Antoine Pironet

A multi-scale cardiovascular system model can account for the load-dependence of the end-systolic pressure-volume relationship

BackgroundThe end-systolic pressure-volume relationship is often considered as a load-independent property of the heart and, for this reason, is widely used as an index of ventricular contractility. However, many criticisms have been expressed against this index and the underlying time-varying elastance theory: first, it does not consider the phenomena underlying contraction and second, the end-systolic pressure volume relationship has been experimentally shown to be load-dependent.MethodsIn place of the time-varying elastance theory, a microscopic model of sarcomere contraction is used to infer the pressure generated by the contraction of the left ventricle, considered as a spherical assembling of sarcomere units. The left ventricle model is inserted into a closed-loop model of the cardiovascular system. Finally, parameters of the modified cardiovascular system model are identified to reproduce the hemodynamics of a normal dog.ResultsExperiments that have proven the limitations of the time-varying elastance theory are reproduced with our model: (1) preload reductions, (2) afterload increases, (3) the same experiments with increased ventricular contractility, (4) isovolumic contractions and (5) flow-clamps. All experiments simulated with the model generate different end-systolic pressure-volume relationships, showing that this relationship is actually load-dependent. Furthermore, we show that the results of our simulations are in good agreement with experiments.ConclusionsWe implemented a multi-scale model of the cardiovascular system, in which ventricular contraction is described by a detailed sarcomere model. Using this model, we successfully reproduced a number of experiments that have shown the failing points of the time-varying elastance theory. In particular, the developed multi-scale model of the cardiovascular system can capture the load-dependence of the end-systolic pressure-volume relationship.

Structural identifiability analysis of a cardiovascular system model

The six-chamber cardiovascular system model of Burkhoff and Tyberg has been used in several theoretical and experimental studies. However, this cardiovascular system model (and others derived from it) are not identifiable from any output set. In this work, two such cases of structural non-identifiability are first presented. These cases occur when the model output set only contains a single type of information (pressure or volume). A specific output set is thus chosen, mixing pressure and volume information and containing only a limited number of clinically available measurements. Then, by manipulating the model equations involving these outputs, it is demonstrated that the six-chamber cardiovascular system model is structurally globally identifiable. A further simplification is made, assuming known cardiac valve resistances. Because of the poor practical identifiability of these four parameters, this assumption is usual. Under this hypothesis, the six-chamber cardiovascular system model is structurally identifiable from an even smaller dataset. As a consequence, parameter values computed from limited but well-chosen datasets are theoretically unique. This means that the parameter identification procedure can safely be performed on the model from such a well-chosen dataset. Thus, the model may be considered suitable for use in diagnosis.

Model-based computation of total stressed blood volume from a preload reduction manoeuvre

Total stressed blood volume is an important parameter for both doctors and engineers. From a medical point of view, it has been associated with the success or failure of fluid therapy, a primary treatment to manage acute circulatory failure. From an engineering point of view, it dictates the cardiovascular systems behavior in changing physiological situations. Current methods to determine this parameter involve repeated phases of circulatory arrests followed by fluid administration. In this work, a more straightforward method is developed using data from a preload reduction manoeuvre. A simple six-chamber cardiovascular system model is used and its parameters are adjusted to pig experimental data. The parameter adjustment process has three steps: (1) compute nominal values for all model parameters; (2) determine the five most sensitive parameters; and (3) adjust only these five parameters. Stressed blood volume was selected by the algorithm, which emphasizes the importance of this parameter. The model was able to track experimental trends with a maximal root mean squared error of 29.2%. Computed stressed blood volume equals 486 ± 117 ml or 15.7 ± 3.6 ml/kg, which matches previous independent experiments on pigs, dogs and humans. The method proposed in this work thus provides a simple way to compute total stressed blood volume from usual hemodynamic data.

Simulation of left atrial function using a multi-scale model of the cardiovascular system

During a full cardiac cycle, the left atrium successively behaves as a reservoir, a conduit and a pump. This complex behavior makes it unrealistic to apply the time-varying elastance theory to characterize the left atrium, first, because this theory has known limitations, and second, because it is still uncertain whether the load independence hypothesis holds. In this study, we aim to bypass this uncertainty by relying on another kind of mathematical model of the cardiac chambers. In the present work, we describe both the left atrium and the left ventricle with a multi-scale model. The multi-scale property of this model comes from the fact that pressure inside a cardiac chamber is derived from a model of the sarcomere behavior. Macroscopic model parameters are identified from reference dog hemodynamic data. The multi-scale model of the cardiovascular system including the left atrium is then simulated to show that the physiological roles of the left atrium are correctly reproduced. This include a biphasic pressure wave and an eight-shaped pressure-volume loop. We also test the validity of our model in non basal conditions by reproducing a preload reduction experiment by inferior vena cava occlusion with the model. We compute the variation of eight indices before and after this experiment and obtain the same variation as experimentally observed for seven out of the eight indices. In summary, the multi-scale mathematical model presented in this work is able to correctly account for the three roles of the left atrium and also exhibits a realistic left atrial pressure-volume loop. Furthermore, the model has been previously presented and validated for the left ventricle. This makes it a proper alternative to the time-varying elastance theory if the focus is set on precisely representing the left atrial and left ventricular behaviors.

The Parametrized Diastolic Filling Formalism: Application in the Asklepios Population

The parametrized diastolic filling formalism is a kinematic model for early left ventricular diastolic function, and is believed to provide quantitative information on relaxation and stiffness. Application of this model in the Asklepios population provided normal values of the model parameters x0 (initial spring displacement), k (spring stiffness) and c (damping constant). In addition, a potentially important difference in c of about 20% between men and women was observed. The underlying mechanism is not clear and additional analyses are needed to verify whether or not this suggests intrinsic relaxation differences between men and women.Copyright

Model-Based Computation of Total Stressed Blood Volume from a Preload Reduction Experiment

Abstract Total stressed blood volume is an important parameter for both doctors and engineers. From a medical point of view, it has been associated with the success or failure of fluid resuscitation therapy, which is a treatment for cardiac failure. From an engineering point of view, this parameter dictates the cardiovascular systems dynamic behavior. Current methods to determine this parameter involve repeated phases of circulatory arrests followed by fluid administration. In this work, a method is developed to compute stressed blood volume from preload reduction experiments. A simple six-chamber cardiovascular system model is used and its parameters are adjusted to pig experimental data. The parameter adjustment process has three steps: (1) compute nominal values for all model parameters; (2) determine the most sensitive parameters; and (3) adjust only these sensitive parameters. Stressed blood volume was determined sensitive for all datasets, which emphasizes the importance of this parameter. The model was able to track experimental trends with a maximal mean squared error of 11.77 %. Stressed blood volume has been computed to range between 450 and 963 ml, or 15 to 28 ml/kg, which matches previous independent experiments on pigs, dogs and humans. Consequently, the method proposed in this work provides a simple way to compute total stressed blood volume from usual hemodynamic data.

Next-generation, personalised, model-based critical care medicine: a state-of-the art review of in silico virtual patient models, methods, and cohorts, and how to validation them

Critical care, like many healthcare areas, is under a dual assault from significantly increasing demographic and economic pressures. Intensive care unit (ICU) patients are highly variable in response to treatment, and increasingly aging populations mean ICUs are under increasing demand and their cohorts are increasingly ill. Equally, patient expectations are growing, while the economic ability to deliver care to all is declining. Better, more productive care is thus the big challenge. One means to that end is personalised care designed to manage the significant inter- and intra-patient variability that makes the ICU patient difficult. Thus, moving from current “one size fits all” protocolised care to adaptive, model-based “one method fits all” personalised care could deliver the required step change in the quality, and simultaneously the productivity and cost, of care. Computer models of human physiology are a unique tool to personalise care, as they can couple clinical data with mathematical methods to create subject-specific models and virtual patients to design new, personalised and more optimal protocols, as well as to guide care in real-time. They rely on identifying time varying patient-specific parameters in the model that capture inter- and intra-patient variability, the difference between patients and the evolution of patient condition. Properly validated, virtual patients represent the real patients, and can be used in silico to test different protocols or interventions, or in real-time to guide care. Hence, the underlying models and methods create the foundation for next generation care, as well as a tool for safely and rapidly developing personalised treatment protocols over large virtual cohorts using virtual trials. This review examines the models and methods used to create virtual patients. Specifically, it presents the models types and structures used and the data required. It then covers how to validate the resulting virtual patients and trials, and how these virtual trials can help design and optimise clinical trial. Links between these models and higher order, more complex physiome models are also discussed. In each section, it explores the progress reported up to date, especially on core ICU therapies in glycemic, circulatory and mechanical ventilation management, where high cost and frequency of occurrence provide a significant opportunity for model-based methods to have measurable clinical and economic impact. The outcomes are readily generalised to other areas of medical care.

Practical identifiability analysis of a minimal cardiovascular system model.

BACKGROUND AND OBJECTIVE Parameters of mathematical models of the cardiovascular system can be used to monitor cardiovascular state, such as total stressed blood volume status, vessel elastance and resistance. To do so, the model parameters have to be estimated from data collected at the patients bedside. This work considers a seven-parameter model of the cardiovascular system and investigates whether these parameters can be uniquely determined using indices derived from measurements of arterial and venous pressures, and stroke volume. METHODS An error vector defined the residuals between the simulated and reference values of the seven clinically available haemodynamic indices. The sensitivity of this error vector to each model parameter was analysed, as well as the collinearity between parameters. To assess practical identifiability of the model parameters, profile-likelihood curves were constructed for each parameter. RESULTS Four of the seven model parameters were found to be practically identifiable from the selected data. The remaining three parameters were practically non-identifiable. Among these non-identifiable parameters, one could be decreased as much as possible. The other two non-identifiable parameters were inversely correlated, which prevented their precise estimation. CONCLUSIONS This work presented the practical identifiability analysis of a seven-parameter cardiovascular system model, from limited clinical data. The analysis showed that three of the seven parameters were practically non-identifiable, thus limiting the use of the model as a monitoring tool. Slight changes in the time-varying function modeling cardiac contraction and use of larger values for the reference range of venous pressure made the model fully practically identifiable.

Minimally invasive estimation of ventricular dead space volume through use of Frank-Starling curves

This paper develops a means of more easily and less invasively estimating ventricular dead space volume (Vd), an important, but difficult to measure physiological parameter. Vd represents a subject and condition dependent portion of measured ventricular volume that is not actively participating in ventricular function. It is employed in models based on the time varying elastance concept, which see widespread use in haemodynamic studies, and may have direct diagnostic use. The proposed method involves linear extrapolation of a Frank-Starling curve (stroke volume vs end-diastolic volume) and its end-systolic equivalent (stroke volume vs end-systolic volume), developed across normal clinical procedures such as recruitment manoeuvres, to their point of intersection with the y-axis (where stroke volume is 0) to determine Vd. To demonstrate the broad applicability of the method, it was validated across a cohort of six sedated and anaesthetised male Pietrain pigs, encompassing a variety of cardiac states from healthy baseline behaviour to circulatory failure due to septic shock induced by endotoxin infusion. Linear extrapolation of the curves was supported by strong linear correlation coefficients of R = 0.78 and R = 0.80 average for pre- and post- endotoxin infusion respectively, as well as good agreement between the two linearly extrapolated y-intercepts (Vd) for each subject (no more than 7.8% variation). Method validity was further supported by the physiologically reasonable Vd values produced, equivalent to 44.3–53.1% and 49.3–82.6% of baseline end-systolic volume before and after endotoxin infusion respectively. This method has the potential to allow Vd to be estimated without a particularly demanding, specialised protocol in an experimental environment. Further, due to the common use of both mechanical ventilation and recruitment manoeuvres in intensive care, this method, subject to the availability of multi-beat echocardiography, has the potential to allow for estimation of Vd in a clinical environment.

Modelling of the nonlinear end-systolic pressure-volume relation and volume-at-zero-pressure in porcine experiments

The End-Systolic Pressure-Volume Relation (ESPVR) is generally modelled as a linear relationship between P and V as cardiac reflexes, such as the baroreflex, are typically suppressed in experiments. However, ESPVR has been observed to behave in a curvilinear fashion when cardiac reflexes are not suppressed, suggesting the curvilinear function may be more clinically appropriate. Data was gathered from 41 vena cava occlusion manoeuvres performed experimentally at a variety of PEEPs across 6 porcine specimens, and ESPVR determined for each pig. An exponential model of ESPVR was found to provide a higher correlation coefficient than a linear model in 6 out of 7 cases, and a lower Akaike Information Criterion (AIC) value in all cases. Further, the exponential ESPVR provided positive V0 values in a physiological range in 6 out of 7 cases analysed, while the linear ESPVR produced positive V0 values in only 3 out of 7 cases, suggesting linear extrapolation of ESPVR to determine V0 may be flawed.