A novel non-invasive method for estimating biomechanical properties of the internal carotid

1

Keywords:

• Blood velocity
• wave speed
• arterial compliance
• elastance
• cepstral analysis

1. Introduction

Arterial stiffness leads to serious cardiovascular complications, particularly atherosclerosis diabetes and hypertension (Benetos et al. 2002; Luo et al. 2012). It can be evaluated globally from arterial compliance (C) or intrinsically from Young’s modulus (E). C quantifies the capacity of the artery to distend. It is defined by Chen (Chen et al. 2011) as a variation of the radius R of the artery for a given pressure P variation.

Wave speed (c) was expressed in two forms, the first by Moens-Korteweg (Korteweg 1878) (Eq. (1)(1) $$c=\sqrt{\frac{Eh}{2\rho R}}$$(1) ) and the second by Bramwell Hills (Eq. (2)(2) $$c=\sqrt{\frac{R}{2\rho \frac{dR}{dP}}}$$(2) ): (1) $$c=\sqrt{\frac{Eh}{2\rho R}}$$(1) (2) $$c=\sqrt{\frac{R}{2\rho \frac{dR}{dP}}}$$(2)

Moens-Korteweg speed is highly related to rheological proprieties of the vessel wall, as Young’s modulus (E), radius (R), the wall thickness (h) and the fluid density ($\rho$).

Arterial compliance appears in the expression 2 of c: (3) $$c=\sqrt{\frac{1}{2\rho C}}$$(3)

The purpose of this study is to quantify the elastic biomechanical properties of the internal carotid (ICA) wall by applying the cepstral analysis on healthy subjects.

2. Methods

2.1. Study population

Twenty subjects were enrolled in this study (9 males and 11 females): 10 young volunteers having an average age of 29 ± 7 years, and 10 old aged between 50 and 86 years.

2.2. Data acquisition

MRI recordings were performed using a 3 T–machine (dStream, Philips Healthcare, Best, Netherlands). Three-dimensional time of flight cerebral angiogram was determined by sagittal scout images. These acquisitions which measure blood velocity were synchronized with the cardiac cycle. The data were registered with a 2D sequence cine phase-contrast (cine-PC) (Balédent et al. 2006).

2.3. The steps to work with our method

The wave speed was calculated by measuring the arrival time of the reflected wave of the blood velocity signal by using cepstral analysis (Ayadi et al. 2018). The cepstral analysis is defined as the inverse Fourier transform of the logarithm of the Fourier transform. It allows separating the incident and reflected waves of the blood velocity signal and detecting the arrival time of the reflected waves. If, t₀₁ and t₀₂ are the arrivals times of reflected wave in the two arterial sites at z₁ and z₂. c was calculated from the following relation (Eq. (4)(4) $$c\left[m{s}^{-1}\right]=\frac{2(z_2-z_1)}{t_{01}-t_{02}}=\frac{2\Delta z}{\Delta t_0}$$(4) ): (4) $$c\left[m{s}^{-1}\right]=\frac{2(z_2-z_1)}{t_{01}-t_{02}}=\frac{2\Delta z}{\Delta t_0}$$(4)

Where Δz = z₁–z₂ and Δt₀=t₀₁–t₀₂.

Through calculated values of c; C and Eh can be estimated via the Bramwell-Hill and Moens-Korteweg Equation (1)(1) $$c=\sqrt{\frac{Eh}{2\rho R}}$$(1) and (2)(2) $$c=\sqrt{\frac{R}{2\rho \frac{dR}{dP}}}$$(2) . Indeed, arterial compliance becomes can be expressed as: (5) $$C\left[P{a}^{-1}\right]=\frac{1}{2\rho c^2}=\frac{R}{Eh}$$(5)

The wall elastance can be defined as: (6) $$Eh[Pa\cdot m^{-1}]=c^{2}2\rho R=\frac{R}{C}$$(6)

3. Results and discussion

3.1. Carotid wave speed assessment

Wave speed increased from 5.48 ± 0.29 ms⁻¹ to 6.4 ± 0.4 ms⁻¹ with advancing age and changing genre (Ayadi et al. 2018). These findings are agreed with the theoretical results (Borlotti et al. 2012).

3.2. Carotid compliance assessment

Arterial compliance values are shown in Figure 1.

Figure 1. Variation of C against the age.

We found that carotid compliance decreased from 15.9 ± 1.5 10⁻⁶Pa⁻¹ (2.1 ± 0.21 10⁻³mmHg⁻¹) for young subjects to 10.9 ± 0.97 10⁻⁶Pa⁻¹ (1.4 ± 0.12 10⁻³mmHg⁻¹) for older subjects. These results are agree with those obtained by Juonala et al. (2008) and Marlatt et al. (2013).

3.3. Eh assessment

Eh values are displayed in Figure 2.

Figure 2. Variation of Eh as versus the age.

The elastance increased from 145 ± 10 KPa for the young group to 237 ± 28 kPa for the old group, which corresponds to an increase of 38%. Accordingly, our approach is sensitive to detect wall elastic properties variation as it is the case with age.

4. Conclusions

The goal of the present study is to estimate noninvasively elastic properties in the internal carotid artery. It suggested a simple and accurate method that can noninvasively determine the wave speed arterial, compliance, and elastance locally in the carotid artery as the function of age and gender. The proposed method presents several advantages over the existing one. It can examine short vessels, which were difficult to access by other approaches.