A novel method for the noninvasive estimation of cardiac output with brachial oscillometric blood pressure measurements through an assessment of arterial compliance Short title:

A novel method for the noninvasive estimation of cardiac output with brachial oscillometric blood pressure measurements through an assessment of arterial

compliance

Short title: Noninvasive estimation of cardiac output from brachial blood pressure

Diego Álvarez-Montoya^a, Camilo Madrid-Muñoz^a, Luis Escobar-Robledo^a, Jaime Gallo- Villegas^a,b, Dagnovar Aristizábal-Ocampo^a,c

aCentro Clínico y de Investigación SICOR (Soluciones Integrales en Riesgo Cardiovascular), ^bFacultad de Medicina, Universidad de Antioquia, ^cCellular & Molecular Biology Unit, Corporación para Investigaciones Biológicas, Medellín (Colombia).

Supplementary material 1

Validation of the trapezoidal approach for estimating mean systolic pressure in the two-element Windkessel model with Montecarlo simulations

Ten thousand correlated scenarios were generated from combinations of the two-element Windkessel model (2-WK) parameters. Model input variables were stroke volume (SV), heart rate (HR), total arterial compliance (Ct) and, total peripheral resistance (TPR). Output variables were generated preserving the statistical properties of the one hundred subjects with echocardiographic measurements [1, 2]. Table 1SDC1 shows the descriptive statistics and Table 2SDC2 shows correlation matrix of the variables included in the model. Normal distributions were used and correlation was added using “single value decomposition” from the correlation matrix.

The input flow curve when the blood flow to the aorta is:

𝑖(𝑡) = {𝐼_𝑜∗ 𝑠𝑖𝑛²(𝜋. 𝑡

𝑇_𝑠 ) , 𝑡 ∈ 〈0, 𝑇_𝑠〉 0, 𝑡 ∈ 〈𝑇_𝑠,𝑇〉

𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 1𝑆𝐷𝐶1

Where, i(t) is the flow, T cardiac period, and Ts is the ejection time. A scale factor (Io) was used to ensure that the peak flow integral was fitted to the SV (Fig. 1SDC1).

To simulate pressures, the recursive 2-WK formula was used as:

𝜌_𝑖 ≈ 𝜌_𝑖 (1 − ∆𝑡

𝜏 ) + 𝑄 (𝑡_𝑖) ∆𝑡

𝐶_𝑡 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 2𝑆𝐷𝐶1

Where, ρi, instant pressure; Δt, time resolution (10 ms), τ, diastolic pressure decay time constant (the product of TPR and Ct); Q(𝑡_𝑖), instant flow at time i, and Ct, total arterial compliance.

One hundred seconds were simulated with a time resolution (Δt) of 10 ms. Calculations were carry out in the last 15 s to make sure the simulation was in a steady state. For the duration of the ejection period, the equation 1SDC1 was employed.

Mean systolic pressure (MSP) was calculated by the trapezoidal approximation as:

𝑀𝑆𝑃 =𝑆𝐵𝑃 + 𝑀𝐴𝑃

2 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 3𝑆𝐷𝐶1

Where, MSP, mean systolic pressure; SBP, systolic blood pressure and MAP, mean arterial pressure. The pressures corresponding to the ejection period were averaged.

From 10,000 scenarios, those with systolic blood pressure (SBP) between 90 and 140 mmHg, diastolic blood pressure (DBP) between 60 and 105 mmHg and mean arterial pressure (MAP) between 80 and 105 mmHg were considered (Fig. 2SDC1). A total of 2,475 scenarios were used to make the comparison between the two methods (integrated MSP and trapezoidal estimated MSP.) (Table 3SDC1).

Table 1SDC1 Descriptive statistics of the variables included in the model

Statistical

Stroke volume

(mL)

Heart rate (beats/min)

Total arterial compliance (mL/mmHg)

Total peripheral resistance (mmHg. s/mL)

Mean 82 68 1.34 1.15

SD 13 11 0.31 0.23

Maximum 108 96 2.18 1.92

Minimum 54 40 0.44 0.68

SD, standard deviation

Table 2SDC1 Correlation matrix of the variables included in the model

Variables

Stroke volume (mL)

Heart rate (beats/min)

Total arterial compliance (mL/mmHg)

Total peripheral

resistance (mmHg. s/mL) Stroke volume

(mL) 1.00 -0.30 0.60 -0.46

Heart rate

(beats/min) -0.30 1.00 -0.42 -0.38

Total arterial compliance

(mL/mmHg) 0.60 -0.42 1.00 -0.26

Total peripheral

resistance

(mmHg. s/mL) -0.46 -0.38 -0.26 1.00

Table 3SDC1 Bland-Altman analysis of 2,475 scenarios for the comparison between integrated mean systolic pressure and trapezoidal estimated mean systolic pressure.

Statistical Value Standard

error Lower Upper

Mean difference (mmHg) -0.116 0.013 -0.141 -0.091

Lower limit (mmHg) -1.361 0.022 -1.404 -1.319

Upper limit (mmHg) 1.129 0.022 1.086 1.172

Standard deviation of

difference (mmHg) 0.635 Percentage error (%) 1.163 Coefficient of variation

(%) 8.048

Root mean squared error

(mmHg) 0.645

Pearson correlation

coefficient 0.999 Intraclass correlation

coefficient 0.999 Sample size 2,472

Alpha 0.050

Fig. 1SDC1

Flow simulation curve.

Fig. 2SDC1

Area under the blood pressure curve during the systolic period employing numeric integration.

References

1. Tsanas A, Goulermas JY, Vartela V, Tsiapras D, Theodorakis G, Fisher AC, et al. The Windkessel model revisited: a qualitative analysis of the circulatory system. Med Eng Phys. 2009;31(5):581-8.

2. Eck VG, Donders WP, Sturdy J, Feinberg J, Delhaas T, Hellevik LR, et al. A guide to uncertainty quantification and sensitivity analysis for cardiovascular applications. Int J Numer Method Biomed Eng. 2016;32(8).