An integrated set-up for ex vivo characterisation of biaxial murine artery biomechanics under pulsatile conditions

Figures

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  Figure 1. Set-up specialised for biaxial biomechanical assessment of murine arteries under pulsatile conditions. p and d, proximal and distal pipettes for mounting the artery. P0, P1, and P2 are sensors registering reservoir and proximal and distal pipette pressures, respectively. Note that sensor P2 is at a de-aired closed end. For detailed description, see main text.

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  Figure 2. (A) Schematic model of the pipette configuration and pressure recording positions. P1 indicates the proximal pressure sensor; P2 indicates the distal pressure sensor; and Pvessel indicates the true pressure inside the vessel under test. Rclosed_end models the stopcock distal to sensor P2 which during measurements is closed to prevent any flow through the distal pipette (modelled by Rdist_pipette). We used the “Cvessel = f (Pvessel)” notation to indicate that Cvessel is strongly dependent on transmural pressure (due to nonlinear arterial elasticity). (B) Phase (top) and amplitude (bottom) bode diagrams, showing amplitude relationships of P2 and P1 to Pvessel, as a function of frequency. A phase of zero degrees indicates no phase error; an amplitude of 1.0 indicates no amplitude error. Continuous lines indicate the situation for an RC-time (defined as Rprox_pipette∙Cvessel) of about 5 ms and the dashed lines for a tripled RC-time (i.e. 15 ms, with Cvessel assumed 3 times larger and Rprox_pipette kept constant). P1 shows considerable, frequency-dependent errors, whereas P2 shows flat curves with no errors in the relevant frequency range (i.e. 5 Hz cycle times 10 harmonics to…

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  Figure 3. Representative examples of inner diameter (A) and pressure (B) tracings, and the resulting pressure-diameter plot (C), exposing considerable curvilinearity but rather limited loop area.

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  Figure 4. Quasi-static arterial stiffness increased with increasing stretch. (A) pulse wave velocity (PWV) determined from quasi-static diameter relationships for different stretch ratios. PWV was determined at 120/80 mmHg (orange area in (B)). Lines indicate median PWV. (B) Representative example of quasi-static pressure-diameter relationships from one vessel at different stretch ratios. Dashed lines reflect the pressure-diameter relation during inflation (ascending line) and deflation (descending line), the straight line reflects the average. (C) Distensibility coefficient (DC) determined from quasi-static pressure-diameter curve at reference pressure 120/80 mmHg. (D) Compliance coefficient (CC) determined from quasi-static pressure-diameter curve at reference pressure 120/80 mmHg. *p < 0.05, n = 20.

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  Figure 5. Static experiments underestimate stiffness determined under pulsatile (in vivo) conditions. (A) PWV determined from dynamic pressure-diameter curves compared to the corresponding quasi-static pressure-diameter curve. (B) Representative set of quasi-static (grey) and dynamic pressure-diameter curves (the latter obtained for maximum pressures Pmax of 80, 120, 160 mmHg). (C) Distensibility coefficient (DC) determined from dynamic pressure-diameter curves compared to the corresponding quasi-static pressure-diameter curve. (D) Compliance coefficient (CC) determined from dynamic pressure-diameter curves compared to the corresponding quasi-static pressure-diameter curve. *p < 0.05, n = 21.

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  Figure 6. Axial stiffness coefficient increases with increasing pressure. (A) Axial stiffness coefficient was determined as the local derivative at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\uplambda }_{z} = {\uplambda }_{z,iv}$$\end{document}λz=λz,iv (mean crossing points of force-stretch curves (B)). Asterisks indicate statistically significant differences between groups. *p < 0.05, n = 20. (B) Representative quasi-static force-stretch relation under different static pressures.

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  Figure 7. Schematic overview showing how diameters and pressures are obtained for pulse wave velocity calculation for both quasi-static and dynamic experiments. Maximum and minimum pressure (Pmax and Pmin, respectively) are taken from the dynamic measurement. At these given pressures, the corresponding minimum and maximum diameters (dmin and dmax) are obtained for the dynamic (blue line) and quasi-static (grey line) diameter recordings.

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  Figure 8. Timeline of experimental protocol. CCA common carotid artery, PWV pulse wave velocity.