Physiological relevance of T-tube model parameters with emphasis on arterial compliances

Abstract

The T-tube model of systemic arterial circulation was examined with respect to the physiological relevance of model parameters. root aortic pressure [Pao(t)] and flow [Qao(t)] and descending aortic flow [Qb(t)] were measured in anesthetized, open-chest dogs under control conditions, during inflation of a balloon positioned in the left external iliac artery (n = 5), and during infusion of vasoactive drugs nitroprusside (NTP, n = 4) and phenylephrine (PHL, n = 5). With Pao(t) as the input, the model accurately predicted both Qao(t) and Qb(t) under all conditions (r2 > 0.96). The balloon inflation data established the ability of the model to discriminate between proximal and distal arterial mechanical properties. Furthermore, proximal properties (i.e., tube characteristic impedances and transit times) were independent of distal properties such as terminal compliances and resistances (or equivalently, wave reflections). The effects of NTP and PHL were pharmacologically consistent and served to further validate this model. NTP primarily affected distal (load) properties, whereas PHL altered both load and tube parameters. Physiological interpretation of model parameters, particularly compliance, is also discussed. The ability of the model to correctly discriminate between proximal and distal arterial properties is relevant because these properties may affect cardiovascular function differently.

Misinterpretation of the Determinants of Elevated Forward Wave Amplitude Inflates the Role of the Proximal Aorta

“…The systemic arterial system was modeled as a finite PWV system represented by an asymmetric T‐tube model with complex frequency‐dependent loads (Figure 1). 20, 21 This model consists of 2 parallel pathways, represented as elastic tubes, through which pressure and flow waves can propagate: (1) head‐end and (2) body‐end. The head‐end pathway represents the combined circulatory path to the head and upper limbs, whereas the body‐end pathway represents that of the descending aorta.…”

“…Each tube is terminated in a complex load parameterized by distal compliance, viscous resistance of the vessel wall, and a terminal peripheral resistance. The asymmetric T‐tube model used here has been previously validated to accurately discern between proximal and distal arterial system properties and successfully applied to various animal species and humans 20, 21, 24, 25, 26, 27, 28. The mathematical formulation of the model is described in detail elsewhere 29…”

A Priori Identifiability Analysis of Cardiovascular Models

“…Shroff et al 26 used the T-tube model to fit experimental data with one input and one output, but the parameter estimation was poor. It was possible, in their experimental system, to measure a second output, the flow to the body portion of the model, Q b ( t ).…”

“…This parameters space can be reduced to seven free parameters by enforcing the following three constraints: (1) $\mathit{TVR}=\left(\text{mean}{P}_{\mathrm{ao}}\right)∕\left(\text{mean}{Q}_{\mathrm{ao}}\right)=\frac{R_{\mathrm{pb}}{R}_{\mathrm{ph}}}{R_{\mathrm{pb}}+R_{\mathrm{ph}}}$, (2) $Z_{\mathrm{cb}}=\frac{R_{\mathrm{pb}}{R}_{\mathrm{ob}}}{R_{\mathrm{pb}}+R_{\mathrm{ob}}}$ (high-frequency matching of the body-ward with its terminal load), 26 (3) $Z_{\mathrm{ch}}=\frac{R_{\mathrm{ph}}{R}_{\mathrm{oh}}}{R_{\mathrm{ph}}+R_{\mathrm{oh}}}$ (high-frequency matching of the head-ward tube with its terminal load). 26 Thus, the seven free parameters are: τ b , τ h , C lb , C lh , R ob , R oh , and R pb (or R ph ). The τ parameters are time delays, which DAISY cannot handle, and so were replaced with second order Taylor series expansions.…”

“…Shroff et al 26 measured a second output, the blood flow to the body, Q b ( t ): $$\begin{array}{cc}right{Q}_{\mathrm{b}}\left(t\right)=& left\frac{1}{Z_{\mathrm{cb}}}{P}_{\mathrm{ao}}(t-{\tau }_{\mathrm{d}})\\ right& left-\frac{1}{2R_{\mathrm{ob}}}\left[P_{\mathrm{cb}}\right(t-{\tau }_{\mathrm{b}}+{\tau }_{\mathrm{d}})-P_{\mathrm{cb}}(t-{\tau }_{\mathrm{b}}-{\tau }_{\mathrm{d}}\left)\right]\end{array}$$ where τ d is a known time constant (delay between upstroke of P ao and the onset of Q b ). The second model output makes it possible to calculate R pb and R ph , since pressure and flow are known for each load ( R pb = mean P ao /mean Q b and R ph = mean P ao /(mean Q ao − mean Q b )), leaving six free parameters to estimate: τ b , τ h , C lb , C lh , R ob , and R oh .…”