Regional in vivo transit time measurements of aortic pulse wave velocity in mice with high-field CMR at 17.6 Tesla

During each systole the left ventricle of the heart ejects one stroke volume of blood into the aortic root, hence, generating a pulse beat. The pulse beat that in fact is a local increase of blood pressure and flow velocity propagates down the aorta with a velocity that is named the pulse wave velocity (PWV).

The principle to measure arterial PWV with the TT method is as follows. At least two measurement sites, I and II in Figure 1a, are to be selected on the aorta at a mutual distance, Δz. The transit time, Δt, which the pulse needs to travel from location I to II is to be measured (see Figure 1b). The PWV is calculated as PWV = Δz/Δt. This procedure is called the two-point TT method.

The generalization of the two-point TT method is the multi-point TT method [28‐30]. It measures the transit times of the pulse waves in multiple locations along the path of wave propagation. The PWV is the constant of proportionality between the distances and the corresponding transit times.

Figure 1b and 2a reveal that flow and pressure pulse curves show a gradual rather than an instantaneous increase. However, a distinctive feature, the foot of the pulse wave, is necessary to determine the transit time. The foot of the pulse wave is defined as the intersection point of a regression line fitted to the velocity or pressure values before the pulse and another line fitted to the early increasing values.

The accuracy of the MR method was tested on an elastic vessel phantom that was connected to a custom built flow and pressure pulse generator. The phantom allowed for the determination of PWVs by CMR measurements of flow waveforms and for reference measurements of pressure waveforms utilizing a pressure catheter that was inserted in the outlet end of the vessel (Figure 3). The PWVs obtained by the two different measurement methods were compared to each other in order to give evidence of the accuracy and precision of the MR method.

The phantom material had to have appropriate physical properties, e.g., mechanical strength, uniformity, long-term stability, and a modulus of elasticity resembling animal tissue. Poly(vinyl alcohol) cryogel (PVA-C), discovered independently by Peppas et al. and Nambu et al. [31, 32], has high breaking strengths and physiologic elastic moduli ranging from 0.1 to 1.0 MPa [33] and was, therefore, used to build the phantom vessel. Aqueous poly(vinyl alcohol) solution (15% w/w) was injected into an acrylic mold and crosslinked to form the gel by repeated freezing and thawing. The elastic modulus of the gel depends amongst others on the number of the freeze-thaw cycles, on the concentration of the aqueous solution, and essentially on the thaw rate [33, 34].

The vessel phantom had an inner diameter of 6 mm and a wall thickness of 0.25 mm. Its length was approximately 8 cm. The vessel was dimensioned according to Eq.[1], the Moens-Korteweg equation [35], to have a PWV in the physiological range of 2.0 to 6.5 m/s.

E is Young's modulus of elasticity, h and d are the vessel wall thickness and the diameter, and ρ is the fluid density. The phantom was stored in a water bath to stabilize for at least 14 days prior to measurements because PVA-C is subject to an aging process that can affect its elasticity [34].

A homemade pressure and flow pulse generator was connected to the inlet end of the vessel phantom. A function generator (F34, Interstate Electronics Corporation, Anaheim, CA, USA) controlled the pulse generator. The function generator was set to generate pressure pulses every 1.8 s. Therewith, residual waves reflected at impedance mismatches inside the vessel phantom setup could decay completely between pulses. The function generator also triggered the data acquisitions of the MR system and of the setup used to record the pressure waves inside the vessel phantom.

The setup to record pressure waves comprised a pressure catheter, a signal amplifier, and a storage oscilloscope. The catheter was compounded of a blunted canula (TSK-Supra, Ebhardt-Söhne GmbH, Geislingen, Germany) and a Statham P23XL pressure transducer (Viggo-Spectramed, Inc., Oxnard, CA, USA). The signal amplifier was an MBS STAT ZAK (ZAK Psychologische und Physiologische Instrumente GmbH, Simbach, Germany). The storage oscilloscope was a TDS 3032 (Tektronix Inc., Beaverton, OR, USA).

The outlet end of the vessel was connected to a reservoir filled with an aqueous solution of 1.75 mM CuSO₄. The height of the reservoir was adjusted in order that the vessel did not bloat or collapse. Two plastic rods supported the vessel on one side to prevent it from swinging in the transversal direction but allowed it to expand during the transit of the pulse.

The multi-point TT method was used to determine the PWV of the vessel phantom by pressure measurements. The measurement positions of the pressure catheter were determined at its protruding end with a calliper gauge. The pressure data were analyzed in MATLAB (The Mathworks, Inc., Natick, MA, USA) to determine the onset times of the pressure waves for each measurement position of the pressure catheter. The measurement positions were plotted versus the corresponding pressure pulse onset times. The slope of the linear regression yielded the PWV (see Figure 2b). The multi-point TT measurements were performed at six different installation heights of the vessel phantom that ranged from -13 mm to 12 mm from the MR iso-center. The PWV at the MR iso-center was determined by linear regression through the PWV and installation height values.

The MR system that was used for the phantom and in vivo measurements was a Bruker AVANCE 750 spectrometer (Bruker Biospin, Rheinstetten, Germany) with a vertical main magnetic field of 17.6 T and a bore size of 89 mm. The self-shielded gradient insert, a Bruker Micro 2.5, had a maximum gradient strength of 993 mT/m and an inner diameter of 40 mm. The homebuilt transversal electromagnetic mode radio frequency (RF) resonator had an accessible inner diameter of 25 mm.

The MR sequence applied phase velocity encoding to record the time courses of the flow velocities. The sequence was based on a two-dimensional FLASH sequence with incorporated velocity compensating gradients in all three gradient directions (Figure 4). To encode through-slice flow velocities, bipolar velocity encoding gradients were superposed onto the velocity compensating gradients in the slice direction. Three flow encoding steps were applied to each scan. The velocity-encoding window of the MR sequence was set to ± 0.20 m/s to accommodate the maximal flow velocities. The flow encoding gradients required the maximal available gradient power.

Transit times of the pulse waves are in the range of a few milliseconds, therefore, a temporal resolution of 1 ms was necessary to be able to obtain the PWV from the time courses of arterial blood flow velocities. The intrinsic temporal resolution of the MR sequence, equivalent to its repetition time, was 5 ms. Hence the time courses of the flow velocities had to be sampled in an interleaved fashion. The sequence was initiated five times, every time with an additional delay of 1 ms between the trigger signal and the initiation of the sequence. The resulting five data streams were interleaved in the post processing to generate a recording of flow velocities with a temporal resolution of 1 ms. The detailed timing and loop structure of the MR sequence are visualized in Figure 4.

The spatial in-plane resolution was 147 × 147 μm² and the slice thickness was 1 mm. The field of view (FOV) was 22 × 22 mm². The echo time was 1.6 ms. The Gauss RF excitation pulse had a length of 200 μs and an excitation angle of 20°. Signal averaging was not applied.

The two-point and multi-point TT methods were used to determine the PWV of the vessel phantom by MR measurements. A set of two-dimensional Fast Low Angle Shot (FLASH) experiments was leading the measurement protocol to localize the measurement positions on the vessel phantom. The MR imaging slices were positioned perpendicularly to the vessel at positions ±2.5 mm, ± 5.0 mm, ± 7.5 mm, and ± 10.0 mm from the magnets iso-center. A perpendicular slice orientation was crucial to avoid displacement artifacts caused by fluid flowing out of the imaging slice.

MR data were processed with a custom written routine using MATLAB. Velocity information was computed for pixels inside the vessel lumen by fitting a line to the phase values as a function of the first moments of the velocity encoding gradients (phase difference method). For every time frame the velocities were averaged over the luminal area.

64 pressure measurements were performed before 80 MR measurements. Differences in the mean PWV values obtained on the vessel phantom by the two measurement methods were tested by a two-sided t-test for unpaired data points for the hypothesis of equality against the alternative of differing values. The data points were not paired because many parameters, such as static pressure, temperature, and acoustic noise could not be held constant during the transition from pressure to MR measurements due to limited access and the strong magnetic field inside the magnet. The hypothesis was accepted for p-values ≥ 0.05. PWV values are given as mean ± standard error (SE).

The proposed MR method was designed to utilize the two-point TT method in vivo in the descending murine aorta. Nine MR measurements were performed on a group of five female eight-month-old ApoE^(-/-) mice and eight measurements on a group of four age- and sex-matched C57Bl/6J mice. The ApoE^(-/-) mice were fed a western type diet (TD 88137, Harlan Laboratories, Inc., Indianapolis, IN, USA) 10 weeks prior to MR measurements. During the MR examinations, the mice were anesthetized with an isoflurane inhalation (1.5 - 2.0 Vol.%) in O₂ (2 L/min) applied by means of a nose cone. Mice were placed vertically (head up) in the RF resonator. Due to the small diameters of the gradient insert and the RF resonator, their body temperature could be kept constant at 37°C by adjusting the temperature of the gradient insert temperature control unit.

A pressure sensitive pneumatic balloon (Graseby Medical Limited, Watford, United Kingdom) was placed between the inner RF resonator wall and thoraces of mice to detect cardiac trigger and respiratory gating signals. Outside of the gradient insert, a pressure transducer (24PCEFA6 D, Honeywell S&C, Golden Valley, MN, USA) transformed the pressure signal from the balloon into an electrical signal that was amplified and processed in real-time by a homebuilt unit. Thus, electrical interference between the trigger signal and gradient fields oscillating in the same frequency domain was avoided.

All experimental procedures were in accordance with institutional and internationally recognized guidelines and were approved by the Regierung von Unterfranken (Government of Lower Franconia, Germany). The reference number of the permit of the animal experiments is 55.2-2531.01-19/07.

Two imaging slices were positioned perpendicularly to the thoracic and the abdominal aorta (as illustrated in Figure 1a). Reasonable in vivo experiment times only allowed for the two-point TT method to be applied. Slice separations were maximized in order to minimize the errors in the measured PWVs. Again, a perpendicular slice orientation was of crucial importance. To localize the descending aorta, a set of two-dimensional FLASH experiments was leading the measurement protocol.

The velocity-encoding window was set to ± 1.66 m/s to accommodate the maximal blood flow velocities. The RF excitation pulse had an excitation angle of 40°. The mice had a heart period of approximately 115 ms. A time window of 40 ms was sufficient to sample the late diastole and early systole. All other parameters of the measurement protocol were set as in the measurements on the vessel phantom. The total image acquisition times ranged from 15 to 20 min.

MR data were processed using the MATLAB routine that was also used for the analysis of the data acquired on the vessel phantom. The curve progression in the velocity-time diagrams showed sharp bends between the sections before and during the pulse. This allowed for a semi automatic selection of the fit ranges that defined the onset times of the flow pulse. The fit range before the pulse was selected manually. It included data points on an approximate horizontal line. The beginning of the pulse fit region was set automatically as a series of three consecutive data points with velocity values at least two standard deviations above the extrapolated fit line of the section before the pulse. The end point was selected manually as the last data point on the first straight portion of the flow pulse section. The program AMIRA (Visage Imaging, Inc., San Diego, CA, USA) was applied to gauge the distance between the two measurement locations. Therefore, straight-line segments were drawn along the luminal midline in a longitudinal reference scan of the aorta.

Isoflurane causes respiratory depression and, therefore, anesthetized mice develop a gasping breathing pattern with a period of approximately 1 s to 1.5 s. The duration of each respiratory movement is approximately 0.4 s. The MR data were acquired in the intermediate movement-free time intervals. From the periodicity of previous respirations, the homebuilt heart-triggering/breath-gating unit anticipates the next phase of respiratory motion and stops the MR data acquisition before the respiratory motion sets in. Data acquisition is continued approximately 0.4 s after the detected onset of breathing motion. Occasionally, the breathing pattern was not precisely periodic. Then data was acquired during the respiratory movement and motional artifacts in the MR images were the result. Sporadic non-periodic respiration was observed during all measurements, but showed no adverse motional artifacts in most of the measurements. In some of the motional artifacts, the signal amplitude and phase information of extra-luminal pixels were shifted into the vessel lumen. Those pixels were excluded from the calculation of the flow velocities when the anatomical structures that those pixels belonged to could be identified visually.

Differences in the mean PWV values of the two animal groups were tested by a two sided t-test for the hypothesis of equality against the alternative of a higher value for the ApoE^(-/-) group. The hypothesis was rejected in favor of the alternative for p-values < 0.05. In this work all in vivo PWV values are given as mean ± standard deviation (SD).

On the vessel phantom, a reference PWV = 3.31 ± 0.18 m/s was obtained by the pressure catheter measurements. The multi-point MR measurements determined a PWV = 3.32 ± 0.18 m/s. The PWV values of the pressure and MR measurements are not different with statistical significance (p = 0.999). The parameters and results of the validation measurements are summarized in Table 1. The PWV values of the two-point MR measurements agree within their standard errors. A representative pressure wave in the vessel phantom and the multi-point TT method (explained in the method section) are shown in Figure 2.

Figure 1 shows representative time courses of flow velocities, which were recorded on an ApoE^(-/-) mouse. The measured PWV values (Figure 5) ranged from 1.9 m/s in a C57Bl/6J mouse to 3.8 m/s in an ApoE^(-/-) mouse. The average values of each animal group are PWV = 3.0 ± 0.6 m/s for ApoE^(-/-) mice and PWV = 2.4 ± 0.4 m/s for C57Bl/6J mice. The mean value of the ApoE^(-/-) group was higher than that of the C57Bl/6J group with statistical significance (p = 0.014). The change of the heart periods of examined mice was smaller than 5 ms during experiments. The experiment parameters and the results for both animal groups are summarized in Table 2.