Simple model of circulatory system dynamics including heart valve mechanics

This paper describes an extension of the Windkessel model of circulatory system dynamics, which takes into account the opening action of the mitral and aortic valves, including stenotic and regurgitant orifices. The starting point for the model is the ventricular emptying/filling curve which is taken from a quasi-physiological ventricular flow relationship which incorporates variation of systolic and diastolic intervals with cycle rate. The valves are assumed to open with a linear rise in area up to maximum orifice, followed by a period at maximum orifice and then a linear fall-off in area to the closed position (which may allow regurgitation). Flow through the valves is assumed to be governed by the Gorlin equation. Peripheral resistance and compliance are considered as fixed parameters of the arterial system. The model is useful in helping to understand the complex interaction between valvular mechanics and the rest of the cardiovascular system. Applications of the model are illustrated by considering isolated aortic stenosis, isolated aortic regurgitation, cardiac adaptation in the presence of these two abnormalities and the effects of variation of peripheral resistance on pressures within the cardiovascular system.

Validation of the orifice formula for estimating effective heart valve opening area

Interest in the Gorlin formula for estimating heart valve effective orifice area (EOA) has recently been rekindled and the formula itself has been challenged. In this validation study, explanted native heart valves, unimplanted mechanical prostheses, unimplanted bioprostheses and explanted bioprostheses have been tested in vitro in a pulsatile flow simulator. Pressures have been measured 30 mm upstream and 100 mm downstream from the plane of the valve sewing ring (to give pressure drop, pd in kPa). Flow (Q in 1 min-1) has been measured directly by electromagnetic flowmeter and orifice areas have either been taken from manufacturer supplied data (mechanical valves) or have been digitised from video images at maximum orifice (biological valves). The formula EOA = Q/(6.96 x pd 1/2) - 0.7 fitted the data with good correlation, r = 0.96 (n = 179). The orifice assumption on which this formula is based (cf. Gorlin formula) is confirmed though it is recommended that the formula should be modified to account for (i) the pressure recovery phenomenon and (ii) the fact that forward flow through a valve only occurs over a portion of the cycle in pulsatile flow. Heart rates used in the study ranged from 40 to 140 min-1, stroke volumes ranged from 20 to 114.3 ml, cardiac outputs from 2.0 to 8.0 1 min-1 and peripheral resistance from 0.1 to 1.6 kPa 1-1 min (1 - 12 mmHg l-1 min). Application of the formula was independent of the flow conditions.

A microcomputer-controlled cardiac stimulator

Detailed investigation of abnormal heart rhythms requires electrical stimulators that can deliver sophisticated sequences of stimuli to the heart under controlled laboratory conditions. A dual-channel stimulator that provides an appropriate hardware interface between a controlling microcomputer and the patient is described. The computer gives the system power and flexibility and, most importantly, provides a suitable user interface. The hardware interface is designed to have an ergonomic division between set-up and run-time tasks. Both software and hardware are discussed, and clinical examples of typical usage of the stimulator are given.

Ventricular stroke work loss: validation of a method of quantifying the severity of aortic stenosis and derivation of an orifice formula

Because aortic stenosis results in the loss of left ventricular stroke work (due to resistance to flow through the valve and turbulence in the aorta), the percentage of stroke work that is lost may reflect the severity of stenosis. This index can be calculated from pressure data alone. The relation between percent stroke work loss and anatomic aortic valve orifice area (measured by planimetry from videotape) was investigated in a pulsatile flow model. Thirteen valves were studied (nine human aortic valves obtained at necropsy and four bioprosthetic valves) at stroke volumes of 40 to 100 ml, giving 57 data points. Valve area ranged from 0.3 to 2.8 cm2 and mean systolic pressure gradient from 3 to 84 mm Hg. Percent stroke work loss, calculated as mean systolic pressure gradient divided by mean ventricular systolic pressure x 100%, ranged from 7 to 68%. It was closely related to anatomic orifice area with an inverse exponential relation and was not significantly related to flow (r = -0.15). An orifice formula was derived that predicted anatomic orifice area with a 95% confidence interval of +/- 0.5 cm2 (orifice area [cm2] = 4.82 [2.39 x log percent stroke work loss], r = -0.94, SEE = 0.029). These results support the clinical use of percent stroke work loss as an easily obtained index of the severity of aortic stenosis.

A comparison of the effects of two commonly used vasoconstrictors on nasal mucosal blood flow and nasal airflow

This study compared two commonly used vasoconstrictors, cocaine and xylometazoline. Non-invasive techniques of measurement were utilised, with active anterior rhinomanometry indirectly assessing changes in nasal mucosal blood volume, and laser Doppler flowmetry assessing changes in nasal mucosal blood flow. Twelve healthy volunteers received 0.1 ml of the topical vasoconstrictor at the anterior end of both inferior turbinates. Following the application of xylometazoline, a significant rise in nasal airflow (p less than 0.005), and a significant fall in blood flux occurred in the probe nostril (p less than 0.05). Following the application of cocaine, no significant change in nasal airflow occurred (p less than 0.05), but a significant fall in blood flux occurred in the probe nostril (p less than 0.02). A comparison of the paired data for the same subject demonstrated no significant difference in the change in blood flux produced by xylometazoline and cocaine, but a significant difference in the change in airflow produced by the two vasoconstrictors (p less than 0.005).

The effect of flow on Doppler estimates of bioprosthetic mitral valve function in vitro

In order to assess the effect of flow on peak transmitral velocity and pressure half time and to test the Hatle orifice area formula, four Carpentier-Edwards mitral prostheses were studied in a positive displacement flow simulator at 20 different stroke volume/rate combinations using a constant left ventricular filling curve. Peak transmitral velocity was directly related to mean flow and differed significantly between the individual values (F79 = 38; p less than 0.00001). There was, however, no significant difference in pressure half time between the four values (F79 = 0.04; p = 0.99). Pressure half time was directly related to diastolic time interval (r = 0.98, y = 0.41x - 17.84; p less than 0.00001), but was independent of stroke volume. There was only a moderate inverse correlation between pressure half time (T1/2) and orifice area (r = 0.56, y = 0.67 + 69/T1/2; p less than 0.0001). These results are consistent with the suggestion that pressure half time is more closely related to the shape of the left ventricular filling curve than to orifice area in normally functioning bioprostheses.

A comparison of the effects of xylometazoline on nasal airflow, and on blood flux as measured by laser Doppler flowmetry

The purpose of this study was to examine whether changes in mucosal blood flow measured directly by laser Doppler flowmetry corresponded to changes in turbinate blood volume measured indirectly as changes in nasal airflow. Fifteen healthy subjects underwent active anterior rhinomanometry and laser Doppler flowmetry prior to and following the topical application of 100 micrograms of xylometazoline to each nostril. A significant decrease in nasal resistance occurred in the probe nostril (p less than 0.001) and the non probe nostril (p less than 0.005) following xylometazoline. A significant fall in blood flux occurred with xylometazoline (p less than 0.05). There was no correlation between the percentage change in airflow (rhinomanometry) and the percentage change in blood flux (laser Doppler) following xylometazoline. These results suggest that laser flowmetry and rhinomanometry measure different parts of the inferior turbinate vascular bed.

Efficacy of aortic balloon valvoplasty: direct measurement of orificial area in a model with pulsatile flow

The efficacy of balloon valvoplasty of calcific aortic stenosis remains controversial. We studied, therefore, 5 human aortic valves obtained at necropsy in a positive-displacement pulse duplicator which delivered stroke volumes of 40-100 ml with a quasiphysiological waveform of flow. All valves had three leaflets without commissural fusion and were preserved in antibiotic solution before study. Orificial area was planimetered from videotape of opening of the valve and varied with flow in all cases. Valvoplasty with a 20 mm diameter balloon had no effect on the orifice of the normal valve but increased the orifice of 2 mildly calcified valves from 0.70-1.77 cm2 (range) at baseline to 1.06-1.95 cm2. In 2 valves with severe calcification of the leaflets, the orifice was increased from 0.31-0.82 cm2 to 0.73-1.07 cm2. Dual balloon valvoplasty achieved a variable but small further increase in orificial area. No valve showed tears of the leaflets or fracture of calcific deposits after valvoplasty. We conclude that balloon valvoplasty can acutely increase orificial area, independently of any change in stroke volume. In valves without commissural fusion, its mechanism appears to be an increase in the pliability of the leaflets which does not require macroscopic fracture of calcific deposits.

The Gorlin formula validated against directly observed orifice area in porcine mitral bioprostheses

To assess the effect of fluid flow on orifice area and to test the Gorlin formula, six Carpentier-Edwards mitral valve prostheses were studied in a positive displacement pulse duplicator at 20 different rate-stroke volume combinations. Peak transvalvular velocity (V max) was measured by continuous wave Doppler ultrasound, and orifice area was determined from hard copy of video images. Orifice area was directly related to mean flow (Q), although cusp opening behavior was asymmetric and complex and varied among the individual valves. There was a strong correlation between measured orifice area (OA) and the modified Gorlin relation, Q/V max (r = 0.88; p less than 0.00001) given by the regression formula OA = 0.18 x Q/V max - 0.15. There was also a good correlation between measured orifice area and the conventional Gorlin relation, Q/root mean pressure drop. The derived empiric Gorlin constant did not vary significantly with flow.

Reduced hyperaemic response under the diabetic neuropathic foot

Diabetic neuropathic ulcers typically occur at high pressure sites. Microvascular blood flow has been assessed on the plantar surface of the foot in three matched groups each of 12 subjects free from macrovascular disease: (a) patients with diabetic neuropathy with abnormal foot pressures and previous neuropathic ulceration; (b) non-neuropathic diabetic patients; (c) non-diabetic control subjects. Resting flow was measured at the highest pressure point under the metatarsal heads (defined by pedobarograph) using laser doppler flowmetry, and the hyperaemic response was assessed at the same site following 3 min standing. Peak flow was significantly reduced in neuropathic patients (2.3 +/- 1.4 (SD) volts) compared with control subjects (4.0 +/- 2.0 volts; p less than 0.03). The time for blood flow return to baseline was significantly prolonged in neuropaths (159 +/- 72 s) compared with normal subjects (93 +/- 18 s; p less than 0.01), with a significant delay also seen in non-neuropaths (151 +/- 38 s; p less than 0.0001 compared with normal).

Comparison of laser Doppler and Doppler ultrasound in lower limb vascular diagnosis

This study represents a preliminary investigation into the use of laser Doppler flowmetry in lower limb vascular diagnosis. The method is compared with the accepted method of continuous wave Doppler ultrasound. Fifty-six patients with symptoms of lower limb vascular disease were investigated consecutively and independently using both techniques. In approximately two-thirds of patients the two methods showed broad agreement in their classification of disease severity (correlation coefficient = 0.63, P less than 0.001, n = 41). However, about 30% of those studied had impaired microvascular responses on laser Doppler evaluation with no detectable major vessel disease on continuous wave ultrasound investigation. The results indicate that more information is obtained about a subject's vascular status when results from both methods are combined. Thus laser Doppler flowmetry may be useful adjunct to Doppler ultrasound and segmental pressure measurements in the vascular laboratory.

A one-dimensional model of atrioventricular nodal conduction

A computer model of the cardiac conduction process and an integral equation mathematical model have been employed to study the functions of the atrioventricular (AV) node. Special attention has been paid to the dependence of conduction delay on cycle length. The models have been used to evaluate the question as to whether simple cycle length dependences of AV nodal conduction could cause the oscillations of cycle length which are sometimes observed in AV reentry tachycardia. The models consider the AV node as a linear structure in which the depolarisation wavefront radiates in one dimension only. A model representing the node by two parallel linear structures has also been examined. Some results obtained do not conform with those of natural circumstance and clinical experiments, suggesting that the above hypotheses of AV nodal function are too simple and restricted to explain the natural processes.

Rapid autonomic tone regulation of atrioventricular nodal conduction in man

The changes in P-P intervals and atrioventricular nodal (AVN) conduction during the Valsalva maneuver were studied in 17 patients. In spite of a significant decrease in the sinus P-P interval during phase II of the maneuver (733 +/- 143 to 520 +/- 86 msec, p less than 0.005) and prolongation during phase IV (884 +/- 171 msec, p less than 0.01), there was no change in the AH interval (control: 78 +/- 15: phase II: 76 +/- 15: phase IV: 72 +/- 14 msec, N.S.). In six patients consecutive P-P intervals during phase II were recorded in solid-state memory and were used to trigger pacing of the high right atrium at rest. This showed a significant increase in the AH interval (75 +/- 10 to 123 +/- 45 msec, p less than 0.05). Valsalva maneuver during constant rate atrial pacing resulted in a significant decrease in the AH interval during phase II (115 +/- 36 to 80 +/- 15 msec, p less than 0.001). During phase IV there was prolongation of the AH interval (156 +/- 58 msec) but in 11 patients (61%) a variable degree of Wenckebach periodicity appeared. Thus autonomic tone modulates the changes in AVN conduction induced during physiologic heart rate variation, resulting in maintenance of adequate 1:1 AVN conduction.

Computer simulation of cardiac rhythm and artificial pacemakers using a ten-element heart model

This paper describes a universal simulation system which enables simulation models of cardiac rhythm disturbances and of artificial pacemaker actions to be constructed. Three types of heart element are introduced according to the way in which excitation impulses are propagated or produced. Cycle rate dependence of repolarization periods and of impulse transmission speeds is incorporated. Random and predetermined deviations from natural behavior are also allowed for in the model. Using the universal system, a model of simple configuration has been developed. There are five physiological and five pathological heart components joined together by uni- and bidirectional connectors. Additional bidirectional channels allow a variety of pacemakers to be "implanted" in the simulated heart.

Some aspects of computer modelling in cardiac electrophysiology

A computer model simulating the electrical activity of the heart is described. The model is designed for use in clinical cardiological research. Its implementation is based on the methods of discrete process simulation. The simulation program is written in FORTRAN, has approximately 12,000 lines and requires 160 kilobytes of memory to run. The whole heart is modelled, including a realistic description of the conduction system and a 'hollow shell' structure with a central plane representing the atrial, ventricular and septal components of the cardiac musculature. The myocardium itself is represented by simple hexagonal elements, which are pieced together to form the 'hollow shell'. The ideas used to develop the model are briefly described, but emphasis is given to clinical applications. The model is first validated by examining its output under well-known pathological conditions. Clinical applications, including predictive value, testing of hypotheses, and evaluation of pacemaker function, are then described, results being presented in the form of orthogonal lead projections.

Laser Doppler flowmetry: in the assessment of peripheral vascular disorders? A preliminary evaluation

Skin is a representative microvascular bed providing easy access for the study of capillary haemodynamics. In this preliminary evaluation we have used laser Doppler flowmetry to measure the response of skin capillary blood flow to local thermal stimulation. The purpose of our study was to see if such measurements can be used to derive useful clinical information. Thirty subjects, 15 male and 15 female, were selected to establish "normal' patterns of behaviour. All normal subjects studied showed similar patterns of response. There was a slight downward trend in red-blood-cell flux with age. Periods of vasomotor activity were present at rates ranging from 4-17 cycles/min. The mean temperature rise in the heated skin area was 4 degrees C. Blood flow over this range increased by a factor of 10 or more. Clinical cases studied were strictly limited to three categories of disease with known or suspected microvascular changes: algodystrophy, lower-limb ischaemia and diabetic neuropathy. All the clinical cases studied showed deviations from the normal pattern. Patients with algodystrophy had impaired peripheral vascular function in the affected area. Patients with lower-limb ischaemic problems all had poor peripheral perfusion. In the limited number of diabetic neuropathic feet studied two patterns emerged: patients with no evidence of ulceration displayed striking vasomotor activity; those with more severe problems had reduced red-blood-cell flux and little evidence of vasomotor control.

Shell computer model of cardiac electropotential changes

A discrete process computer model has been developed to simulate the electropotential changes of heart musculature and the operation of the cardiac conduction system. The model is implemented on an ICL-4/72 computer and is oriented to cardiac rhythm studies, allowing practically all rhythm pathologies, including pacemaker applications, to be simulated. The paper describes in detail the principles on which the model is based, compares the model with other models of the same system and shows concisely some results of simulation experiments in the form of computer generated ECG records.

Software control of sensing and stimulation for cardiac electrophysiological study

A software-controlled cardiac stimulator for clinical investigations is described. The stimulator is programmed by the user at a keyboard, while current status and values of parameters are presented on a visual display screen. A menu of predefined cardiac electrophysiological tests is available for user selection. Validity checks on data keyed in by the user and internal checks on safe pacing limits are incorporated in case of malfunction or user error. The system consists of a separate relatively simple isolated sensing and stimulation unit which communicates, via a standard digital input output interface, with a controlling microcomputer. All timing and control functions are performed in software by the computer. The use of high-level FORTRAN as the main programming language provides the system with a high degree of adaptability.

Computer simulation of the cardiac conduction system

A discrete computer model simulating the operation of the cardiac impulse transmission apparatus and the electropotential changes of the heart musculature has been developed on a NORD-100 minicomputer. The model is written in NORD-FORTRAN and allows description of practically all basic pathologies of the transmission apparatus. A simulated ECG curve is produced in each case. The current version of the model is especially suited for studies of heart rhythms. Pacemaker descriptions (of most important pacemaker types) have been introduced into the model and the computer computations make it possible to assess the effects of different pacemaker modes under different pathological situations. The principles on which the model is based is described and the paper shows concisely several examples in the form of simulated ECG records.

Cardiac electrophysiological studies: computer analysis using a digitiser and interactive visual display unit

Recording of localised intracardiac electrical potentials provides useful and important information on conduction disease in man. Analysis of intracardiac recordings involves measurement of large numbers of timing intervals representing the sequence of activation of the various part of the cardiac conduction system. In this paper we describe a semi-automatic computer based analysis system tailored to the specific requirements of cardiac electrophysiological measurement. A digitising tablet is used in conjunction with a visual display oriented data handling package to input data directly to computer memory for sorting and further analysis. Particular attention is paid to providing the user with a system that is simple to learn yet is robust and flexible in use. The computer software is written entirely in the high level FORTRAN language. It is modular in design and is therefore easily adapted for the changing needs of a research oriented department.