Jonathan P. Mynard

A simple, versatile valve model for use in lumped parameter and one-dimensional cardiovascular models.

Lumped parameter and one-dimensional models of the cardiovascular system generally employ ideal cardiac and/or venous valves that open and close instantaneously. However, under normal or pathological conditions, valves can exhibit complex motions that are mainly determined by the instantaneous difference between upstream and downstream pressures. We present a simple valve model that predicts valve motion on the basis of this pressure difference, and can be used to investigate not only valve pathology, but a wide range of cardiac and vascular factors that are likely to influence valve motion.

Mechanisms of a reduced cardiac output and the effects of milrinone and levosimendan in a model of infant cardiopulmonary bypass

Objectives: A low cardiac output state is an important cause of morbidity after pediatric cardiopulmonary bypass. The objectives of our study were to define the early precipitants of the reduced cardiac output and to investigate the effects on these of milrinone and levosimendan in a model of pediatric cardiopulmonary bypass. Design: Experimental study. Setting: Research laboratory at a university‐affiliated, tertiary pediatric center. Subjects: Eighteen piglets. Interventions: Piglets, instrumented with systemic, pulmonary arterial, and coronary sinus catheters, pulmonary and circumflex arterial flow probes, and a left ventricular conductance‐micromanometer‐tipped catheter, underwent cardiopulmonary bypass with aortic cross‐clamp and cardioplegic arrest. At 120 mins, they were assigned to control, milrinone, or levosimendan groups and studied for a further 120 mins. Measurements and Main Results: In controls, between 120 and 240 mins, cardiac output decreased by 15%. Systemic vascular resistance was unchanged, but pulmonary vascular resistance increased by 19%. Systemic arterial elastance increased by 17%, indicating increased afterload. End‐systolic elastance was unchanged, and coronary sinus oxygen tension decreased by 4.0 ± 1.7 mm Hg. In animals receiving milrinone cardiac output was preserved, and in animals receiving levosimendan cardiac output increased by 14%. Both drugs prevented an increase in arterial elastance and pulmonary vascular resistance after cardiopulmonary bypass. Systemic vascular resistance decreased by 31% after levosimendan, and end‐systolic elastance increased by 48%, indicating improved contractility. Both agents prevented a decrease in coronary sinus oxygen tension. Conclusions: Increased afterload, which is not matched by an equivalent elevation in contractility, contributes to the reduced cardiac output early after pediatric cardiopulmonary bypass in this model. This increase is prevented by milrinone and levosimendan. Both agents exert additional beneficial effects on pulmonary vascular resistance and myocardial oxygen balance, although levosimendan has greater inotropic properties.

One-Dimensional Haemodynamic Modeling and Wave Dynamics in the Entire Adult Circulation

One-dimensional (1D) modeling is a powerful tool for studying haemodynamics; however, a comprehensive 1D model representing the entire cardiovascular system is lacking. We present a model that accounts for wave propagation in anatomically realistic systemic (including coronary and cerebral) arterial/venous networks, pulmonary arterial/venous networks and portal veins. A lumped parameter (0D) heart model represents cardiac function via a time-varying elastance and source resistance, and accounts for mechanical interactions between heart chambers mediated via pericardial constraint, the atrioventricular septum and atrioventricular plane motion. A non-linear windkessel-like 0D model represents microvascular beds, while specialized 0D models are employed for the hepatic and coronary beds. Model-derived pressure and flow waveforms throughout the circulation are shown to reproduce the characteristic features of published human waveforms. Moreover, wave intensity profiles closely resemble available in vivo profiles. Forward and backward wave intensity is quantified and compared along major arteriovenous paths, providing insights into wave dynamics in all of the major physiological networks. Interactions between cardiac function/mechanics and vascular waves are investigated. The model will be an important resource for studying the mechanics underlying pressure/flow waveforms throughout the circulation, along with global interactions between the heart and vessels under normal and pathological conditions.

The reservoir-wave paradigm introduces error into arterial wave analysis: a computer modelling and in-vivo study

Objectives: Arterial wave reflection has traditionally been quantified from pressure and flow measurements using wave separation and wave intensity (WI) analysis. In the recently proposed reservoir-wave paradigm, these analyses are performed after dividing pressure into ‘reservoir’ and ‘excess’ components, yielding a modified wave intensity (WIRW). This new approach has led to controversial conclusions about the nature and significance of arterial wave reflection. Our aim was to assess whether WI or WIRW more accurately represent wave phenomena. Methods: We studied two computer models (a simple network and a full model of the systemic arterial tree) in which all systolic forward waves and reflection properties were known a priori. Results of these models were compared with haemodynamic measurements in the ascending aorta of five adult sheep at baseline and after incremental arterial constriction. Results: The key findings of model studies were that the reservoir-wave approach markedly underestimated or eliminated reflected compression waves, overestimated or artefactually introduced forward and backward expansion waves, and displayed nonphysical interactions between distal reflection sites and early systolic waves. These errors arose because, contrary to a key assumption of the reservoir-wave approach, reservoir pressure was not spatially uniform during systole. In-vivo results were qualitatively similar to model results, with baseline WI and WIRW suggesting that the arterial network was dominated by positive and negative wave reflection, respectively, while under all conditions, reflected WIRW compression waves were substantially smaller than corresponding WI waves. Conclusion: We conclude that the reservoir-wave paradigm introduces error into arterial wave analyses.

Simultaneous pulmonary trunk and pulmonary arterial wave intensity analysis in fetal lambs: evidence for cyclical, midsystolic pulmonary vasoconstriction.

The physiological basis of a characteristically low blood flow to the fetal lungs is incompletely understood. To determine the potential role of pulmonary vascular interaction in this phenomenon, simultaneous wave intensity analysis (WIA) was performed in the pulmonary trunk (PT) and left pulmonary artery (LPA) of 10 anesthetized late-gestation fetal sheep instrumented with PT and LPA micromanometer catheters to measure pressure (P) and transit-time flow probes to obtain blood velocity (U). Studies were performed at rest and during brief complete occlusion of the ductus arteriosus to augment pulmonary vasoconstriction (n = 4) or main pulmonary artery to abolish wave transmission from the lungs (n = 3). Wave intensity (dI(W)) was calculated as the product of the P and U rates of change. Forward and backward components of dI(W) were determined after calculation of wave speed. PT and LPA WIA displayed an early systolic forward compression wave (FCW(is)) increasing P and U, and a late systolic forward expansion wave decreasing P and U. However, a marked midsystolic fall in LPA U to near-zero was related to an extremely prominent midsystolic backward compression wave (BCW(ms)) that arose approximately 5 cm distal to the LPA, was threefold larger than the PT BCW(ms) (P < 0.001), of similar size to FCW(is) at rest (P > 0.6), larger than FCW(is) following ductal occlusion (P < 0.05) and abolished after main pulmonary artery occlusion. These findings suggest that the absence of pulmonary arterial midsystolic forward flow which accompanies a low fetal lung blood flow is due to a BCW(ms) generated in part by cyclical vasoconstriction within the pulmonary microcirculation.

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.

Errors in the estimation of wall shear stress by maximum Doppler velocity

OBJECTIVE Wall shear stress (WSS) is an important parameter with links to vascular (dys)function. Difficult to measure directly, WSS is often inferred from maximum spectral Doppler velocity (Vmax) by assuming fully-developed flow, which is valid only if the vessel is long and straight. Motivated by evidence that even slight/local curvatures in the nominally straight common carotid artery (CCA) prevent flow from fully developing, we investigated the effects of velocity profile skewing on Vmax-derived WSS. METHODS Velocity profiles, representing different degrees of skewing, were extracted from the CCA of image-based computational fluid dynamics (CFD) simulations carried out as part of the VALIDATE study. Maximum velocities were calculated from idealised sample volumes and used to estimate WSS via fully-developed (Poiseuille or Womersley) velocity profiles, for comparison with the actual (i.e. CFD-derived) WSS. RESULTS For cycle-averaged WSS, mild velocity profile skewing caused ±25% errors by assuming Poiseuille or Womersley profiles, while severe skewing caused a median error of 30% (maximum 55%). Peak systolic WSS was underestimated by ~50% irrespective of skewing with Poiseuille; using a Womersley profile removed this bias, but ±30% errors remained. Errors were greatest in late systole, when skewing was most pronounced. Skewing also introduced large circumferential WSS variations: ±60%, and up to ±100%, of the circumferentially averaged value. CONCLUSION Vmax-derived WSS may be prone to substantial variable errors related to velocity profile skewing, and cannot detect possibly large circumferential WSS variations. Caution should be exercised when making assumptions about velocity profile shape to calculate WSS, even in vessels usually considered long and straight.

Wave intensity amplification and attenuation in non-linear flow: Implications for the calculation of local reflection coefficients

Local reflection coefficients (R) provide important insights into the influence of wave reflection on vascular haemodynamics. Using the relatively new time-domain method of wave intensity analysis, R has been calculated as the ratio of the peak intensities (R(PI)) or areas (R(CI)) of incident and reflected waves, or as the ratio of the changes in pressure caused by these waves (R(DeltaP)). While these methods have not yet been compared, it is likely that elastic non-linearities present in large arteries will lead to changes in the size of waves as they propagate and thus errors in the calculation of R(PI) and R(CI). To test this proposition, R(PI), R(CI) and R(DeltaP) were calculated in a non-linear computer model of a single vessel with various degrees of elastic non-linearity, determined by wave speed and pulse amplitude (DeltaP(+)), and a terminal admittance to produce reflections. Results obtained from this model demonstrated that under linear flow conditions (i.e. as DeltaP(+)-->0), R(DeltaP) is equivalent to the square-root of R(PI) and R(CI) (denoted by R(PI)(p) and R(CI)(p)). However for non-linear flow, pressure-increasing (compression) waves undergo amplification while pressure-reducing (expansion) waves undergo attenuation as they propagate. Consequently, significant errors related to the degree of elastic non-linearity arise in R(PI) and R(CI), and also R(PI)(p) and R(CI)(p), with greater errors associated with larger reflections. Conversely, R(Delta)(P) is unaffected by the degree of non-linearity and is thus more accurate than R(PI) and R(CI).

Pulmonary trunk, ductus arteriosus, and pulmonary arterial phasic blood flow interactions during systole and diastole in the fetus

Although the distribution of average fetal pulmonary trunk (PT) blood flow favors the ductus arteriosus (DA) over the lungs, the phasic aspects of this distribution during systole and diastole are not well understood. Accordingly, flow profile and wave intensity (WI) analyses were performed at baseline and during brief flow increases accompanying an extrasystole (ES) in 10 anesthetized late-gestation fetal sheep instrumented with PT, DA, and left pulmonary artery (PA) micromanometer catheters and transit-time flow probes. At baseline, 83% of mean PT flow crossed the DA and 17% entered the lungs. However, early systolic flow associated with a forward-running compression wave (FCW(is)) was higher in the PA and predominant DA flow only emerged in midsystole when a large PA backward-running compression wave (BCW(ms)), which reduced PA flow, was transmitted into the DA as a forward-running compression wave (FCW(ms)) that increased flow. Subsequent protodiastolic forward DA flow occurring during pulmonary valve closure was associated with substantial retrograde PA flow, but insignificant PT flow. Conversely, forward DA flow in the remainder of diastole occurred with forward PT but near-zero PA flow. These flow and WI patterns, in conjunction with the results of mathematical modeling, suggest that 1) fetal PT flow preferentially passes into the PA during early systole due to a lower PA-than-DA characteristic impedance, while DA flow predominates in mid- and late systole due to flow effects arising from the PA BCW(ms), and 2) forward DA flow is mainly sustained by reversal of PA flow in protodiastole but discharge of a more central reservoir in diastole.

Effect of velocity profile skewing on blood velocity and volume flow waveforms derived from maximum Doppler spectral velocity.

Given evidence that fully developed axisymmetric flow may be the exception rather than the rule, even in nominally straight arteries, maximum velocity (V(max)) can lie outside the Doppler sample volume (SV). The link between V(max) and derived quantities, such as volume flow (Q), may therefore be more complex than commonly thought. We performed idealized virtual Doppler ultrasound on data from image-based computational fluid dynamics (CFD) models of the normal human carotid artery and investigated how velocity profile skewing and choice of sample volume affected V(max) waveforms and derived Q variables, considering common assumptions about velocity profile shape (i.e., Poiseuille or Womersley). Severe velocity profile skewing caused substantial errors in V(max) waveforms when using a small, centered SV, although peak V(max) was reliably detected; errors with a long SV covering the vessel diameter were orientation dependent but lower overall. Cycle-averaged Q calculated from V(max) was typically within ±15%, although substantial skewing and use of a small SV caused 10%-25% underestimation. Peak Q derived from Womersleys theory was generally accurate to within ±10%. V(max) pulsatility and resistance indexes differed from Q-based values, although the Q-based resistance index could be predicted reliably. Skewing introduced significant error into V(max)-derived Q waveforms, particularly during mid-to-late systole. Our findings suggest that errors in the V(max) and Q waveforms related to velocity profile skewing and use of a small SV, or orientation-dependent errors for a long SV, could limit their use in wave analysis or for constructing characteristic or patient-specific flow boundary conditions for model studies.