Oscillometric blood pressure measurement: modeling and analysis of the area oscillogram and height oscillogram

Figures

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  FIGURE 1. (A) Exemplary cuff pressure oscillations and applied cuff pressure measured with an upper arm oscillometric device. (B) Variation in the shape of the oscillometric pulses at different cuff pressures.

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  FIGURE 2. (A) Computation of simple shape features of an oscillometric pulse for which analytical modeling is feasible. (B) Four features plotted against adjusted cuff pressure for all 173 patient oscillometric measurements in the study. The cuff pressure was adjusted so that the main fiducial marker of all the plots for each feature occurred at 0 mmHg.

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  FIGURE 3. (A) Exemplary normalized area oscillogram (oscillation area vs. cuff pressure function) and normalized height oscillogram (oscillation height vs. cuff pressure function) measurements. These oscillograms were constructed from the cuff pressure measurements in Figure 1A. PAmax and PHmax are the cuff pressures at which the area oscillogram and height oscillogram are maximal, respectively. (B) PHmax plotted against PAmax over the 173 oscillometric measurements.

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  FIGURE 4. (A) The oscillometric models in this study are based on the sigmoidal relationship (f(∙)) from transmural pressure ( Pt = internal BP ( Pat – external cuff pressure ( Pc )) to blood volume ( Vt ) in arteries. This relationship is represented by the integral of an exponential-linear function with parameters b and c denoting the widths of the relationship over the negative and positive transmural pressure ranges, respectively, and parameter a determining the height of the relationship (Dhamotharan et al., 2023). u· is the unit step function. (B) Vt is formed as the response of the model to a slowly decreasing linear cuff pressure ramp Pc (t) (left). Vt plotted against Pc (t) (right) indicates that the previous height oscillogram model ( OH ( Pc )) is given by the difference in the x-axis reversed sigmoidal functions evaluated at systolic BP ( Ps ) and diastolic BP ( Pd ) with scaling by k to convert Vt oscillations to the observed cuff pressure oscillations (Chandrasekhar et al., 2019; Dhamotharan et al., 2023). (C) The proposed area oscillogram model ( OA ( Pc )) is computed as the oscillation area of kVt above the diastolic level for each heartbeat. (D) For analytical solution of…

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  FIGURE 5. Automated algorithm to form the measured area oscillogram and height oscillogram from the cuff pressure waveform. The cuff pressure waveform, which is measured during fast cuff inflation and then slow cuff deflation followed by a constant cuff pressure of 60 mmHg is analyzed to form tail-trimmed oscillogram measurements. Important user-selected variables: Band-pass filter of 6th order with cut-off frequencies of 0.75 and 5 Hz (step 2); amplitude thresholds < 0.2 mmHg for peaks and > −0.1 mmHg for valleys and pulse interval variability < 0.65/PR and > 1.35/PR, where PR is FFT-based pulse rate (steps 3 and 4); and 5th order moving average filter (Step 6).

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  FIGURE 6. Framework for evaluating the impact of key assumptions of the models on the model fitting errors and parameter estimates. This framework assessed the impact of the triangular BP waveform ( Patrit ) assumption for the area oscillogram model by comparison with a real simultaneously measured invasive brachial BP waveform ( Painv (t)); the purely elastic model assumption by comparison with standard viscoelastic models with a single additional parameter reflecting the filter cutoff frequency ( w ) (Landry et al., 2024b); and the constant scale factor relating Vt oscillations to cuff pressure oscillations ( Ot ) by comparison to a model-based variable scale factor where Patm is atmospheric pressure (Drzewiecki et al., 1994).

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  FIGURE 7. (A) Exemplary area oscillogram and height oscillogram model fits with normalized-root-mean-squared-errors (NRMSEs) of 7.5% and 9.1%, respectively. (B) NRMSEs and (C) parameter estimates of both model fits over all 173 measurements. Data presented as mean ± SE. Horizontal lines indicate significant difference at p < 0.05 level.

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  FIGURE 8. (A) Comparison of overall NRMSEs of the height oscillogram model fits for Elastic (E), Hammerstein viscoelastic (H), and Wiener viscoelastic (W) models. (B) Comparison of the overall NRMSEs of the area oscillogram model fits for the three models and invasive and triangle BP waveform inputs. Note that the triangle BP waveform input is not assumed by the height oscillogram model. (C) Comparison of the overall NRMSEs of both model fits for constant ( k ) and variable ( kv ) scale factors relating blood volume oscillations to cuff pressure oscillations. Although the results were generated using the W model and invasive BP waveform input, they are representative of all comparisons between k and kv scale factors. Data presented as mean ± SE. Horizontal lines indicate significant differences at p < 0.005 level.

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  FIGURE 9. (A) Comparison of overall b and c parameter estimates of the height oscillogram model fits for the elastic and two viscoelastic models. (B) Comparison of overall b and c parameter estimates of the area oscillogram model fits for the different models and BP waveform inputs. Data presented as mean ± SE. Horizontal lines indicate significant differences at p < 0.005 level.

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  FIGURE 10. (A) Exemplary nonlinear pressure-volume relationship of a standard cuff on a mandrel wrapped with foam to simulate arm tissue. (B) Area oscillogram and height oscillogram model fits (black) to measurements (red and blue). (C) Area oscillogram and height oscillogram model fits (black) to mathematically adjusted measurements (red and blue) to approximately eliminate cuff nonlinearity in line with (A).