the Guyton/Karaaslan model of blood pressure regulation. The model incorporates a detailed submodel of the renin-angiotensin-aldosterone system (RAAS), allowing therapies that target different parts of this pathway to be distinguished. Literature data on RAAS biomarker and blood pressure responses to different classes of therapies were used to refine the physiological actions of ANG II and aldosterone on renin secretion, renal vascular resistance, and sodium reabsorption. The calibrated model was able to accurately reproduce the RAAS biomarker and blood pressure responses to combinations of dual-RAAS agents, as well as RAAS therapies in combination with diuretics or calcium channel blockers. The final model was used to explore the impact of underlying mechanisms of hypertension on the blood pressure response to different classes of antihypertensive agents. Simulations indicate that the underlying etiology of hypertension can impact the magnitude of response to a given class of therapy, making a patient more sensitive to one class and less sensitive others. Given that hypertension is usually the result of multiple mechanisms, rather than a single factor, these findings yield insight into why combination therapy is often required to adequately control blood pressure.

Sequentiality of daily life physiology: an automatized segmentation approach

Based on the hypotheses that (1) a physiological organization exists inside each activity of daily life and (2) the pattern of evolution of physiological variables is characteristic of each activity, pattern changes should be detected on daily life physiological recordings. The present study aims at investigating whether a simple segmentation method can be set up to detect pattern changes on physiological recordings carried out during daily life. Heart and breathing rates and skin temperature have been non-invasively recorded in volunteers following scenarios made of "daily life" steps (13 records). An observer, undergoing the scenario, wrote down annotations during the recording time. Two segmentation procedures have been compared to the annotations, a visual inspection of the signals and an automatic program based on a trends detection algorithm applied to one physiological signal (skin temperature). The annotations resulted in a total number of 213 segments defined on the 13 records, the best visual inspection detected less segments (120) than the automatic program (194). If evaluated in terms of the number of correspondences between the times marks given by annotations and those resulting from both physiologically based segmentations, the automatic program was better than the visual inspection. The mean time lags between annotation and program time marks remain <60 s (the precision of annotation times marks). We conclude that physiological variables time series recorded in common life conditions exhibit different successive patterns that can be detected by a simple trends detection algorithm. Theses sequences are coherent with the corresponding annotated activity.

Mathematical modeling of respiratory system mechanics in the newborn lamb

In this paper, a mathematical model of the respiratory mechanics is used to reproduce experimental signal waveforms acquired from three newborn lambs. As the main challenge is to determine specific lamb parameters, a sensitivity analysis has been realized to find the most influent parameters, which are identified using an evolutionary algorithm. Results show a close match between experimental and simulated pressure and flow waveforms obtained during spontaneous ventilation and pleural pressure variations acquired during the application of positive pressure, since root mean square errors equal to 0.0119, 0.0052 and 0.0094. The identified parameters were discussed in light of previous knowledge of respiratory mechanics in the newborn.

Virtual patients and sensitivity analysis of the Guyton model of blood pressure regulation: towards individualized models of whole-body physiology

Mathematical models that integrate multi-scale physiological data can offer insight into physiological and pathophysiological function, and may eventually assist in individualized predictive medicine. We present a methodology for performing systematic analyses of multi-parameter interactions in such complex, multi-scale models. Human physiology models are often based on or inspired by Arthur Guyton's whole-body circulatory regulation model. Despite the significance of this model, it has not been the subject of a systematic and comprehensive sensitivity study. Therefore, we use this model as a case study for our methodology. Our analysis of the Guyton model reveals how the multitude of model parameters combine to affect the model dynamics, and how interesting combinations of parameters may be identified. It also includes a "virtual population" from which "virtual individuals" can be chosen, on the basis of exhibiting conditions similar to those of a real-world patient. This lays the groundwork for using the Guyton model for in silico exploration of pathophysiological states and treatment strategies. The results presented here illustrate several potential uses for the entire dataset of sensitivity results and the "virtual individuals" that we have generated, which are included in the supplementary material. More generally, the presented methodology is applicable to modern, more complex multi-scale physiological models.

Reduced models for unidirectional block conduction and their geometrical setting

This article revisits a reduced model of cardiac electro-physiology which was proposed to understand the genesis of unidirectional block pathology and of ectopic foci. We underline some specificities of the model from the viewpoint of dynamical systems and bifurcation theory. We point out that essentially the same properties are shared by a simpler system more accessible to analysis. With this simpler system, it becomes possible to give a new presentation of the phenomenon in a phase plane with time moving slow manifolds. This presentation can be of interest both for cardiac electro-physiologists and for mathematicians.

Torsion of the human left ventricle: experimental analysis and computational modeling

We set a twofold investigation: we assess left ventricular (LV) rotation and twist in the human heart through 3D-echocardiographic speckle tracking, and use representative experimental data as benchmark with respect to numerical results obtained by solving our mechanical model of the LV. We aim at new insight into the relationships between myocardial contraction patterns and the overall behavior at the scale of the whole organ. It is concluded that torsional rotation is sensitive to transmural gradients of contractility which is assumed linearly related to action potential duration (APD). Pressure-volume loops and other basic strain measures are not affected by these gradients. Therefore, realistic torsional behavior of human LV may indeed correspond to the electrophysiological and functional differences between endocardial and epicardial cells recently observed in non-failing hearts. Future investigations need now to integrate the mechanical model proposed here with minimal models of human ventricular APD to drive excitation-contraction coupling transmurally.