Intra-arterial blood pressure measurement: sources of error and solutions

Abstract

Intra-arterial blood pressure measurement is the cornerstone of hemodynamic monitoring in intensive care units (ICU). Accuracy of the measurement is dependent on the dynamic response of the measuring system, defined by its natural frequency (f_natural) and damping coefficient (Z_damping). Gardner’s plot (1981) has long been the only way to determine the accuracy of the pressure measurement. Specific objectives: (i) estimation of the amplitude of error in pressure measurement through simulations based on real-world data, (ii) a novel method to correct the error. Simulated blood pressure waveforms of various heart rates were passed through simulated measurement systems with varying f_natural and Z_damping. The numerical errors in systolic and diastolic pressures and mean error in the measured pressure were used to generate heat maps for the various recording conditions, in the same plot as that by Gardner (1981). f_natural and Z_damping from 121 patient recordings are plotted on these heat maps to demonstrate the fraction of unacceptable recordings. Performance of a tunable filter to correct the error is demonstrated. In many clinical settings, the measurement of intra-arterial pressure is prone to significant error. The proposed tunable filter is shown to improve the accuracy of intra-arterial pressure recording.

Graphic Abstract

Appendix

1.1 Blood pressure waveform

The arterial pressure waveform can be simulated compactly by Fourier synthesis, with at least 20 sinusoids with magnitude, ${M}_{k}$, and phase, ${\phi }_{k}$: $P(t)={P}_{d}+({P}_{s}-{P}_{d})\sum_{k=0}^{20}{M}_{k}\mathrm{cos}(2\pi k{f}_{o}t-{\phi }_{k})$. f_o = (heart rate in beats/min)/60, P_s= systolic pressure, and P_d = diastolic pressure.

k	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
${M}_{k}$	0.4486	0.365	0.1825	0.1194	0.0567	0.0294	0.0448	0.0277	0.0117	0.0208	0.0172	0.0064	0.0112	0.0124	0.0044	0.0066	0.0074	0.0054	0.0023	0.0045	0.0030
${\phi }_{k}$	0.0	3.169	5.034	0.709	2.8	3.843	5.445	1.378	2.712	4.061	6.142	1.6	2.7	4.831	0.453	1.307	3.522	5.61	5.73	1.197	4.0

1.2 Calculation of catheter system characteristics from physical properties

The effective resistance, R, capacitance, C, and inductance (inertance), L, of the system and the natural frequency, f_n, and damping coefficient, ζ, are calculated using the equations given below. The total capacitance depends on the compliance of the diaphragm, the compliance of the catheter, and the isothermal compression of the air bubbles trapped in the fluid.

$$R=\frac{8\eta l}{\pi {r}^{4}}, L=\frac{\rho l}{\pi {r}^{2}}, C=\frac{1}{{F}_{d}}+{C}_{c}+{|\frac{\Delta V}{\Delta P}|}_{bubble},{ C}_{c}=\frac{2\pi {r}^{3}l}{{E}_{c}h}{, f}_{n}=\frac{1}{2\pi \sqrt{LC}}, \zeta =\frac{R}{2}\sqrt{\frac{C}{L}}$$

1.3 Calculation of catheter system characteristics from fast-flush test

Measuring the time, t_n, and amplitude swing, y_n, (deviation from the mean arterial pressure) of the nth maximum, the natural frequency and damping coefficient can be calculated as follows:

$$\zeta =\frac{\alpha }{1+{\alpha }^{2}},{f}_{n}=\frac{1}{{t}_{n+1}-{t}_{n}}\cdot \frac{1}{\sqrt{1-{\zeta }^{2}}},where,\alpha ={\mathrm{log}}_{e}(\frac{{y}_{n}}{{y}_{n+1}})$$

1.4 Definition of waveform errors

• (a) Mean error: ${e}_{mean}=\frac{1}{T}\underset{0}{\overset{T}{\int }}[{P}_{m}(t)-{P}_{i}(t-\tau )]dt$, T = cardiac cycle duration,$\tau$= time shift to compensate for phase lag of the measurement system (i.e., shift at which the mean error is minimum)

• (b) Systolic error, ${e}_{s}=max[{P}_{m}(t)]-max[{P}_{i}(t)]$

• (c) Diastolic error, ${e}_{d}=min[{P}_{m}(t)]-min[{P}_{i}(t)]$

(subscript “m” is for the measured waveform and subscript “i” for the true waveform).