Impact of coronary bifurcated vessels flow-diameter scaling laws on fractional flow reserve based on computed tomography images (FFRCT)

Na Li; Bao Li; Yili Feng; Junling Ma; Liyuan Zhang; Jian Liu; Youjun Liu; Na Li; Bao Li; Yili Feng; Junling Ma; Liyuan Zhang; Jian Liu; Youjun Liu

doi:10.3934/mbe.2022145

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 3: 3127-3146. doi: 10.3934/mbe.2022145

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Impact of coronary bifurcated vessels flow-diameter scaling laws on fractional flow reserve based on computed tomography images (FFRCT)

1.
College of Life Science and Chemistry, Faculty of Environment and Life, Beijing University of Technology, Beijing, China
2.
Peking University People's Hospital, Beijing, China

Academic Editor: Hao Gao

Received: 23 October 2021 Revised: 12 December 2021 Accepted: 27 December 2021 Published: 20 January 2022

Objective
To explore the influence of the blood flow-diameter scaling laws of $ \mathrm{Q}\mathrm{\alpha }{\mathrm{D}}^{3} $, $ \mathrm{Q}\mathrm{\alpha }{\mathrm{D}}^{2.7} $ and $ \text{Q}\alpha \text{D}{}^{7}\!\!\diagup\!\!{}_{3}\; $ on the numerical simulation of fraction flow reserve based on CTA images and to find the optimal exponents.

Methods
1) 26 patients with coronary artery disease were screened according to the inclusion criteria; 2) Microcirculation resistance (R_m) was calculated under the 3, 2.7 and 7/3 power of the flow-diameter scaling law, which were recorded as 3R_m, 2.7R_m and 7/3R_m, respectively; 3) 3R_m, 2.7R_m and 7/3R_m were used as exit boundary conditions to simulate FFRCT, quoted as 3FFRCT, 2.7FFRCT and 7/3FFRCT, respectively; 4) The correlation and diagnostic performance between three kinds of FFRCT and FFR were analyzed.

Results
The p-values of comparing 3Rm, 2.7Rm and 7/3Rm with FFR were 0.004, 0.005 and 0.010, respectively; the r value between 7/3FFRCT and FFR (0.96) was better than that of 3FFRCT (0.95) and 2.7FFRCT (0.95); the 95% LoA between 7/3FFRCT and FFR (-0.08~0.11) was smaller than that of 3FFRCT (-0.10~0.12) and 2.7FFRCT (-0.09~0.11); the AUC and accuracy of 7/3FFRCT [0.962 (0.805-0.999), 96.15%] were the same as those of 2.7FFRCT [0.962 (0.805-0.999), 96.15%] and better than those of 3FFRCT [0.944 (0.777-0.996), 92.3%]. The prediction threshold of 7/3FFRCT (0.791) was closer to 0.8 than that of 3FFRCT (0.816) and 2.7FFRCT (0.787).

Conclusion
The blood flow-diameter scaling law affects the FFRCT simulation by influencing the exit boundary condition R_m of the calculation. With $ Q\alpha D{}^{7}\!\!\diagup\!\!{}_{3}\; $, FFRCT had the highest diagnostic performance. The blood flow-diameter scaling law provides theoretical support for the blood flow distribution in the bifurcated vessel and improves the FFRCT model.
- blood flow-diameter scaling law,
- FFRCT,
- 0D/3D geometric multi-scale model,
- microcirculation resistance,
- numerical calculation
Citation: Na Li, Bao Li, Yili Feng, Junling Ma, Liyuan Zhang, Jian Liu, Youjun Liu. Impact of coronary bifurcated vessels flow-diameter scaling laws on fractional flow reserve based on computed tomography images (FFRCT)[J]. Mathematical Biosciences and Engineering, 2022, 19(3): 3127-3146. doi: 10.3934/mbe.2022145

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Abstract

Objective

To explore the influence of the blood flow-diameter scaling laws of $ \mathrm{Q}\mathrm{\alpha }{\mathrm{D}}^{3} $, $ \mathrm{Q}\mathrm{\alpha }{\mathrm{D}}^{2.7} $ and $ \text{Q}\alpha \text{D}{}^{7}\!\!\diagup\!\!{}_{3}\; $ on the numerical simulation of fraction flow reserve based on CTA images and to find the optimal exponents.

Methods

1) 26 patients with coronary artery disease were screened according to the inclusion criteria; 2) Microcirculation resistance (R_m) was calculated under the 3, 2.7 and 7/3 power of the flow-diameter scaling law, which were recorded as 3R_m, 2.7R_m and 7/3R_m, respectively; 3) 3R_m, 2.7R_m and 7/3R_m were used as exit boundary conditions to simulate FFRCT, quoted as 3FFRCT, 2.7FFRCT and 7/3FFRCT, respectively; 4) The correlation and diagnostic performance between three kinds of FFRCT and FFR were analyzed.

Results

The p-values of comparing 3Rm, 2.7Rm and 7/3Rm with FFR were 0.004, 0.005 and 0.010, respectively; the r value between 7/3FFRCT and FFR (0.96) was better than that of 3FFRCT (0.95) and 2.7FFRCT (0.95); the 95% LoA between 7/3FFRCT and FFR (-0.08~0.11) was smaller than that of 3FFRCT (-0.10~0.12) and 2.7FFRCT (-0.09~0.11); the AUC and accuracy of 7/3FFRCT [0.962 (0.805-0.999), 96.15%] were the same as those of 2.7FFRCT [0.962 (0.805-0.999), 96.15%] and better than those of 3FFRCT [0.944 (0.777-0.996), 92.3%]. The prediction threshold of 7/3FFRCT (0.791) was closer to 0.8 than that of 3FFRCT (0.816) and 2.7FFRCT (0.787).

Conclusion

The blood flow-diameter scaling law affects the FFRCT simulation by influencing the exit boundary condition R_m of the calculation. With $ Q\alpha D{}^{7}\!\!\diagup\!\!{}_{3}\; $, FFRCT had the highest diagnostic performance. The blood flow-diameter scaling law provides theoretical support for the blood flow distribution in the bifurcated vessel and improves the FFRCT model.

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