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Analysis of the impact of left ventricular assist devices on the systemic circulation

  • Sergey S. Simakov , Alexander E. Timofeev EMAIL logo , Timur M. Gamilov , Philipp Yu. Kopylov , Dmitry V. Telyshev and Yuri V. Vassilevski
Published/Copyright: October 30, 2020
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Russian Journal of Numerical Analysis and Mathematical Modelling
From the journal Russian Journal of Numerical Analysis and Mathematical Modelling Volume 35 Issue 5

Abstract

In this work we analyze the impact of left ventricular assist devices on the systemic circulation in subjects with heart failure associated with left ventricular dilated cardiomyopathy. We use an integrated model of the left heart and blood flow in the systemic arteries with a left ventricular assist device. We study the impact of the rotation speed of the pump on haemodynamic characteristics of distal arteries. We identify the rotation speed for simultaneous recovery of the healthy average values in all systemic arteries, the heart and the aorta. Our numerical experiments show that blood distribution over the graph of systemic vessels does not depend on flow regimes in ascending aorta. We also observe that the optimal pump rotation speed changes in the atherosclerotic vascular network and depends on stenoses localization.

Keywords: Left ventricular assist device; lumped model; cardiac dynamics; haemodynamics; aortic valve; atherosclerosis
MSC 2010: 65D25; 37M05; 92B99

Funding statement: The research was supported by the Russian Foundation for Basic Research (grant Nos. 18-00-01661, 18-00-01524, 18-00-01659, 18-31-20048, 19-51-45001) and the world-class research center ‘Moscow Center for Fundamental and Applied Mathematics' (agreement with the Ministry of Education and Science of the Russian Federation No. 075-15-2019-1624).

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AA

Aortic arch

AV

Aortic valve

DCM

Dilated cardiomyopathy

HF

Heart failure

LA

Left atrium

LV

Left ventricle

LVAD

Left ventricular assist device

MV

Mitral valve

PV

Pulmonary veins

CA

Coronary artery

RAF

Relative average flow

Appendix A

Tables A.1 and A.2 present the parameters of the systemic and coronary arteries, while Table A.3 contains the parameters of the Windkessel compartments.

Tab. A1

Parameters of the systemic arteries (see Fig. 2 for the vessels numbering).

No.Artery titleLength (cm)Radius (mm)c0 (cm/s)mean RAF(%)
1aAortic arch Ip01.515.0640042.85
1bAortic arch Ip12.9415.0640043.32
1cAortic arch Ip23.013.5640094.94
2Brachiocephalic Trunk4.746.4444013.96
3Aortic arch II0.9612.7641080.98
4Subclavian Right I1.574.544704.65
5Common carotid right8.123.95009.31
6Vertebral right20.451.346300.88
7aSubclavian right II4.113.245203.76
7bAxillary right12.02.195703.76
7cBrachial right22.311.955803.76
8Radial right30.091.386251.71
9Ulnar right I2.981.416202.05
10aCommon interosseous right1.630.966600.36
10bPosterior interosseous right23.060.686900.36
11Ulnar right II23.931.416201.70
12External carotid right6.092.275602.29
13Internal carotid right13.212.775307.02
14Common carotid left12.133.94909.21
15Aortic arch III0.712.4241071.77
16External carotid left6.092.275602.28
17Internal carotid left13.212.775306.93
18Subclavian left I4.944.194804.64
19aAortic arch IV4.3111.4241067.13
19bThoracic aorta I0.9910.4641567.12
20Vertebral left20.421.346300.88
21aSubclavian left II4.112.895303.76
21bAxillary left12.02.195703.76
21cBrachial left22.311.955803.76
22Radial left31.091.386251.73
23Ulnar left I2.981.416202.02
24aCommon interosseous left1.630.966600.36
24bPosterior interosseous left23.060.686900.36
25Ulnar left II23.931.416201.67
26Posterior intercostal T6 R19.691.46200.09
27Thoracic aorta II0.7910.2941567.04
28Posterior intercostal T6 left17.81.46220.08
29Thoracic aorta III1.5610.0741566.95
30Posterior intercostal T7 R20.161.556100.09
31Thoracic aorta IV0.539.8741566.86
32Posterior intercostal T7 left18.521.556100.09
33aThoracic aorta V12.168.6842066.76
33bThoracic aorta VI0.327.5243066.76
34Celiac trunk1.683.2851010.99
35Abdominal aorta I1.47.4143055.77
36Common hepatic6.662.695406.41
37Splenic I0.392.175704.58
38Left gastric9.291.516100.06
39Splenic II6.442.175704.52
40Superior mesenteric21.643.934909.85
41Abdominal aorta II0.437.2943045.92
42Renal left2.182.715409.49
43Abdominal aorta III1.27.1943036.43
44Renal right3.773.15209.47
45Abdominal aorta IV5.416.7744026.96
46Inferior mesenteric9.022.085700.90
47Abdominal aorta V4.226.1744026.06
48Common iliac right7.644.2948013.04
49Common iliac left7.44.2948013.02
50aExternal iliac right10.223.285107.86
50bFemoral right I3.163.175157.86
51Internal iliac right7.252.825305.18
52Profunda femoris right23.842.145706.09
53aFemoral right II31.932.915301.77
53bPopliteal right I13.22.535501.76
54Anterior tibial right38.621.176400.81
55aPopliteal right II0.882.365550.95
55bTibiofibular trunk right3.622.355550.95
55cPosterior tibial right38.291.236400.95
56aExternal iliac left10.223.285107.85
56bFemoral left I3.163.175157.85
57Internal iliac left7.252.825305.16
58Profunda femoris left23.842.145706.09
59aFemoral left II31.932.915301.76
59bPopliteal left I13.22.535501.76
60Anterior tibial left38.621.176400.81
61aPopliteal left II0.882.365550.95
61bTibiofibular trunk left3.622.355550.95
61cPosterior tibial left38.291.236400.95
62Basilar2.61.757001.76
63Posterior cerebral right I1.01.07000.88
64Posterior cerebral left I1.01.07000.88
65Posterior cerebral right II3.01.07001.43
66Posterior cerebral left II3.01.07001.42
67Posterior communicating right3.00.757000.54
68Posterior communicating left3.00.757000.54
69Anterior cerebral left I1.21.27001.82
70Anterior cerebral right I1.21.27001.89
71Middle cerebral left5.21.37004.57
72Middle cerebral right4.31.257004.58
73Anterior cerebral right II10.31.27001.86
74Anterior cerebral left II10.31.27001.86
75Anterior communicating0.30.757000.03

Tab. A2

Parameters of the coronary arteries (see Fig. 3 for the vessels numbering).

No.Artery titleLength (cm)Radius (mm)c0 (cm/s)R (kBa⋅s/ml)mean RAF (%)
3Left coronary artery root2.612.481200—3.71
4Left anterior descending I1.832.071200—1.92
52.450.891200—0.39
60.650.451200643.370.20
71.580.451200643.370.19
8Left anterior descending II2.041.521200—1.53
9Diagonal branch2.760.981200—0.50
103.30.441200505.080.22
111.980.481200425.320.28
12Left anterior descending III1.321.161200—1.03
132.660.561200305.910.39
14Left anterior descending IV3.670.891200—0.64
152.260.491200405.880.29
161.940.531200—0.35
170.970.451200643.370.18
181.840.451200643.370.17
19Left cirmcuflex I3.131.961200—1.79
20Left cirmcuflex II4.971.451200—0.46
212.160.651200449.280.28
224.050.921200—0.18
232.490.4512001.35⋅1030.09
241.970.4412001.35⋅1030.09
25Left marginal branch2.471.511200—1.32
262.450.891200—0.34
271.50.531200714.040.18
281.110.521200762.120.17
292.581.191200—0.98
301.340.541200698.980.18
310.710.941200—0.80
322.10.511200779.190.16
332.220.721200—0.64
341.230.4512005.84⋅1030.02
350.710.941200196.830.62
36Right coronary artery root1.741.731300—1.35
372.350.921300—0.12
380.380.4513002.20⋅1030.06
390.270.4413002.20⋅1030.06
402.050.981300290.670.44
41Right coronary I2.421.631300—0.79
420.811.271300—0.25
431.860.781300—0.12
440.750.4513002.20⋅1030.06
450.620.4413002.20⋅1030.06
462.950.81300—0.13
470.470.4613001.68⋅1030.08
480.760.4613002.20⋅1030.06
49Right coronary II4.531.291300—0.54
50Right marginal branch1.840.991300—0.22
511.340.5413001.14⋅1030.11
522.340.761300—0.11
533.170.3613002.20⋅1030.05
541.050.2713002.20⋅1030.05
55Right coronary III4.60.931300—0.32
56Posterior descending3.370.71300—0.11
572.340.313002.20⋅1030.05
581.880.3413002.20⋅1030.05
592.420.751300—0.21
603.140.4413002.20⋅1030.06
610.660.671300—0.15
621.470.4513002.20⋅1030.06
630.870.581300—0.10
642.750.313002.20⋅1030.05
651.230.2113002.20⋅1030.05

Tab A3

Parameters of the Windkessel compartments (compartments numbering coincides with the terminal arteries numbering in Fig. 2).

No.Artery titleR1 (kBa⋅s/ml)R2 (kBa⋅s/ml)C (ml/kBa)
8Radial right16.9667.854.91⋅10−3
10bPosterior interosseous right70.28281.141.18⋅10−3
11Ulnar right II17.2769.084.82⋅10−3
12External carotid right13.855.226.03⋅10−3
16External carotid left13.8555.416.01⋅10−3
22Radial left16.6666.635.00⋅10−3
24bPosterior interosseous left70.54282.161.18⋅10−3
25Ulnar left II17.670.424.73⋅10−3
26Posterior intercostal T6 right366.221.46⋅1032.27⋅10−4
28Posterior intercostal T6 left375.711.50⋅1032.22⋅10−4
30Posterior intercostal T7 right341.681.37⋅1032.44⋅10−4
32Posterior intercostal T7 left344.611.38⋅1032.42⋅10−4
36Common hepatic4.9219.691.69⋅10−2
38Left gastric504.792.02⋅1031.65⋅10−4
39Splenic II6.9627.831.20⋅10−2
40Superior mesenteric3.2112.832.60⋅10−2
42Renal left3.3313.32.50⋅10−2
44Renal right3.3413.352.49⋅10−2
46Inferior mesenteric35.15140.612.37⋅10−3
51Internal iliac right6.0924.381.37⋅10−2
52Profunda femoris right5.0420.151.65⋅10−2
54Anterior tibial right36.05144.212.31⋅10−3
55cPosterior tibial right31.1124.42.68⋅10−3
57Internal iliac left6.1124.451.36⋅10−2
58Profunda femoris left5.0420.161.65⋅10−2
60Anterior tibial left36.06144.252.31⋅10−3
61cPosterior tibial left31.11124.452.68⋅10−3
65Posterior cerebral right II21.1184.443.13⋅10−3
66Posterior cerebral left II21.2685.022.94⋅10−3
71Middle cerebral left6.3826.379.80⋅10−3
72Middle cerebral right6.3626.299.83⋅10−3
73Anterior cerebral right II16.1664.624.13⋅10−3
74Anterior cerebral left II16.1664.624.13⋅10−3

Received: 2020-07-30
Accepted: 2020-09-30
Published Online: 2020-10-30
Published in Print: 2020-10-27

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Application of mutual information estimation for predicting the structural stability of pentapeptides
  3. Induced drift of scroll waves in the Aliev–Panfilov model and in an axisymmetric heart left ventricle
  4. Spatially averaged haemodynamic models for different parts of cardiovascular system
  5. Analysis of the impact of left ventricular assist devices on the systemic circulation
  6. A stable method for 4D CT-based CFD simulation in the right ventricle of a TGA patient
https://doi.org/10.1515/rnam-2020-0025
Keywords for this article
Left ventricular assist device; lumped model; cardiac dynamics; haemodynamics; aortic valve; atherosclerosis

Articles in the same Issue

  1. Frontmatter
  2. Application of mutual information estimation for predicting the structural stability of pentapeptides
  3. Induced drift of scroll waves in the Aliev–Panfilov model and in an axisymmetric heart left ventricle
  4. Spatially averaged haemodynamic models for different parts of cardiovascular system
  5. Analysis of the impact of left ventricular assist devices on the systemic circulation
  6. A stable method for 4D CT-based CFD simulation in the right ventricle of a TGA patient
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