Electrical lumped model for arterial vessel beds

Cardiovascular Circulatory System and Left Carotid Model: A Fractional Approach to Disease Modeling

Cardiovascular diseases (CVDs) remain the leading cause of death worldwide, according to recent reports from the World Health Organization (WHO). This fact encourages research into the cardiovascular system (CVS) from multiple and different points of view than those given by the medical perspective, highlighting among them the computational and mathematical models that involve experiments much simpler and less expensive to be performed in comparison with in vivo or in vitro heart experiments. However, the CVS is a complex system that needs multidisciplinary knowledge to describe its dynamic models, which help to predict cardiovascular events in patients with heart failure, myocardial or valvular heart disease, so it remains an active area of research. Firstly, this paper presents a novel electrical model of the CVS that extends the classic Windkessel models to the left common carotid artery motivated by the need to have a more complete model from a medical point of view for validation purposes, as well as to describe other cardiovascular phenomena in this area, such as atherosclerosis, one of the main risk factors for CVDs. The model is validated by clinical indices and experimental data obtained from clinical trials performed on a pig. Secondly, as a first step, the goodness of a fractional-order behavior of this model is discussed to characterize different heart diseases through pressure–volume (PV) loops. Unlike other models, it allows us to modify not only the topology, parameters or number of model elements, but also the dynamic by tuning a single parameter, the characteristic differentiation order; consequently, it is expected to provide a valuable insight into this complex system and to support the development of clinical decision systems for CVDs.

Arterial ammonia levels in cirrhosis are determined by systemic and hepatic hemodynamics, and by organ function: a quantitative modelling study

BACKGROUND & AIMS

Hyperammonaemia is a common complication of chronic liver failure. Two main factors are thought to underlie this complication: a loss of hepatic detoxification function and the development of portosystemic shunting. However, few studies have tried to quantify the importance of portosystemic shunting. Here, we used a theoretical approach to test the hypothesis that the development of portosystemic shunting is sufficient to cause hyperammonaemia in cirrhosis.

METHODS

Two mathematical models are developed. The first one describes the main vascular resistances of the circulation and is used to provide scenarios for the distributions of organ blood flow in cirrhosis, which are necessary to run the second model. The second model predicts arterial ammonia levels resulting from ammonia metabolism in gut, liver, kidney, muscle and brain, and the distribution of organ blood flow.

RESULTS

The fraction of gastrointestinal blood flow shunted through collaterals was estimated to be 41% in mild cirrhosis, 69% in moderate and 85% in severe cases. In the second model, the redistribution of organ blood flow associated with severe cirrhosis was sufficient to cause hyperammonaemia, even when the hepatic detoxification function and the ammonia production were set to normal.

CONCLUSIONS

The model indicates that the development of portosystemic shunting in cirrhosis is sufficient to cause hyperammonaemia. Interventions that reduce the fraction of shunting may be future targets of therapy to control severity of hyperammonaemia.

A novel distributed model of the heart under normal and congestive heart failure conditions

Conventional models of cardiovascular system frequently lack required detail and focus primarily on the overall relationship between pressure, flow and volume. This study proposes a localized and regional model of the cardiovascular system. It utilizes noninvasive blood flow and pressure seed data and temporal cardiac muscle regional activity to predict the operation of the heart under normal and congestive heart failure conditions. The analysis considers specific regions of the heart, namely, base, mid and apex of left ventricle. The proposed method of parameter estimation for hydraulic electric analogy model is recursive least squares algorithm. Based on simulation results and comparison to clinical data, effect of congestive heart failure in the heart is quantified. Accumulated results for simulated ejection fraction percentage of the apex, mid and base regions of the left ventricle in congestive heart failure condition were 39 ± 6, 36 ± 9 and 38 ± 8, respectively. These results are shown to satisfactorily match those found through clinical measurements. The proposed analytical method can in effect be utilized as a preclinical and predictive tool for high-risk heart patients and candidates for heart transplant, assistive device and total artificial heart.

Non-invasive vascular impedance measures demonstrate ocular vasoconstriction during isometric exercise

AIMS

The calculation of impedance for a vascular network is a common method used in circulation studies. Impedance indices (the ratios of the harmonics of pressure to the harmonics of flow) provide the investigator with a measure of the opposition to blood flow in a pulsatile system and are a proven indicator for vasculopathy. Previous studies investigating the eye's opposition to blood flow have concentrated on simple measures of resistance (the ratio of mean pressure difference to mean flow) which are more appropriate to a steady state or non-pulsatile system. The purpose of this study is to demonstrate a new, non-invasive, method to determine the vascular impedance of the eye during the known physiologic stress of sustained isometric exercise.

METHODS

Waveforms of ocular blood flow and carotid arterial blood pressure were measured non-invasively. Ocular blood flow waveforms were calculated using the Langham-Silver method by measuring the small fluctuations in intraocular pressure intraocular pressure over time with a high fidelity pneumatonometer. Carotid arterial blood pressure waveforms were determined using a SphygmoCor electronic tonometer held over the common carotid artery of the neck. Both waveforms were recorded simultaneously in normal volunteers under two conditions: (1) a baseline resting state and (2) during sustained isometric exercise. The components of the two waveforms (the harmonics) were calculated using a Fast Fourier transform and expressed as a ratio in order to determine a set of impedance values for each condition. The first four impedance values were calculated.

RESULTS

12 volunteers (six male: six female) with a mean age of 27 years (range 22-32 years) were recruited to the study. In comparison to baseline resting conditions, mean carotid blood pressure and heart rate both increased significantly during exercise: baseline mean carotid blood pressure, 82.6+/-8.2 mm Hg vs exercise mean carotid blood pressure, 93.8+/-12.8 mm Hg (p<0.001); baseline pulse rate, 64.6+/-9.1 BP(m) vs exercise pulse rate, 71.8+/-9.7 BP(m) (p<0.001). Compared to resting conditions, the first and third impedance values demonstrated significant change during exercise: the first impedance value rose (83.9+/-25.6 mm Hg-s/microl to 117.1 +/- 40.9 mm Hg-s/microl, p = 0.01) and the third impedance value fell (487.9 +/- 294.7 mm Hg-s/microl to 248.3+/-206.8 mm Hg-s/microl, p = 0.01).

CONCLUSIONS

The present study demonstrates, for the first time, a practical non-invasive method of calculating an index of impedance moduli for the pulsatile quotient of blood flow to the eye. Furthermore, during controlled isometric exercise, the impedance moduli displayed changes consistent with that known for a vascular system during vasoconstriction. The calculation of impedance moduli for the eye therefore shows promise for future investigations into ocular conditions where vascular obstruction is an aetiological factor.

Development of a Mathematical Model of the Human Circulatory System

A mathematical lumped parameter model of the human circulatory system (HCS) has been developed to complement in vitro testing of ventricular assist devices. Components included in this model represent the major parts of the systemic HCS loop, with all component parameters based on physiological data available in the literature. Two model configurations are presented in this paper, the first featuring elements with purely linear constitutive relations, and the second featuring nonlinear constitutive relations for the larger vessels. Three different aortic compliance functions are presented, and a pressure-dependent venous flow resistance is used to simulate venous collapse. The mathematical model produces reasonable systemic pressure and flow behaviour, and graphs of this data are included.