Joaquin Mura1,2, Julio Sotelo1,2,3, Hernan Mella1,3, Andrew Tran4, Tarique Hussain5, Bram Ruijsink6, and Sergio Uribe1,2,7,8
1Biomedical Imaging Center, Pontificia Universidad Catolica de Chile, Santiago, Chile, 2Millennium Nucleus for Cardiovascular Magnetic Resonance, Santiago, Chile, 3Electrical Engineering, Pontificia Universidad Catolica de Chile, Santiago, Chile, 4Heart Institute, Cincinnati Children's Hospital, Cincinnati, OH, United States, 5Pediatrics, UT Southwestern, Dallas, TX, United States, 6Imaging and Biomedical Engineering, Kings College of London, London, United Kingdom, 7Radiology, Pontificia Universidad Catolica de Chile, Santiago, Chile, 8Institute for Biological and Medical Engineering, Pontificia Universidad Catolica de Chile, Santiago, Chile
Synopsis
An improved version of continuous pulse-wave
velocity estimation uses 4D-Flow data with time-delay recovered from a faster formulation
using FFT. The novelty also relies upon neglecting regressive time-delay zones,
yielding stable and reliable results. Numerical simulations are shown to assess
the method. We also present its application in patients with Familial
Hypercholesterolemia and Fontan. Consistently with previous findings, adult
controls have stiffer aortic walls compared to young controls. Also, Fontan
patients appear with stiffer aortic arch than other subjects. More
interestingly, all subjects show a softening in the aortic arch respect to the
rest of the vessel.
Introduction
Pulse Wave Velocity (PWV) is a biomarker widely used to estimate the
global arterial distensibility for several Cardiovascular diseases (CVD). In this study, we present an updated version of a
previously introduced method to estimate local PWV measurements1,
being more robust and accurate. The method has been tested using
Fluid-Structure interaction simulation models and in young and adult volunteers
data as well as in patients with Fontan circulation and patients with Familial
Hypercholesterolemia. The refined methodology confirms differences in
the mean between young and adult controls2. Moreover, we detect an increment
of 144% in PWV located in the aortic arch
of Fontan patients with repaired aortas, compared to control and
Familial-Hypercholesterolemia (FH) patients. More remarkably, we show that in
all subjects, aortic arch is softer than descending aorta, and ascending aorta
is slightly stiffer than descending aorta.Methods
In most approaches, PWV is derived from
time-delay (TD) of a pulse associated with
the systolic impulse. We follow the same concept but automating the procedure.
After 4D-Flow acquisition and segmentation of aortic morphologies (with our
home-made software3), we combine the fast-implicit calculations over
distance maps with fast evaluations of cross-correlations performed with an FFT
formulation. Thus, the continuous characterization of TD is obtained along the
aorta also considering a short sensibility analysis. The key point is to note
that some sudden non-causal TD points (this is when the TD-curve is regressive
in time) can be related to rapid morphology changes or wave reflections. By
neglecting such regions, we can construct a robust local PWV map
semi-automatically, without centerlines.
The validation
study was carried out considering first numerical simulations (fluid-structure
interaction4 with our new validated home-made simulator written in
Python+Fenics project library5). Two cases were under consideration.
The first case, a straight tube with 1cm of diameter, constant Young modulus
E=7,5x105 [dyn/cm2]. In the second case, we choose the
same geometry but E=1,75x106 [dyn/cm2] between positions
2,5[cm] and 5,5[cm] from the inlet. A cohort of 33 patients
and 23 volunteers were collected using 4D-Flow acquisitions. The volunteers are
classified as adults (N=18, age:30,4±6,3 years old, BMI:23,3±6,5) and young
(N=5, age: 13,6±1,7 years old, BMI:20,5±5,6). The patients also have two
subclasses: Familial-Hypercholesterolemia (FH) (N=25, age:14,6±3,3 years old,
BMI:23,4±6,7) and patients with univentricular physiology (Hypoplastic left
heart syndrome) after Fontan procedure (N=8, age: 7,7±2,5 years old., BMI:16,5±1,6).
We collect 100 waveforms along the aortas using our method, producing 100
points to evaluate TD and then PWV.
Results
According to the
Moens-Korteweg (MK) theory (valid only for small and long straight vessels), PWV is proportional to the
square-root of E6. In our simulations, the
augmented stiffness produces an increment in a factor 2,33.
Thus, the expected increment of PWV is in a factor 1,53=√(2,33). Regarding
figure 1, we note that the ratio of approximated mean values per section can be
estimated as 625[cm/s]/425[cm/s]=1,47, corresponding to an error below 4%
respect to the MK theory.
In the case of 4D-Flow data, significant
differences were found between control volunteers at different ages (p<0,01
using Wilcoxon signed-rank test). In table 1, the mean values obtained for
different subjects. In the case of young-adult comparison, it has been found that
they approximately preserve the same trend at different sections in the aorta,
having a proportion near a factor 2 regarding the ratio adult-to-young volunteers
(mean ages are 30,4 and 13,6, respectively). The comparison between patients
and volunteers show that, at least with this technique, it was not possible to
detect significant differences between young controls and FH patients. But, a comparison
between Fontan patients and Young controls, Fontan patients had increased PWV values in the aortic arch
(2,69 compared to 1,87 represent an increment of 144%) and slightly increased
in the ascending aorta, corresponding to the areas of intervention.Discussion and Conclusions
Realistic numerical simulations demonstrate that the presented method is capable to localize sharp variations in vessels. Further simulations are required to assess sensibility respect to noise and size of the alterations. In the case of 4D-Flow data, although the comparison with FH patients do not reveal significant differences (also reported7 for global PWV), we still cannot discard the finding of more significant differences, due to the small number of subjects (e.g. N=8 for Fontan patients and N=5 for Young controls). Up to our knowledge, the local and non-invasive characterization of human aortas has not been reported yet using similar non-invasive techniques7,8,9 for Fontan or other conditions, opening interesting perspectives for future studies. Acknowledgements
This publication has received funding from Millenium Science Initiative of the Ministry of Economy, Development and Tourism, grant Nucleus for Cardiovascular Magnetic Resonance. Also, has been supported by CONICYT - PIA - Anillo ACT1416, CONICYT FONDEF/I Concurso IDeA en dos etapas ID15|10284, and FONDECYT # 1181057. Sotelo J. thanks to FONDECYT Postdoctorado 2017 #3170737.References
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