Tracking time-varying properties of the systemic vascular bed

Particle swarm optimizer for arterial blood flow models

BACKGROUND AND OBJECTIVE

Mathematical modeling and computational simulations of arterial blood flow network can offer an insilico platform for both diagnostics and therapeutic phases of patients that suffer from cardiac diseases. These models are normally complex and involve many unknown parameters. For physiological relevance, these parameters should be optimized using in-vivo human/animal data sets. The main goal of this work is to develop an efficient, yet an accurate optimization algorithm to compute parameters in the arterial blood flow models.

METHODS

The particle swarm optimization (PSO) method is proposed herein for the first time, as an accurate algorithm that applies to computing parameters in the Windkessel type model of blood flow in the arterial system. We begin by defining a 6-element Windkessel (WK6) arterial flow model, which is then implemented and validated using multiple flow rate and aortic pressure measurements obtained from different subjects including dogs, pigs and humans. The parameters in the model are obtained using the PSO technique which minimizes the pressure root mean square (P-RMS) error between the computed and the measured aortic pressure waveform.

RESULTS

Model parameters obtained using the proposed PSO method were able to recover the pressure waveform in the aorta during the cardiac cycle for both healthy and diseased species (animals/humans). The PSO method provides an accurate approach to solve this challenging multi-dimensional parameter identification problem. The results obtained by PSO algorithm was compared with the classical gradient-based, namely the non-linear square fit (NLSF) algorithm.

CONCLUSIONS

The results indicate that the PSO method offers alternative and accurate method to find optimal physiological parameters involved in the Windkessel model for the study of arterial blood flow network. The PSO method has performed better than the NLSF approach as depicted from the P-RMS calculations. Finally, we believe that the PSO method offers a great potential and could be used for many other biomedicine optimization problems.

Determination of radial artery compliance can increase the diagnostic power of pulse wave velocity measurement

Pulse wave velocity (PWV) is an indicator associated with the arterial stiffness. Although this technique has been used in the diagnosis of systemic arterial hypertension (SAH), it cannot supply alone enough information about the pathogenesis of this disturbance. This paper aims to determine the compliance of brachial-radial arterial segment by applying a three-element windkessel model, and by using the same pressure waveforms acquired to calculate the PWV. The proposed method to determine the arterial compliance was evaluated with a physical simulation of the arterial system, where parameters were known, resulting in an estimation error of 0.73 x 10(-7) cm5 dyne(-1). In a clinical study the estimated compliance was statistically different (p < 0.01) in a controlled group ((3.12 +/- 3.53) x 10(-7) cm5 dyne(-1)) and in an SAH group ((1.04 +/- 0.74) x 10(-7) cm5 dyne(-1)). It was observed that the PWV value calculated using the maximum of the first derivative of the pressure waveform upstroke as characteristic points was the best correlated (r = -0.71) with the determined compliance. Because SAH normally results, among other causes. from a decreased arterial compliance the results suggest that the determined compliance could be used concomitantly with PWV to supply more diagnostic information about the pathogenesis of SAH.

Velocity profile method for time varying resistance in minimal cardiovascular system models

This paper investigates the fluid dynamics governing arterial flow used in lumped parameter cardiovascular system (CVS) models, particularly near the heart where arteries are large. Assumptions made in applying equations conventionally used in lumped parameter models are investigated, specifically that of constant resistance to flow. The Womersley number is used to show that the effects of time varying resistance must be modelled in the pulsatile flow through the large arteries near the heart. It is shown that the equation commonly used to include inertial effects in fluid flow calculations is inappropriate for including time varying resistance. A method of incorporating time varying resistance into a lumped parameter model is developed that uses the Navier-Stokes equations to track the velocity profile. Tests on a single-chamber model show a 17.5% difference in cardiac output for a single-chamber ventricle model when comparing constant resistance models with the velocity profile tracking method modelling time varying resistance. This increase in precision can be achieved using 20 nodes with only twice the computational time required. The method offers a fluid dynamically and physiologically accurate method of calculating large Womersley number pulsatile fluid flows in large arteries around the heart and valves. The proposed velocity profile tracking method can be easily incorporated into existing lumped parameter CVS models, improving their clinical application by increasing their accuracy.

Relationship between blood pressure and finger photoplethysmographic waveform during oxygen desaturation test: a model fitting approach

A modified 3-element windkessel model was applied to study the relationship between brachial arterial blood pressure and the photoplethysmographic waveform from pulse oximeters. Data were recorded from 12 healthy volunteers who underwent the oxygen desaturation study. During about 30 minutes recording period, the SpO2 value was regulated down till about 70%. After preprocessing, singular value decomposition (SVD) algorithm was then used to get the best fit of the model parameters.

RESULT

the fitting error (RMSE) was 1.07 +/- 0.48 mmHg. The time constant of the model shown significant difference between the highest and the lowest saturation group.

Modelling the relationship between peripheral blood pressure and blood volume pulses using linear and neural network system identification techniques

The relationships between peripheral blood pressure and blood volume pulse waveforms can provide valuable physiological data about the peripheral vascular system, and are the subject of this study. Blood pressure and volume pulse waveforms were collected from 12 normal male subjects using non-invasive optical techniques, finger arterial blood pressure (BP, Finapres: Datex-Ohmeda) and photoelectric plethysmography (PPG) respectively, and captured to computer for three equal (1 min) measurement phases: baseline, hand raising and hand elevated. This simple physiological challenge was designed to induce a significant drop in peripheral blood pressure. A simple first order lag transfer function was chosen to study the relationship between blood pressure (system input) and blood volume pulse waveforms (system output), with parameters describing the dynamics (time constant, tau) and input-output gain (K). Tau and K were estimated for each subject using two different system identification techniques: a recursive parameter estimation algorithm which calculated tau and K from a linear auto-regressive with exogenous variable (ARX) model, and an artificial neural network which was trained to learn the non-linear process input-output relationships and then derive a linearized ARX model of the system. The identification techniques allowed the relationship between the blood pressure and blood volume pulses to be described simply, with the neural network technique providing a better model fit overall (p < 0.05, Wilcoxon). The median falls in tau following the hand raise challenge were 26% and 31% for the linear and neural network based techniques respectively (both p < 0.05, Wilcoxon). This preliminary study has shown that the time constant and gain parameters obtained using these techniques can provide physiological data for the clinical assessment of the peripheral circulation.

Estimation of cardiac function from computer analysis of the arterial pressure waveform

This paper presents a method for estimating parameters of a cardiovascular model, including the left-ventricular function, using the sequential quadratic programming (SQP) and the least minimum square (LMS) algorithms. In a first stage, a radial arterial-pressure waveform with corresponding cardiac output are used to automatically seek the set of parameters of the diastolic model. Computer simulation of the model using these parameters generate a pressure waveform and a cardiac output very close to those used for the estimation. In a second stage, the estimated arterial load parameters are used to select the best left-ventricular model function, from four different possibilities, and to estimate its optimum parameter values. The method has been tested numerically and applied to real cases, using data obtained from cardiovascular patients. It has also been subjected to preliminary validation using data obtained from laboratory dogs, in which cardiovascular function was artificially altered.

Model-based estimation of vascular parameters: evaluation of robustness and suitability of models

Left ventricular performance depends not only on myocardial state, but also on the properties of the systemic arterial tree. These properties can be assessed from recordings of aortic root pressure and flow by the use of appropriate vascular models. Noninvasive estimates of aortic root pressure and flow can be obtained by the combined use of calibrated external subclavian artery pulse tracing and Doppler echocardiography. With recent advances in computer technology, estimation of model parameters are thus accessible in the clinical setting. We discuss the suitability of different parametric vascular models together with methods for adapting these models to the measured aortic root pressure. We compared the results obtained with simple vascular models (three-component modified Windkessel models) with those of five-component models. The simpler models gave less accurate approximation of the measured pressure waveform, but for a representative set of aortic root pressure and flow data, the simpler models provided adequate estimates of the peripheral arterial resistance, the total arterial compliance, and the proximal aortic area compliance. Furthermore, the simpler models are robust for measurement noise with simple estimation algorithms. Distal arterial pressure and flow waveforms are more oscillatory, and for these the five-component model has more robust estimation schemes with more accurate estimated parameters. Hence, we conclude that for clinical noninvasive assessment of aortic vascular properties, the simpler three-component models provide adequate information. For assessment of the peripheral arteries with large oscillations in the flow, the three-component models can give more than 10% error in the compliance estimate and more complex models can be appropriate.

Real-time cardiac output estimation of the circulatory system under left ventricular assistance

A new method for indirect and real-time estimation of the cardiac output of the circulatory system supported by the left ventricular assist device (LVAD) was proposed. This method has low invasiveness and is useful for clinical application of the LVAD since it needs only two measurements: the outflow rate of blood from the LVAD and the aortic pressure. The proposed method is based on a system identification technique for the time series model of the cardiovascular system and requires less computational time than other methods with similar estimation accuracy. Hence, the proposed method could be implemented in a personal computer system and realize the on-line and real-time estimation of the instantaneous outflow rate of the natural heart. The efficiency and limitation of the method were discussed on the basis of the results obtained from in vitro experiment using a mock circulatory system and in vivo experiment using an adult goat. It was revealed that the method could obtain a fairly high correlation coefficient between the true stroke volume of the natural heart and its estimate of more than 0.99 (in vivo) or 0.95 (in vivo). This means that there is a fair possibility of applying the proposed estimation system to the clinical use.

An automatic control algorithm for the optimal driving of the ventricular-assist device

This paper presents a new method of keeping one of the most suitable driving conditions for regulating the outflow volume from the ventricular-assist device (VAD). The experimental results from a mock circulatory system have shown that the relationship between the stroke volume and the systolic duration of the VAD can be specified by the combination of characteristic curves of the positive and negative drive pressures. The optimal operating point on the characteristic curve have been defined as the point at which thrombosis on the blood-contacting surface and hemolysis due to mechanical damage can be avoided and at which the driving energy can be minimized. The present analysis has been revealed that the optimal operating point is the vertex of the triangular figure obtained from the characteristic curve. The algorithms for keeping the optimal operating point and for regulating the stroke volume have been also proposed.

Real-time tracking of parameters of lung mechanics: emphasis on algorithm tuning

We consider the problem of tracking rapid changes in the viscous and elastic properties of the respiratory system by using mouth flow and transpulmonary pressure data measured during mechanical ventilation. A recursive least-squares algorithm with adjustable compensator is used for online estimation of an R-C model of the breathing mechanics. Specific simulation experiments are presented to provide guidelines to select suitable values for the key variable, which controls the compromise between tracking ability and noise sensitivity. The results obtained confirm the critical role of the optimum tuning in relation to the noise level. Experimental results obtained from data measured on mechanically-ventilated dogs, in which respiratory distress syndrome was intravenously induced by oleic acid, demonstrate that the tuned algorithm is able to track appropriately both the viscous and elastic properties of lung mechanics. Parameter estimates are consistent with those obtained by standard and robust offline algorithms and their time course is in qualitative agreement with known physiopathological behaviour.