Pulse Pressure Variation Estimation Based on Rank ... - CiteSeerX

2003 PROCEEDINGS OF THE 25TH ANNUAL EMBS INTERNATIONAL CONFERENCE, SEPTEMBER 17–21, CANCUN, MEXICO

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Pulse Pressure Variation Estimation Based on Rank-Order Filters M. Aboy1 , J. McNames1, T. Thong2, C.R. Phillips3 , M.S. Ellenby4 , B. Goldstein4 1

Biomedical Signal Processing Laboratory, Electrical and Computer Engineering, Portland State University, Portland, OR, USA Biomedical Engineering, OGI School of Science and Engineering, Oregon Health and Science University, Portland, OR, USA 3 Pulmonary and Critical Care Medicine, Oregon Health and Science University, Portland, OR, USA 4 Complex Systems Laboratory, Pediatrics, Oregon Health and Science University, Portland, OR, USA

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Abstract— We describe a methodology to estimate the pulse pressure variation ∆Pp index from the arterial blood pressure (ABP) signal alone. This eliminates the need for simultaneously acquiring and monitoring airway pressure. The technique uses nonlinear rank-order filters to demodulate the respiratory component modulating the ABP signal. Furthermore, we present a simple mathematical model that can be used to generate synthetic arterial pressure signals with similar time, frequency, and variability characteristics to real ABP signals. Preliminary results on synthetic ABP suggest that rank-based estimation of ∆Pp may be as accurate as the current methods, which require simultaneous ABP and airway pressure acquisition and monitoring. Keywords— Cardiac index (CI), fluid responsiveness, pulse pressure (PP), pulse pressure variation (∆Pp), positive endexpiratory pressure (PEEP), rank-order filters, respiratory changes in systolic pressure, volume expansion (VE).

I. I NTRODUCTION Clinical studies have shown that respiratory changes in pulse pressure (∆Pp) can be used to predict and assess the hemodynamic effects of volume expansion (VE), and to assess changes in VE-induced cardiac index (CI). VE is the first-line therapy proposed in septic patients in an attempt to improve hemodynamics [1]. In mechanically ventilated patients with acute circulatory failure related to sepsis, ∆Pp has been shown to be a more reliable indicator of fluid responsiveness than other static and dynamic indices. Specifically, Michard et al. found that ∆Pp predicted the effect of VE on the cardiac output in 40 hypotensive patients with septic shock. They demonstrated that dynamic pulse pressure indices such as ∆Pp and systolic pressure variation (SVP) are superior to right atrial pressure (RAP) and pulmonary artery occlusion pressure (Ppao), for predicting fluid responsiveness [2]. Respiratory changes in arterial pulse pressure have also been investigated in ventilated patients with acute lung injury (ALI). Studies suggest that ∆Pp could be used to predict adverse hemodynamic effects of positive end-expiratory pressure (PEEP), and to assess changes in CI that occur when PEEP is applied. Furthermore, changes in ∆Pp induced by fluid may be helpful in predicting and assessing the effects of fluid loading on hemodynamics [3]. Current methods of calculating ∆Pp are based on simultaneous recording of systemic arterial and airway pressure. This presents a limitation since airway pressure is not always acquired and monitored simultaneously with arterial blood pressure (ABP). We describe a methodology to estimate ∆Pp

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from the ABP signal. This eliminates the need of simultaneously acquiring airway pressure. II. M ETHODOLOGY A. Modeling Respiratory Changes in Arterial Pressure There are three primary effects of respiration on arterial blood pressure (ABP): amplitude modulation of the stroke volume (pulse pressure modulation), frequency modulation of the heart rate (respiratory sinus arrhythmia) and an additive effect. ∆Pp is primarily affected by the amplitude modulation of ABP with respiration. This effect can be modeled as a double– sideband large carrier (DSB-LC) amplitude modulation (AM) φAM (t) = [f (t) + κ] cos 2πfc t.

(1)

However, the ABP pulse contour is not accurately modeled the by carrier signal cos 2πf c t, since it contains more than one harmonic, and is not exactly periodic. In general, we can model an ABP signal locally as ABPL (t) = [r(t) + κ]

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Cn ejn2πfc t

(2)

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where r(t) is the respiration signal, which modulates an arbitrary pulse that can be expressed as a Fourier Series. Since ABP signals contain most of their power in the first and second harmonics, we can simplify (2) by considering only these two harmonics. This simplification also makes sense from the physiology point of view, since pulse pressure is the result of summation of incident (ventricular ejection) and reflected pressure waves. Therefore, a simplified model of an ABP signal can be expressed mathematically as ABPL (t) = [r(t) + κ](α cos 2πfc t + β cos(4πfc t + π/2)) r(t) = σ cos 2πfr t, and κ ≥ | min{r(t)}|

(3)

where r(t) represents the respiratory signal as a sinusoid with frequency f r , which modulates the carrier signal α cos 2πf c t+ β cos(4πfc t + π/2)). The heart rate frequency f c (cardiac frequency) is the carrier frequency, and f c  fr . The large carrier term, κ ≥ | min{r(t)}|, enables the recovery (demodulation) of the respiratory component r(t) by envelope detection, without the need for synchronous detection. Pulse morphology is controlled by the α, β, and σ scaling factors. Fig. 1 shows 10 seconds of ABP components (r(t), α cos 2πf c t, β cos(4πfc t + π/2))), for specific values of f r , fc , α, β, and σ.

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Fig. 1. Plot showing 10 s of the arterial blood pressure components (fr =0.4, fc = 1.9, α=1, β=0.65, and σ=0.1). This illustrates the respiratory signal with frequency fr , which modulates the carrier signal α cos 2πfc t + β cos(4πfc t + π/2)). The heart rate frequency fc (cardiac frequency) is the carrier frequency, and fc
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Fig. 3. Plot showing 10 s of the resulting synthetic ABPL signal (fr =0.4, fc = 1.9, α=1, β=0.65, σ=0.1, µ = 80, σ=15, σn = 7.5, cf = 10Hz). Notice how variability is incorporated into the model by adding white Gaussian noise to the deterministic ABP signal, and sending it through a linear filter channel. The resulting signal it is random and closely resembles real ABP.

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Fig. 2. Plot showing 10 s of the resulting synthetic ABPL (fr =0.4, fc = 1.9, α=1, β=0.65, σ=0.1, µ = 80, σ = 15). Notice how due to the deterministic nature of this model the pulse contour does not change shape, and it does not incorporate the beat–to–beat variability typical in real ABP.

Using the model given by (3) it is possible to generate synthetic ABP signals with very similar time and frequency characteristics to real ABP. However, due to the deterministic nature of this model, the pulse contour does not change shape, and therefore it does not incorporate the beat–to–beat variability typical in real ABP. Fig. 2 shows an example illustrating this point. The resulting signal has a very regular pulse morphology. Variability is incorporated into the model by adding white Gaussian noise n(t) to the deterministic ABP signal, and sending it through a linear time-invariant filter (LTI) channel. This can be described mathematically as  ∞ h(t − τ )[ABPL (τ ) + n(τ )]dτ (4) ABPLn =

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Fig. 4. Plot showing 10 s of another synthetic ABPL signal with a different pulse morphology (fr =0.4, fc = 1.9, α=1, β=0.4, σ=0.1, µ = 80, σ=15, σn = 7.5, cf = 10Hz). The only difference with signal in the previous figure is the value of the parameter β.

closely resembles real ABP. Fig. 4 illustrates how the pulse morphology is controlled by the α, β, and σ scaling factors. In this particular example β was set to 0.4 (compared to 0.6 in Fig. 3) which resulted in a different morphology. Specifically, the dichrotic notch is less prominent in Fig. 4. Another important aspect regarding modeling of ABP signals is the issue of nonstationarity, and simulation of different types of noise and artifacts commonly encountered in practice. Different types of noise such as power line interference, motion artifacts, baseline drift, instrumentation noise, etc. can be easily modeled and incorporated into the model we presented here. This type of modeling is particularly important to quantify the relative noise susceptibility of the different methodologies to estimate ∆Pp.

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where h(t) is the impulse response of the LTI filter. Fig. 3 shows the effect of sending the ABP L through the LTI channel. We can see how the resulting signal is random, and

B. Implementation The model was implemented as a MATLAB function which can be used as a random ABP signal generator or to

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minimal values for pulse pressure (Pp max and Ppmin , respectively) are determined for each respiratory cycle. ∆Pp is defined as: Ppmax − Ppmin (5) ∆Pp(%) = 100 × (Ppmax + Ppmin )/2

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Fig. 5. Plot of the ABP signal versus time during six heart beats. The figure illustrates the Ppmax and Ppmin components. Both components are determined over a single respiratory cycle. The respiratory changes in pulse pressure (∆Pp) are calculated as the difference between Ppmax and Ppmin divided by the mean of the two values, and are expressed as a percentage. ∆Pp is evaluated in triplicate over each of three consecutive respiratory cycles. The mean values of the three determinations are then used for statistical analysis.

generate ABP signals with specific characteristics. When the function is called without any input parameters (except for the sampling frequency and duration), it outputs a random ABP signal. Alternatively, all the parameters can be entered to generate an specific waveform. Below we illustrate these two different function calls: >> [ABPLn,ABPL,r] = ABP(125,10); >> [ABPLn,ABPL,r] = ABP(125,1*10,0.5,2.4,0.5,1,0.4,80,15,8,10,1);

The first function call generates 10 s of random ABP sampled at 125 Hz. The second function call generates a synthetic ABP signal also 10 s long and sampled at 125 Hz. In this case, all the parameters are specified, and the function generates a ABP signal with f r = 0.5 (respiration), f c = 2.4 (heart–rate), σ = 0.5 (respiratory component amplitude), α = 1 (cardiac component amplitude, incident wave), β = 0.4 (reflection wave amplitude), µ=80 (mean ABP), σ = 15 (standard deviation of ABP), σ n = 8 (standard deviation of Gaussian white noise), cf = 10 (filter’s cut-off frequency), and pf = 1 (indicates to generate a plot). In both cases, the function outputs the random synthetic ABP (ABP Ln ), the deterministic ABP (ABPL ), and the respiratory component. C. Pulse Pressure Variation Calculation with Airway Pressure Current methods of calculating ∆Pp are based on simultaneous recording of systemic arterial and airway pressure. The availability of airway pressure greatly simplifies the problem of accurately calculating ∆Pp, since it provides a window were Ppmax and Ppmin must be calculated. Furthermore, researchers have observed that the maximal pulse is always exhibited during the inspiratory period, and the minimal pulse during the expiratory period [2]. Finally, having the airway pressure eliminates the problem of having to demodulate the effect of respiration on ABP. The pulse pressure (Pp) is calculated as the difference between systolic and diastolic arterial pressure. Maximal and

∆Pp is evaluated in triplicate over each of three consecutive respiratory cycles. The mean values of the three calculations are then used for statistical analysis. Fig. 5 shows an example illustrating the Ppmax and Ppmin metrics used in the calculation of ∆Pp. D. Pulse Pressure Variation Calculation without Airway Pressure Calculating ∆Pp in situations where simultaneous recordings of systemic arterial and airway pressure are not available is a more difficult problem. To obtain a comparable index for ∆Pp, we must demodulate the respiratory signal r(t) from the ABP. Once the r(t) is obtained, ∆Pp can be calculated following the procedure previously described. The desired signal, r(t), is available in the envelope of the modulated signal (ABP). In the case of DSB-LC AM signal, the simplest form of an envelope detector is a nonlinear charging circuit with a fast charge time and a slow discharge time. This nonlinear circuit can be constructed using a diode in series with a capacitor, and a resistor is placed across the capacitor to control de discharge time constant. In the case of ABP, demodulation of the respiratory component can also be accomplished using a nonlinear system. We decided to use rank-order filters to estimate the envelope. Rank-order filters operate similarly to median filters except that they produce the ith largest sample in the window. The filtering process is performed as follows: (1) a window of length w l is placed at the beginning of the signal to be filtered, (2) the value associated with the ith percentile is computed and stored in the output vector Y (n), and (3) the same procedure is repeated as the window slides through the data, advancing one sample at a time. Y (n) = ith largest value of the set [X(n − K), . . . , X(n), . . . , X(n + k)]

(6)

The two user–specified parameters are the window length (wl ) and the percentile value. The window length controls how much filtering it is done to the signal. 1) Respiration Demodulation Based on Rank–Filters: The technique we propose estimates w l adaptively as a function of the heart rate (f c ) and the sampling frequency (f s ),

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wl = Intodd (

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The signal is filtered using the 1th and the 99th percentile to obtain r1th (t) and r99th(t) , respectivelly. Heart rate f c is estimated based on power spectral density (PSD). The signal is partitioned and the PSD, pˆ(w), of each segment is estimated. We used the Blackman-Tukey method of spectral estimation. In general, any of the standard methods of spectral estimation could be used. To concentrate more power at the heart rate frequency and improve frequency resolution, the algorithm uses a harmonic PSD technique that combines n spectral components according to (8) h(ω) =

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III. R ESULTS Preliminary assessment of the algorithm was based on visual inspection of plots such as the ones shown in Fig. 7, 8, 9, 10. The algorithm was able to estimate the ∆Pp index from the (ABP) signal alone. IV. C ONCLUSION We described a methodology to estimate the ∆Pp index from the (ABP) signal alone. This eliminates the need of simultaneously acquiring and monitoring airway pressure. Preliminary results seem promising, but a more thorough validation is needed to fully asses its performance.

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where α ensures that the power of the harmonics added to h(ω) does not exceed the power at the fundamental by more than a factor of α. For our results we used α = 2 and n = 11. The last step in the demodulation of r(t) consists of filtering the results of the rank–order filters (r 1th (t) and r99th (t)) using a linear lowpass filter with 0.75 Hz as cutoff frequency to obtain rLP 1th (t) and rLP 99th(t) . Ppmax and Ppmin are then calculated performing element by element difference of the two LP filtered signals. Fig. 6 shows a block diagram showing the architecture of the respiration demodulator.

R EFERENCES [1] K. Bendjelid and J. , Romand, “Fluid responsiviness in mechanically ventilated patients: A review of indices used in intensive care,” Intensive Care Med, vol. 29, pp. 352–360, 2003. [2] F. Michard, D. Boussat, D. , Chemla, and N. Anguel, “Relation between respiratory changes in arterial pulse pressure and fluid responsiveness in septic patients with acute circulatory failure,” Am J Respir Crit Care Med, vol. 162, pp. 134–138, 2000. [3] F. Michard, D. , Chemla, and C. Richard, “Clinical use of respiratory changes in arterial pulse pressure to monitor the hemodynamic effects of peep,” Am J Respir Crit Care Med, vol. 159, pp. 935–939, 1998.

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