Forward and backward waves in the arterial system: nonlinear separation using Riemann invariants

Pythoud, Frédéric; Stergiopulos, N.; Jj, Meister

doi:10.3233/thc-1995-3305

Cited by 16 publications

(7 citation statements)

References 16 publications

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“…Importantly, since defining dp ± , du ± and wi ± on the basis of Riemann variables is a nonlinear approach, it is generally not the case that components are additive [14].…”

Section: Non-linear Wave Separationmentioning

confidence: 99%

“…Wave separation can be achieved in the frequency-domain [21] or time-domain [7,8], and to date has generally assumed linearity, i.e. forward and backward waves are additive and local wave speed is constant throughout the cardiac cycle [12,14,21]. However, wave speed is known to be pressure-dependent, with intra-beat variation of 20 30% − [5] or substantially more in patients with hypertension [4].…”

Section: Introductionmentioning

confidence: 99%

“…Several studies have investigated the effects of mild non-linearities on pressure decomposition [13][14][15]20] and concluded that, under normal physiological conditions, errors involved in the linear approach are comparable to measurement uncertainty (i.e. 5 10%).…”

Section: Introductionmentioning

confidence: 99%

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Non-linear separation of pressure, velocity and wave intensity into forward and backward components

Mynard

Davidson

Penny

et al. 2012

Med Biol Eng Comput

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Separating pressure, flow/velocity and wave intensity signals into forward and backward components provides insights about arterial wave propagation and reflection. A linear wave separation is normally used, but ignores the pressure-dependence of wave speed. While a nonlinear separation could incorporate this pressure-dependence, no such method exists for wave intensity decomposition. Moreover, although linear separation errors for pressure (5-10%) have been quantified previously, errors for velocity and wave intensity have not. Accordingly, we describe a non-linear wave separation technique based on the method of characteristics. Data from a computer model suggest that the percentage linear separation errors for velocity and wave intensity are approximately one-half and twice that for pressure respectively. Although comparable to measurement uncertainty in many instances, linear separation errors may become more significant 1) if wave speed varies substantially over the cardiac cycle, e.g. if pulse pressure or vessel compliance is high, 2) if the degree of wave reflection in the arterial system is large, or 3) if the constant wave speed used for the linear separation is closer to the minimum or maximum pressure-dependent value rather than the mean. Consideration of linear separation errors may therefore be important in some physiological settings.

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“…Importantly, since defining dp ± , du ± and wi ± on the basis of Riemann variables is a nonlinear approach, it is generally not the case that components are additive [14].…”

Section: Non-linear Wave Separationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Non-linear separation of pressure, velocity and wave intensity into forward and backward components

Mynard

Davidson

Penny

et al. 2012

Med Biol Eng Comput

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“…In (Berger et al, 1993) the linear superposition of multiple forward and reflected waves is considered. In (Pythoud et al, 1995) and (Pythoud et al, 1996), a nonlinear separation is proposed using Riemann invariants which takes into account nonlinearities in the area-pressure relationship and in the convective term.…”

Section: Reduced Arterial Blood Pressure Modelmentioning

confidence: 99%

“…This has been explained by the linear superposition of direct and reflected waves, the reflected waves being created when the forward waves, from the heart to the periphery, encounter discontinuities in the arterial properties like a bifurcation or a stenosis. This model has been well known for decades and many studies have been carried out in order to separate the PP into its forward and backward components, as in the pioneering work of Westerhof (Westerhof et al, 1972), followed by many others (Li, 1986), (Parker and Jones, 1990), (Berger et al, 1993), (Stergiopulos et al, 1993), (Pythoud et al, 1995) and (Pythoud et al, 1996).…”

Section: Introductionmentioning

confidence: 99%

Separation of Arterial Pressure Into Solitary Waves and Windkessel Flow

Laleg

Crépeau

Sorine

2006

IFAC Proceedings Volumes

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A simplified model of arterial blood pressure intended for use in model-based signal processing applications is presented. The main idea is to decompose the pressure into two components: a travelling wave describes the fast propagation phenomena predominating during the systolic phase and a windkessel flow represents the slow phenomena during the diastolic phase. Instead of decomposing the blood pressure pulse into a linear superposition of forward and backward harmonic waves, as in the linear wave theory, a nonlinear superposition of travelling waves matched to a reduced physical model of the pressure, is proposed. Very satisfactory experimental results are obtained by using forward waves, the Nsoliton solutions of a Korteweg-de Vries equation in conjunction with a two-element windkessel model. The parameter identifiability in the practically important 3soliton case is also studied. The proposed approach is briefly compared with the linear one and its possible clinical relevance is discussed.

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Numerical modelling of the pressure wave propagation in the arterial flow

Pontrelli

Rossoni

2003

Numerical Methods in Fluids

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SUMMARYA di erential model of blood ow through an arterial vessel is presented. It consists of a one-dimensional model describing the non-linear uid-wall interaction coupled with a simple lumped parameter model which accounts for outlet boundary conditions. The model includes a local sti ening of the vessel and the wave propagation of disturbances due to prosthetic implantations is also studied. The non-linear problem is solved by a ÿnite-di erence method on a staggered grid and some numerical simulations are analysed and discussed.

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Forward and backward waves in the arterial system: nonlinear separation using Riemann invariants

Cited by 16 publications

References 16 publications

Non-linear separation of pressure, velocity and wave intensity into forward and backward components

Non-linear separation of pressure, velocity and wave intensity into forward and backward components

Separation of Arterial Pressure Into Solitary Waves and Windkessel Flow

Numerical modelling of the pressure wave propagation in the arterial flow

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