Development of a maternal cardiovascular network
model over the course of pregnancy
J. Carson1, M. Lewis2 and R. Van Loon1
Zienkiewicz Centre for Computational Engineering, College of Engineering,
Swansea University, Swansea, UK1.
School of Sport and Exercise Sciences, College of Engineering,
Swansea University, Swansea, UK2
Systemic Venous System
1.15
1.05
1
0.95
0.9
1
2
3
1.1
1
0.95
2
trimester
(a) Measured data from various studies [3].
180
1.05
0.9
1
3
trimester
(b) Model values (initial TPR shown).
200
3rd Trimester
2nd Trimester
1st Trimester
160
160
140
140
120
100
80
I Motivations
. To better understand the mechanisms involved in
maternal cardiovascular adaptation during pregnancy.
. Many health problems can develop from poor maternal
cardiovascular adaptation.
. Maternal hypertension, hypotension and pre-eclampsia
can be a danger to both foetus and mother.
. Low blood flow to foetus can hinder development.
I Model Components
100
80
60
40
40
20
20
0.2
0.4
0.6
0.8
1
Dimensionless Time
0
0
0.2
0.4
0.6
0.8
1
Dimensionless Time
(a) Digitised uterine artery waveforms [4].
Figure 1: Comparison of HR, TPR, CO, SV
Motives and Model Components
120
60
0
0
3rd Trimester
2nd Trimester
1st Trimester
180
Velocity cm/s
1.1
200
SV
CO
HR
TPR
Velocity cm/s
SV
CO
HR
TPR
dimensionless quantity
dimensionless quantity
1.15
Systemic Arterial System
(b) Model uterine artery waveforms.
Figure 2: Comparing uterine artery waveforms
Method, Results and Conclusions
I Method
. Governing equations solved using the implicit enhanced
trapezoidal rule method (ETM) [1].
. The method was built for speed.
. Super-linear convergence in both time and space.
. Rigorously tested on benchmark problems.
. Robust, even in the presence of discontinuous solutions.
I Results
. Simulation for supine position takes 18 seconds per
cardiac cycle (typically 10-12 cycles needed).
. Figure 1 shows good agreement for model outputs
(cardiac output and stroke volume).
. Initial (maximum) TPR shown for the model.
. Model shows good agreement with uterine artery
waveforms in Figure 2.
. Vascular network a modified version of [2].
. 417 1D vessels from arteries and veins in systemic
(including coronaries and cerebral circulation) and
pulmonary systems.
. Utero-ovarian vessels which supply (or drain) the
ovaries, womb and placenta with blood, are shown by
I Conclusions and Future Work
the purple vessels in the cardiovascular networks above.
. Model captures general behaviour for all trimesters.
. Heart model with three types of chamber interaction.
. Compression of IVC decreases CO from 2nd to 3rd
. Generic 0D vascular beds, with specialised vascular
trimesters, can lead to supine hypotensive syndrome.
beds for the liver, coronaries and brain.
. More cardiovascular response mechanisms required to
. Collapsible systemic veins with venous valves.
improve venous return in standing and sitting positions.
. External pressure exerted from gravid uterus on the
. Future developments include improving auto-regulation
inferior vena cava (IVC).
mechanisms, and comparing with beat-to-beat data.
. Muscle pump squeezes veins to aid venous return.
http://www.swansea.ac.uk/staff/engineering/r.vanloon/
References
[1] J. Carson, R. van Loon. An implicit solver for 1D
arterial network models. Int J Numer Meth
Biomed Engng, 2016. doi:10.1002/cnm.2837.
[2] J. Mynard, J. Smolich. One-Dimensional
Haemodynamic Modeling and Wave Dynamics in
the Entire Adult Circulation. Annals of
Biomedical Engineering, 43:6:1443–1460, 2015,
doi: 10.1007/s10439-015-1313-8.
[3] R. Carpenter, S. Emery, D. Rassi, O. Uzun,
M. Lewis. Recruitment of pregnant women to an
exercise-intervention study: a flexible
randomisation approach. Journal of Obstetrics
and Gynaecology, 36(2):200–207, 2016, doi:
10.3109/01443615.2015.1049988.
[4] A. Sciscione, E. Hayes. Uterine artery Doppler
flow studies in obstetric practice. American
Journal of Obstetrics & Gynecology,
201(2):121–6, 2009, doi:
10.1016/j.ajog.2009.03.027.
{485621,M.J.Lewis,r.vanloon}@swansea.ac.uk