Seven hemizygote Fabry patients (age range 22 – 42 years) and eight male control volunteers (age range 23 × 46 years) were enrolled in accordance with institutional guidelines. All volunteers and patients gave informed consent. All study participants were normotensive with serum cholesterols in the normal range. A right intra-brachial arterial line was placed in each subject followed by attachment to an analog disposable pressure transducer kit with a dynamic frequency response of 40 Hz for the fluid filled tubing and > 200 Hz for the pressure transducer alone (TruWave Disposable Pressure Transducer, Edwards Lifesciences, Irvine CA). The brachial artery pressure signal was digitized over a time interval of thirty seconds (National Instruments DAQ Card-AI-16E-4 digitizing frequency 2000 Hz, graphical user interface constructed in LabVIEW (version 5.1, 11500 Mopac Expwy, Austin, TX 78759-3504)). The real time signal was stored simultaneously with the right index finger pulse oximetry waveform right wrist radial artery external tonometry and EKG. The pulse wave speed was calculated by taking the difference between the upstroke of the brachial artery, radial artery external tonometer and the index finger pulse ensemble average waveforms. A total of three pulse wave speeds were measured as follows:- (a) between the intra-arterial brachial line and the external radial tonometer (b) between the intra-arterial brachial line and the index finger and (c) between the radial artery external tonometer and the index finger. The wave speed used in the Womersley flow calculation was taken as the average of the three measured wave speeds across the whole of the forearm vascular bed.
A representative pressure time waveform was calculated by taking the ensemble average of the sampled intra-arterial pulse pressure waveforms using the initial systolic upstroke as the reference point. The intra-brachial arterial line was used for infusion of acetylcholine (ACh) (dosage range 7.5 mg/min × 30 mg/min) and sodium nitroprusside (SNP) (dosage range 0.8 mg/min × 3.2 mg/min). Intra-brachial drugs were allowed to reach a steady state by continuous infusion over at least two minutes prior to recording the pressure waveform. At baseline and peak infusion dose of ACh and SNP the radial artery was imaged in real time using B-mode ultrasound (Cl-10 Mhz-5 MHz Probe, HDI 3000 ATL Lab, Bothell, WA) with the images stored on optical disk. Subsequently, the B-mode images were downloaded and converted from AVI video clips to single frame TIFF images followed by calculation of the spatial cross correlation allowing estimation of the peak systolic and diastolic frames. From the peak systolic and diastolic frames the incremental Young's elastic modulus (E) was calculated according to equation below
where ΔP is the pulse pressure range, ΔR is the change in the internal vessel radius over the cardiac-cycle, Ri is the internal vessel radius and Ro is the external vessel radius [4].
The pulse pressure for each subject was derived from the ensemble pressure waveform while estimates of the vessel radii were obtained directly from the TIFF images using NIH Image 1.62 in a blinded fashion. The peak systolic and peak diastolic images were measured separately but in an identical fashion by defining the perimeter of the arterial lumen and the external vessel wall perimeter defined by the medial-adventitial plane with a piece-wise polygon. Using NIH Image the respective internal and external areas were calculated. The caliper line placement along the intimal-medial border and the medial-adventitial interface was judged by review of the video records, and by calculation of a moving edge image by the logical .AND. combination of gradient images, and sequential time difference images. The individual internal and external vessel lengths were also measured and the internal and external vessel radii calculated by dividing the internal and external vessel areas by their respective lengths. This method allowed use of the whole vessel image in estimation of the arterial radii (Figure 1). Subtraction of the internal and external vessel diameters allowed estimation of the vessel wall thickness. The Womersley solution is the only analytical solution for time varying flow in a rigid infinitely long pipe. Validation of the equation for physiological flows has been performed with a high correlation between the calculated mean and observed mean flow [4]. The harmonic volume flow (Q) was calculated by using the following
where R is the internal vessel radius, A* is the complex conjugate of the pressure gradient, α is the Womersley parameter
, ω is the frequency, ρ is the fluid density, μ the fluid viscosity and J1 and J0 are first and zero order complex Bessel functions [7] and i = (-1)½. The calculation included the zeroth harmonic or mean flow up to the sixteenth harmonic. The pressure gradient for each individual measurement was determined by calculating the time derivative of the ensemble pulse pressure waveform
, interpolated with a natural cubic spline of 4096 points, by forward differencing. This derived function was then multiplied by the reciprocal of the wave speed (c) to give the spatial pressure gradient
as in the following equation [4].
An example of an ensemble pressure gradient waveform together with the associated derived Womersley volume flow is shown in Figure 2. The Womersley flow curves were integrated over the systolic and initial diastolic flow to give the estimated mean volume flow for each subject and pharmacological intervention after truncation of late diastolic flow. This was necessary since the integration of Womersley flow derived by estimation of the spatial pressure gradient from the arterial pressure time derivative over the complete time cycle is zero, and since the contribution of the late diastolic phase to volume flow is negligible. Using this model the subject's mean radial arterial Q was calculated at baseline and following the peak infusion of ACh (30 μg/minute) and SNP (3.2 μg /minute). Statistical analysis was performed in Matlab 6.0 (Natick, MA) using the Wilcoxon rank sum test.