Mathematical modelling of cardiac pulse wave reflections due to arterial irregularities

Alexandre Cornet; Alexandre Cornet

doi:10.3934/mbe.2018047

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 5: 1055-1076. doi: 10.3934/mbe.2018047

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Mathematical modelling of cardiac pulse wave reflections due to arterial irregularities

Alexandre Cornet ^{1,2
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1.
Imperial College London, South Kensington Campus, London SW72AZ, United Kingdom
2.
Ecole normale supérieure Paris-Saclay, 61 Avenue du Président Wilson, Cachan 94230, France

Received: 24 December 2016 Accepted: 23 January 2018 Published: 01 October 2018
MSC : Primary: 15A24, 76D05; Secondary: 65F30

This research aims to model cardiac pulse wave reflections due to the presence of arterial irregularities such as bifurcations, stiff arteries, stenoses or aneurysms. When an arterial pressure wave encounters an irregularity, a backward reflected wave travels upstream in the artery and a forward wave is transmitted downstream. The same process occurs at each subsequent irregularity, leading to the generation of multiple waves. An iterative algorithm is developed and applied to pathological scenarios to predict the pressure waveform of the reflected wave due to the presence of successive arterial irregularities. For an isolated stenosis, analysing the reflected pressure waveform gives information on its severity. The presence of a bifurcation after a stenosis tends do diminish the amplitude of the reflected wave, as bifurcations' reflection coefficients are relatively small compared to the ones of stenoses or aneurysms. In the case of two stenoses in series, local extrema are observed in the reflected pressure waveform which appears to be a characteristic of stenoses in series along an individual artery. Finally, we model a progressive change in stiffness in the vessel's wall and observe that the less the gradient stiffness is important, the weaker is the reflected wave.
- Arterial irregularties,
- blood pressure,
- wave mechanics,
- mathematical modelling,
- iterative algorithm
Citation: Alexandre Cornet. Mathematical modelling of cardiac pulse wave reflections due to arterial irregularities[J]. Mathematical Biosciences and Engineering, 2018, 15(5): 1055-1076. doi: 10.3934/mbe.2018047

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Abstract

This research aims to model cardiac pulse wave reflections due to the presence of arterial irregularities such as bifurcations, stiff arteries, stenoses or aneurysms. When an arterial pressure wave encounters an irregularity, a backward reflected wave travels upstream in the artery and a forward wave is transmitted downstream. The same process occurs at each subsequent irregularity, leading to the generation of multiple waves. An iterative algorithm is developed and applied to pathological scenarios to predict the pressure waveform of the reflected wave due to the presence of successive arterial irregularities. For an isolated stenosis, analysing the reflected pressure waveform gives information on its severity. The presence of a bifurcation after a stenosis tends do diminish the amplitude of the reflected wave, as bifurcations' reflection coefficients are relatively small compared to the ones of stenoses or aneurysms. In the case of two stenoses in series, local extrema are observed in the reflected pressure waveform which appears to be a characteristic of stenoses in series along an individual artery. Finally, we model a progressive change in stiffness in the vessel's wall and observe that the less the gradient stiffness is important, the weaker is the reflected wave.

References

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