Oscillometric measurement of systolic and diastolic blood pressures validated in a physiologic mathematical model

Abstract

Background: The oscillometric method of measuring blood pressure with an automated cuff yields valid estimates of mean pressure but questionable estimates of systolic and diastolic pressures. Existing algorithms are sensitive to differences in pulse pressure and artery stiffness. Some are closely guarded trade secrets. Accurate extraction of systolic and diastolic pressures from the envelope of cuff pressure oscillations remains an open problem in biomedical engineering.

Methods: A new analysis of relevant anatomy, physiology and physics reveals the mechanisms underlying the production of cuff pressure oscillations as well as a way to extract systolic and diastolic pressures from the envelope of oscillations in any individual subject. Stiffness characteristics of the compressed artery segment can be extracted from the envelope shape to create an individualized mathematical model. The model is tested with a matrix of possible systolic and diastolic pressure values, and the minimum least squares difference between observed and predicted envelope functions indicates the best fit choices of systolic and diastolic pressure within the test matrix.

Results: The model reproduces realistic cuff pressure oscillations. The regression procedure extracts systolic and diastolic pressures accurately in the face of varying pulse pressure and arterial stiffness. The root mean squared error in extracted systolic and diastolic pressures over a range of challenging test scenarios is 0.3 mmHg.

Conclusions: A new algorithm based on physics and physiology allows accurate extraction of systolic and diastolic pressures from cuff pressure oscillations in a way that can be validated, criticized, and updated in the public domain.

Figure 1

Arrangement of cuff, skin, muscle, bone, and artery for a simple model of the arm during oscillometric blood pressure recording.

Figure 2

Hypothetical pressure-volume relationship for an artery including negative transmural pressures and collapse. P_c is collapse pressure, and P_mid is normal mid-level arterial pressur.

Figure 3

Representative volume vs. pressure curves for an artery segment over a wide range of positive and negative transmural pressure. Standard normal variables a = 0.11 mmHg^-1 , b = 0.03/mmHg^-1, V_a0 = 0.3 ml. Variations in shape occur with combinations of increased (2x normal) and decreased (1/2 normal) values of parameters a and b.

Figure 4

Pressure-volume relationship for an artery (solid curve) including positive and negative transmural pressures. Dashed triangles have equal bases indicating the range of transmural pressure (internal artery blood pressure minus cuff pressure) that determines the change in volume with each pulse. (a) Cuff pressure well above systolic with net distending pressure always negative. (b) Cuff pressure close to systolic. (c) Cuff pressure near mean arterial pressure with maximal volume changes. (d) Cuff pressure just below diastolic. (e) Cuff pressure well below diastolic.

Figure 5

Simulated oscillometric blood pressure determination in a normal patient. (a) Blood pressure and cuff pressure vs. time. (b) High pass filtered cuff pressure oscillations.

Figure 6

Simulated oscillometric blood pressure determination in a normal patient. (a) Cuff pressure oscillations vs. pressure. (b) Amplitude envelope obtained from maximum minus minimum cuff pressure over each heartbeat.

Figure 7

Amplitude envelopes for varying arterial stiffness. Stiffness is represented as inverse compliance. Exponential constants a and b for 1/2 normal stiffness are multiplied by ln(2) = 1.44. Exponential constants a and b for 2x normal stiffness are divided by 1.44. In all cases actual blood pressure was 120/80 mmHg.

Figure 8

Simulations of varying arterial pulse pressure. (a) and (b) blood pressure and cuff pressure vs. time, 140/60 mmHg vs. 110/90 mmHg.

Figure 9

Simulations of varying arterial pulse pressure. (a) and (b) amplitude envelopes for 140/60 mmHg vs. 110/90 mmHg.

Figure 10

Semi-log plots for determining model constants from amplitude envelope data. Note straight line regions in rising and falling phases of the curves.

Figure 11

Contour plot of sum of squares goodness of fit measure showing a minimum value and best agreement at an estimated blood pressure of 119/80 mmHg, evaluated for input data computed with known pressure of 120/80 mmHg. Flat background indicates exceedingly large, off-scale sums of squares.

Figure 12

Agreement of model (curves) and input (filled circles) amplitude functions in the normal pressure case.