Left ventricular wave speed

Scalability and in vivo validation of a multiscale numerical model of the left coronary circulation

Multiscale modeling is a promising tool for the study of coronary hemodynamics. A key strength of this approach is that it accounts for microvascular properties and extravascular forces that differ regionally and transmurally, as well as wave propagation effects in the conduit arteries. However, little validation of such models has been reported and no models of the newborn coronary circulation have been described. We therefore validated a multiscale model of the left coronary circulation using high-fidelity data from nine adult sheep and nine newborn lambs and investigated whether wave propagation effects are more prominent in adults, whose body size (and hence wave transit distance) is greater. The model consisted of a one-dimensional (1D) network of the major conduit arteries and a lumped parameter model of microvascular beds. Intramyocardial pressure was considered to arise via contraction-related myocyte thickening and transmission of ventricular cavity pressure into the heart wall. 1D network geometry from published human anatomical data was scaled using myocardial weights, while subject-specific aortic pressure/flow and ventricular pressure formed model inputs. Total vascular resistance was determined iteratively from measured mean circumflex coronary flow (CxQ), but no fitting of phasic aspects of the waveform was performed. Excellent agreement was obtained between simulated and measured CxQ waveforms in most cases. Detailed flow waveform analysis did not clearly reveal a greater prominence of wave propagation effects in adults compared with newborns. This multiscale model is likely to be useful for investigating wave phenomena and phasic aspects of coronary flow in adults and during development.

Validation of a multi-scale model of the coronary circulation in adult sheep and newborn lambs

We validated a multi-scale model of a left-dominant coronary circulation using high fidelity pressure and flow data acquired in adult sheep and newborn lambs. The model incorporated a one-dimensional representation of the major left conduit coronary arteries, allowing for the study of wave propagation effects. The coronary microvasculature was represented by regional instances of a lumped parameter model consisting of three transmural layers, each with two serial compartments accounting for compliance, resistance and intramyocardial pressure effects. Model inputs comprised measured aortic pressure/flow and ventricular pressure. Minimal data fitting was employed, with only measured mean coronary flow used to iteratively adjust total coronary resistance. The model was adapted to different heart sizes via allometric scaling. Excellent agreement was observed between model and experimental flow waveforms in the proximal circumflex artery, both in terms of the degree of systolic flow impediment and transient waveform features. The proposed multi-scale modelling approach is likely to be useful for studying phasic features of the coronary flow waveform, including coronary waves in different coronary anatomies and throughout development.

Prediction of true circulatory decompensation in chronic heart failure for optimal timing of mechanical circulatory support: non-invasive arterial-ventricular coupling

Background: Prospective comparative studies to predict the risk of hemodynamic deterioration in patients referred for transplantation were performed on the basis of standard invasive and non-invasive data and new wave intensity (WI) parameters. Methods and results: Study Group 1 consisted of 151 consecutive outpatients (age 48.7 ± 12 years; 110 men) with end-stage dilative cardiomyopathy. Group 2, consisting of 11 consecutive patients (age 50 ± 11 years; 6 men) with sinus rhythm and “true” decompensation, was used to create “critical values” of WI. There were no demographic or somatic (weight and height) differences between the groups. The follow-up period of ambulatory patients was 31 ± 8 months. Non-invasive WI was studied in the common carotid artery. Complete invasive and non-invasive data were also recorded on the day of investigation. During follow-up 44 pts were lost; there were 15 cardiac deaths (10%), life-saving ventricular assist device implantation in 10 (6.6%) and transplantation in 19 (12.7%). For statistical purposes this group was named the “events” Group B (n = 44). A predisposing factor for events (death, “true” decompensation and “urgent” transplantation in ambulatory patients) was low first peak (“cut-off value” assessed in Group 2 < 4100 mmHg*s³) (OR 45.6, CI 14.5–143.3, p < 0.001). Less powerful predictors of the risk of deterioration were pulmonary capillary pressure (PCP), diastolic pulmonary artery pressure (PAP) and E/A mitral wave relation (p = 0.05). Conclusions: The new ventricular-arterial coupling parameter 1st peak of WI can potentially be used to distinguish patients at high risk for true deterioration and death. This parameter can be used to predict the need for assist device implantation.

Wave propagation and reflection in the canine aorta: analysis using a reservoir-wave approach

BACKGROUND

Our objective was to demonstrate wave propagation and reflection in the canine aorta. Recently we proposed that aortic pressure is the instantaneous sum of wave-related or "excess" pressure and reservoir or windkessel pressure. Accordingly, in this research we calculated reservoir pressure and subtracted it from measured pressure to identify the change in pressure due to forward- or backward-travelling waves.

METHODS

In 8 anesthetized dogs, excess pressures were calculated from pressure and flow measurements at 4 locations along the aorta; wave intensity analysis was employed to identify wavefronts and the type of waves.

RESULTS

We found that forward compression and decompression waves generated by the left ventricle are reflected, first, from a negative or "open-end" reflection site near the renal arteries (32.0 ± 0.8 cm [SEM] from the aortic root) and, second, from a positive site in the femoral arteries (65.3 ± 2.8 cm or 54.9 ± 2.1 cm, based on 2 alternative extrapolation techniques).

CONCLUSIONS

Aortic wave propagation and reflection can be demonstrated clearly and directly by wave intensity analysis after volume-related changes-changes in reservoir or windkessel pressure-in aortic pressure are accounted for.

Review of zero-D and 1-D models of blood flow in the cardiovascular system

Background

Zero-dimensional (lumped parameter) and one dimensional models, based on simplified representations of the components of the cardiovascular system, can contribute strongly to our understanding of circulatory physiology. Zero-D models provide a concise way to evaluate the haemodynamic interactions among the cardiovascular organs, whilst one-D (distributed parameter) models add the facility to represent efficiently the effects of pulse wave transmission in the arterial network at greatly reduced computational expense compared to higher dimensional computational fluid dynamics studies. There is extensive literature on both types of models.

Method and Results

The purpose of this review article is to summarise published 0D and 1D models of the cardiovascular system, to explore their limitations and range of application, and to provide an indication of the physiological phenomena that can be included in these representations. The review on 0D models collects together in one place a description of the range of models that have been used to describe the various characteristics of cardiovascular response, together with the factors that influence it. Such models generally feature the major components of the system, such as the heart, the heart valves and the vasculature. The models are categorised in terms of the features of the system that they are able to represent, their complexity and range of application: representations of effects including pressure-dependent vessel properties, interaction between the heart chambers, neuro-regulation and auto-regulation are explored. The examination on 1D models covers various methods for the assembly, discretisation and solution of the governing equations, in conjunction with a report of the definition and treatment of boundary conditions. Increasingly, 0D and 1D models are used in multi-scale models, in which their primary role is to provide boundary conditions for sophisticate, and often patient-specific, 2D and 3D models, and this application is also addressed. As an example of 0D cardiovascular modelling, a small selection of simple models have been represented in the CellML mark-up language and uploaded to the CellML model repository http://models.cellml.org/. They are freely available to the research and education communities.

Conclusion

Each published cardiovascular model has merit for particular applications. This review categorises 0D and 1D models, highlights their advantages and disadvantages, and thus provides guidance on the selection of models to assist various cardiovascular modelling studies. It also identifies directions for further development, as well as current challenges in the wider use of these models including service to represent boundary conditions for local 3D models and translation to clinical application.

Wave intensity analysis of left ventricular filling: application of windkessel theory

We extend our recently published windkessel-wave interpretation of vascular function to the wave intensity analysis (WIA) of left ventricular (LV) filling dynamics by separating the pressure changes due to the windkessel from those due to traveling waves. With the use of LV compliance, the change in pressure due solely to LV volume changes (windkessel pressure) can be isolated. Inasmuch as the pressure measured in the cardiovascular system is the sum of its windkessel and wave components (excess pressure), it can be substituted into WIA, yielding the isolated wave effects on LV filling. Our study of six open-chest dogs demonstrated that once the windkessel effects are removed from WIA, the energy of diastolic suction is 2.6 times greater than we previously calculated. Volume-related changes in pressure (i.e., the windkessel or reservoir effect) must be considered first when wave motion is analyzed.

Relationship between right ventricular wave speed and elastance in dogs

Wave speed (c) must be known to separate forward- and backward-going waves during wave-intensity analysis, which measures the energy transported by the waves in the circulation. c is related to elastance; the present study was performed to measure right ventricular (RV) c during the cardiac cycle and to compare c with RV elastance. In 7 dogs, we measured right atrial, pulmonary arterial, pericardial and 2 RV pressures, and pulmonary arterial flow. A pulse generator was connected to the RV apex, and c was measured by determining the transit time between the 2 high-fidelity RV pressure transducers; the distance was measured roentgenographically. Eight sonomicrometry crystals were implanted in the RV endocardium to calculate RV volume and, thereby, elastance. RV c ranged from ~1 m/s during diastole to ~4 m/s during systole. Log–log plots of c vs. elastance were linear. These slopes represent the power relationships between c and elastance and ranged from 0.30 to 0.56; for the combined data, it was 0.31. Given knowledge of c, forward- and backward-going waves can be identified and their energy quantitated. In the canine RV, c is approximately proportional to 1/3 the power of elastance: log c = 0.31·log E – 2.05.

Assessment of left ventricular diastolic suction in dogs using wave-intensity analysis

Two apparently different types of mechanisms have emerged to explain diastolic suction (DS), that property of the left ventricle (LV) that tends to cause it to refill itself during early diastole independent of any force from the left atrium (LA). By means of the first mechanism, DS depends on decreased elastance [e.g., the relaxation time constant (τ)] and, by the second, end-systolic volume (VLVES). We used wave-intensity analysis (WIA) to measure the total energy transported by the backward expansion wave ( IW−) during LV relaxation in an attempt to reconcile these mechanisms. In six anesthetized, open-chest dogs, we measured aortic, LV (PLV), LA (PLA), and pericardial pressures and LV volume by orthogonal ultrasonic crystals. Mitral velocity was measured by Doppler echocardiography, and aortic velocity was measured by an ultrasonic flow probe. Heart rate was controlled by pacing, VLVES by volume loading, and τ by isoproterenol or esmolol administration. IW− was found to be inversely related to τ and VLVES. Our measure of DS, the energy remaining after mitral valve opening, IW−DS, was also found to be inversely related to τ and VLVES and was ∼10% of the total “aspirating” energy generated by LV relaxation (i.e., IW−). The size of the Doppler (early filling) E wave depended on IW−DS in addition to IW+, the energy associated with LA decompression. We conclude that the energy of the backward-going wave generated by the LV during relaxation depends on both the rate at which elastance decreases (i.e., τ) and VLVES. WIA provides a new approach for assessing DS and reconciles those two previously proposed mechanisms. The E wave depends on DS in addition to LA decompression.

Wave Intensity Analysis of Left Ventricular Filling

Wave intensity analysis (WIA) is a powerful technique to study pressure and flow velocity waves in the time domain in vascular networks. The method is based on the analysis of energy transported by the wave through computation of the wave intensity dI=dPdU, where dP and dU denote pressure and flow velocity changes per time interval, respectively. In this study we propose an analytical modification to the WIA so that it can be used to study waves in conditions of time varying elastic properties, such as the left ventricle (LV) during diastole. The approach is first analytically elaborated for a one-dimensional elastic tube-model of the left ventricle with a time-dependent pressure-area relationship. Data obtained with a validated quasi-three dimensional axisymmetrical model of the left ventricle are employed to demonstrate this new approach. Along the base-apex axis close to the base wave intensity curves are obtained, both using the standard method and the newly proposed modified method. The main difference between the standard and modified wave intensity pattern occurs immediately after the opening of the mitral valve. Where the standard WIA shows a backward expansion wave, the modified analysis shows a forward compression wave. The proposed modification needs to be taken into account when studying left ventricular relaxation, as it affects the wave type.

Local and regional wave speed in the aorta: effects of arterial occlusion

Arterial wave speed is widely used to determine arterial distensibility and has been utilised as a surrogate marker for vascular disease. A comparison between the results of the traditional foot-to-foot method for measuring wave speed to those of the pressure-velocity loop (PU-loop) method is one of the primary objectives of this paper. We also investigate the regional wave speed along the aorta, and the effect of arterial occlusion on the PU-loop measured in the ascending aorta. In 11 anaesthetised dogs, a total occlusion lasting 3 min was produced at four sites: upper thoracic, diaphragm, abdominal and left iliac artery. Pressure and flow in the ascending aorta and pressure proximal to the occlusion site were measured, and data were collected before, during the occlusion and after the occlusion had been removed. In control conditions, the wave speeds determined by the PU-loop in the aortic root were systematically lower than those measured by the foot-to-foot method. During thoracic and diaphragm occlusions, mean aortic pressure and wave speed increased significantly but returned to control values after each occlusion had been removed. The PU-loop is an objective and easy to use method for determining wave speed and can be advantageous for use in short arterial segments when local measurements of pressure and velocity are available.

Pericardium modulates left and right ventricular stroke volumes to compensate for sudden changes in atrial volume

The pericardium may modulate acute compensatory changes in stroke volumes seen with sudden changes in cardiac volume, but such a mechanism has never been clearly demonstrated. In eight open-chest dogs, we measured left and right ventricular pressures, diameters, stroke volumes, and pericardial pressures during rapid (approximately 300 ms) systolic infusions or withdrawals of approximately 25 ml blood into and out of the left atrium and right atrium. Control beats, the infusion/withdrawal beat, and 4-10 subsequent beats were studied. With infusions, ipsilateral ventricular end-diastolic transmural pressure, diameter, and stroke volume increased. With the pericardium closed, there was a compensatory decrease in contralateral transmural pressure, diameter, and stroke volume, mediated by opposite changes in transmural end-diastolic pressures. The sum of the ipsilateral increase and contralateral decrease in stroke volume approximated the infused volume. Corresponding changes were seen with blood withdrawals. This direct ventricular interaction was diminished when pericardial pressure was <5 mmHg and absent when the pericardium was opened. Pericardial constraint appears essential for immediate biventricular compensatory responses to acute atrial volume changes.