A novel in vivo procedure for volumetric flow measurements

Pulsatile arterial wall-blood flow interaction with wall pre-stress computed using an inverse algorithm

Background

The computation of arterial wall deformation and stresses under physiologic conditions requires a coupled compliant arterial wall-blood flow interaction model. The in-vivo arterial wall motion is constrained by tethering from the surrounding tissues. This tethering, together with the average in-vivo pressure, results in wall pre-stress. For an accurate simulation of the physiologic conditions, it is important to incorporate the wall pre-stress in the computational model. The computation of wall pre-stress is complex, as the un-loaded and un-tethered arterial shape with residual stress is unknown. In this study, the arterial wall deformation and stresses in a canine femoral artery under pulsatile pressure was computed after incorporating the wall pre-stresses. A nonlinear least square optimization based inverse algorithm was developed to compute the in-vivo wall pre-stress.

Methods

First, the proposed inverse algorithm was used to obtain the un-loaded and un-tethered arterial geometry from the unstressed in-vivo geometry. Then, the un-loaded, and un-tethered arterial geometry was pre-stressed by applying a mean in-vivo pressure of 104.5 mmHg and an axial stretch of 48% from the un-tethered length. Finally, the physiologic pressure pulse was applied at the inlet and the outlet of the pre-stressed configuration to calculate the in-vivo deformation and stresses. The wall material properties were modeled with an incompressible, Mooney-Rivlin model derived from previously published experimental stress-strain data (Attinger et al., 1968).

Results

The un-loaded and un-tethered artery geometry computed by the inverse algorithm had a length, inner diameter and thickness of 35.14 mm, 3.10 mm and 0.435 mm, respectively. The pre-stressed arterial wall geometry was obtained by applying the in-vivo axial-stretch and average in-vivo pressure to the un-loaded and un-tethered geometry. The length of the pre-stressed artery, 51.99 mm, was within 0.01 mm (0.019%) of the in-vivo length of 52.0 mm; the inner diameter of 3.603 mm was within 0.003 mm (0.08%) of the corresponding in-vivo diameter of 3.6 mm, and the thickness of 0.269 mm was within 0.0015 mm (0.55%) of the in-vivo thickness of 0.27 mm. Under physiologic pulsatile pressure applied to the pre-stressed artery, the time averaged longitudinal stress was found to be 42.5% higher than the circumferential stresses. The results of this study are similar to the results reported by Zhang et al., (2005) for the left anterior descending coronary artery.

Conclusions

An inverse method was adopted to compute physiologic pre-stress in the arterial wall before conducting pulsatile hemodynamic calculations. The wall stresses were higher in magnitude in the longitudinal direction, under physiologic pressure after incorporating the effect of in-vivo axial stretch and pressure loading.

Quantification of myocardial blood flow using PET to improve the management of patients with stable ischemic coronary artery disease

ABSTRACT 

Cardiac PET has been evolving over the past 30 years. Today, it is accepted as a valuable imaging modality for the noninvasive assessment of coronary artery disease. PET has demonstrated superior diagnostic accuracy for the detection of coronary artery disease compared with single-photon emission computed tomography, and also has a well-established prognostic value. The routine addition of absolute quantification of myocardial blood flow increases the diagnostic accuracy for three-vessel disease and provides incremental functional and prognostic information. Moreover, the characterization of the vasodilator capacity of the coronary circulation may guide proper decision-making and monitor the effects of lifestyle changes, exercise training, risk factor modification or medical therapy for improving regional and global myocardial blood flow. This type of image-guided approach to individualized patient therapy is now attainable with the routine use of cardiac PET flow reserve imaging.

Womersley number-based estimates of blood flow rate in Doppler analysis: in vivo validation by means of phase-contrast MRI

A common clinical practice during single-point Doppler analysis is to measure the centerline maximum velocity and to recover the time-averaged flow rate by exploiting an assumption on the shape of velocity profile (a priori formula), either a parabolic or a flat one. In a previous study, we proposed a new formula valid for the peak instant linking the maximum velocity and the flow rate by including a well-established dimensionless fluid-dynamics parameter (the Womersley number), in order to account for the hemodynamics conditions (Womersley number-based formula). Several in silico tests confirmed the reliability of the new formula. Nevertheless, an in vivo confirmation is missing limiting the clinical applicability of the formula. An experimental in vivo protocol using cine phase-contrast MRI (2-D PCMRI) technique has been designed and applied to ten healthy young volunteers in three different arterial districts: the abdominal aorta, the common carotid artery, and the brachial artery. Each PCMRI dataset has been used twice: 1) to compute the value of the blood flow rate used as a gold standard and 2) to estimate the flow rate by measuring directly the maximum velocity and the diameter (i.e., emulating the intravascular Doppler data acquisition) and by applying to these data the a priori and the Womersley number-based formulae. All the in vivo results have confirmed that the Womersley number-based formula provides better estimates of the flow rate at the peak instant with respect to the a priori formula. More precisely, mean performances of the Womersley number-based formula are about three times better than the a priori results in the abdominal aorta, five times better in the common carotid artery, and two times better in the brachial artery.

Womersley number-based estimation of flow rate with Doppler ultrasound: sensitivity analysis and first clinical application

In this paper we continue in investigating the approach we have proposed in a paper recently published, for a reliable estimate of (peak systolic) blood flow rate from velocity Doppler measurements. Basic features of this approach together with some in silico test cases were discussed in that work. Here, we provide more insights of this approach by performing a sensitivity analysis of the formulas relating blood flow rate to velocity. In particular we analyze how our estimates are affected by perturbation or errors in measurements in comparison with a standard method for catheter based estimates based on the assumption of a parabolic velocity profile. A first glance to in vivo clinical applications is given as well.

In vivo comparison of three ultrasound vector velocity techniques to MR phase contrast angiography

The objective of this paper is to validate angle independent vector velocity methods for blood velocity estimation. Conventional Doppler ultrasound (US) only estimates the blood velocity along the US beam direction where the estimate is angle corrected assuming laminar flow parallel to vessel boundaries. This results in incorrect blood velocity estimates, when angle of insonation approaches 90 degrees or when blood flow is non-laminar. Three angle independent vector velocity methods are evaluated in this paper: directional beamforming (DB), synthetic aperture flow imaging (STA) and transverse oscillation (TO). The performances of the three methods were investigated by measuring the stroke volume in the right common carotid artery of 11 healthy volunteers with magnetic resonance phase contrast angiography (MRA) as reference. The correlation with confidence intervals (CI) between the three vector velocity methods and MRA were: DB vs. MRA: R=0.84 (p<0.01, 95% CI: 0.49-0.96); STA vs. MRA: R=0.71 (p<0.05, 95% CI: 0.19-0.92) and TO vs. MRA: R=0.91 (p<0.01, 95% CI: 0.69-0.98). No significant differences were observed for any of the three comparisons (DB vs. MRA: p=0.65; STA vs. MRA: p=0.24; TO vs. MRA: p=0.36). Bland-Altman plots were additionally constructed, and mean differences with limits of agreements (LoA) for the three comparisons were: DB vs. MRA=0.17 ml (95% CI: -0.61-0.95) with LoA=-2.11-2.44 ml; STA vs. MRA=-0.55 ml (95% CI: -1.54-0.43) with LoA=-3.42-2.32 ml; TO vs. MRA=0.24 ml (95% CI: -0.32-0.81) with LoA=-1.41-1.90 ml. According to the results, reliable volume flow estimates can be obtained with all three methods. The three US vector velocity techniques can yield quantitative insight into flow dynamics and visualize complex flow patterns, which potentially can give the clinician a novel tool for cardiovascular disease assessment.

Doppler derived quantitative flow estimate in coronary artery bypass graft: a computational multiscale model for the evaluation of the current clinical procedure

In order to investigate the reliability of the so called mean velocity/vessel area formula adopted in clinical practice for the estimation of the flow rate using an intravascular Doppler guide wire instrumentation, a multiscale computational model was used to give detailed predictions on flow profiles within Y-shaped coronary artery bypass graft (CABG) models. At this purpose three CABG models were built from clinical patient's data and used to evaluate and compare, in each model, the computed flow rate and the flow rate estimated according to the assumption of parabolic velocity profile. A consistent difference between the exact and the estimated value of the flow rate was found in every branch of all the graft models. In this study we showed that this discrepancy in the flow rate estimation is coherent to the theory of Womersley regarding spatial velocity profiles in unsteady flow conditions. In particular this work put in evidence that the error in flow rate estimation can be reduced by using the estimation formula recently proposed by Ponzini et al. [Ponzini R, Vergara C, Redaelli A, Veneziani A. Reliable CFD-based estimation of flow rate in haemodynamics measures. Ultrasound Med Biol 2006;32(10):1545-55], accounting for the unsteady nature of blood, applicable in the clinical practice without resorting to further measurements.

Comparisons between electromagnetic and X-beam transit-time flow measurements for evaluating drug actions on cardiac output in the conscious dog

INTRODUCTION

Cardiac output remains an important preclinical measurement for evaluating the cardiovascular effects of drugs. We evaluated the performance of the Triton Active Redirection Transit-Time, ART(2), which represents a new class of X-beam flow systems and compared it in vivo and in vitro to an electromagnetic flow (EMF) system for measuring large vessel flow.

METHODS

In vivo, simultaneous aortic flow measurements were obtained during alpha- and beta-adrenergic receptor stimulation in 5 conscious dogs instrumented with both ART(2) and EMF probes on their ascending aortas. In vitro, simultaneous measurements of volume flow using the ART(2), EMF, and timed-volume collection were made using a novel benchtop flow apparatus that ensured probe alignment and precise timed-volume flow measurements. Accuracy and sensitivity of both systems were assessed by recording flow measurements while varying rates, temperature and hematocrit.

RESULTS

In vivo aortic flow measurements between ART(2) and EMF were closely correlated (linear regression r(2) values ranged from 0.84 to 0.99), with the ART(2) system recording lower flow values than the EMF. In vitro ART(2) flow rates were in excellent agreement with timed-volume flow, while EMF flow rates were lower (p<0.05) and exhibited more variation and dependency upon temperature or hematocrit than the ART(2). Saline flows measured by ART(2) and EMF averaged 97+/-2% and 91+/-5% accuracy, respectively, over the temperature range 32 degrees C to 42 degrees C. For blood hematocrit values between 35% and 45%, ART(2) accuracy averaged 98+/-2%, compared to 89+/-5% accuracy with the EMF.

DISCUSSION

The ART(2) flow measurements in conscious dogs correlated closely to concurrent measurements obtained with the EMF over a wide range of flow rates, even though the absolute aortic flow values differed. Since it accurately measured flow in vitro, the ART(2) system is an appropriate alternative for evaluating cardiovascular effects of disease progression or drug administration in experimental animals.

Reliable CFD-based estimation of flow rate in haemodynamics measures

Physically useful measures in current clinical practice refer often to the blood flow rate, that is related to the mean velocity. However, the direct measurement of the latter is currently not possible using a Doppler velocimetry technique. Therefore, the usual approach to calculate the flow rate with this technique consists in measuring the maximum velocity and in estimating the mean velocity, making the hypothesis of parabolic profile that in realistic situations results in strongly inaccurate estimates. In this paper, we propose a different way for estimating the flow rate regarded as a function of maximum velocity and Womersley number. This relation is obtained by fixing a parametrised representation and by evaluating the parameters by means of a least-square approach working on the numerical results of CFD simulations (about 200). Numerical simulations are carried out by prescribing the flow rate, not the velocity profile. In this way, no bias is implicitly induced in prescribing boundary conditions. Validation tests based on numerical simulations show that the proposed relation improves the flow rate estimation.

Characterizing momentum change and viscous loss of a hemodynamic endpoint in assessment of coronary lesions

Myocardial fractional flow reserve (FFR(myo)) and coronary flow reserve (CFR), measured with guidewire, and quantitative angiography (QA) are widely used in combination to distinguish ischemic from non-ischemic coronary stenoses. Recent studies have shown that simultaneous measurements of FFR(myo) and CFR are recommended to dissociate conduit epicardial coronary stenoses from distal resistance microvascular disease. In this study, a more comprehensive diagnostic parameter, named as lesion flow coefficient, c, is proposed. The coefficient, c, which accounts for mean pressure drop, Delta p, mean coronary flow, Q, and percentage area stenosis, can be used to assess the hemodynamic severity of a coronary artery stenoses. Importantly, the contribution of viscous loss and loss due to momentum change for several lesion sizes can be distinguished using c. FFR(myo), CFR and c were calculated for pre-angioplasty, intermediate and post-angioplasty epicardial lesions, without microvascular disease. While hyperemic c decreased from 0.65 for pre-angioplasty to 0.48 for post-angioplasty lesion with guidewire of size 0.35 mm, FFR(myo) increased from 0.52 to 0.87, and CFR increased from 1.72 to 3.45, respectively. Thus, reduced loss produced by momentum change due to lower percentage area stenosis decreased c. For post-angioplasty lesion, c decreased from 0.55 to 0.48 with the insertion of guidewire. Hence, increased viscous loss due to the presence of guidewire decreased c compared with a lesion without guidewire. Further, c showed a linear relationship with FFR(myo), CFR and percentage area stenosis for pre-angioplasty, intermediate and post-angioplasty lesion. These baseline values of c were developed from fluid dynamics fundamentals for focal lesions, and provided a single hemodynamic endpoint to evaluate coronary stenosis severity.