Biomedical Signal Processing and Control 8 (2013) 333–340
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Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc
Pulse pressure variation tracking using sequential Monte Carlo methods Sunghan Kim a,c,∗ , Mateo Aboy b , James McNames a a b c
Biomedical Signal Processing Laboratory, Portland State University, Portland, OR, USA Electrical Engineering Department, Oregon Institute of Technology, Portland, OR, USA Department of Engineering, East Carolina University, Greenville, NC, USA
a r t i c l e
i n f o
Article history: Received 20 December 2010 Received in revised form 25 January 2013 Accepted 28 January 2013 Available online 17 April 2013 Keywords: Amplitude modulation Pulse pressure variation Sequential Monte Carlo method State-space model
a b s t r a c t The pulse pressure variation (PPV) is a measure of the respiratory effect on the variation of systemic arterial blood pressure (ABP) in patients receiving full mechanical ventilation. It is a promising predictor of increases in cardiac output due to an infusion of fluid. We describe a novel automatic algorithm to estimate the PPV of ABP signals recorded under full respiratory support. The algorithm utilizes our recently developed sequential Monte Carlo method (SMCM), which is called a maximum a-posteriori adaptive marginalized particle filter (MAM-PF). MAM-PF estimates the state-space model parameters of the ABP signal continuously and its upper and lower envelopes are derived as a combination of those parameter estimates. Then, the continuous PPV values can be easily obtained based on those estimated envelopes. We report the assessment results of the proposed algorithm on real ABP signals. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction In many critical care settings clinicians must decide whether patients should be given intravenous fluid boluses and other therapies to improve perfusion [1]. Excessive fluid can be damaging by impairing lung function when it decreases oxygen delivery to tissues and contributes to organ failure. Insufficient fluid can result in insufficient tissue perfusion which can also contribute to organ failure. Determining the best course of fluid therapy for a given patient is difficult and clinicians have few clinical signs to guide them [2–4]. The pulse pressure variation (PPV) is a measure of the respiratory effect on the variation of systemic arterial blood pressure in patients receiving full mechanical ventilation [5]. It is a dynamic predictor of increases in cardiac output due to an infusion of fluid. Numerous studies have demonstrated that PPV is one of the most sensitive and specific predictors of fluid responsiveness [6–9]. Specifically, PPV has been shown to be useful for predicting and assessing the hemodynamic effects of volume expansion and a reliable predictor of fluid responsiveness in mechanically ventilated patients with acute circulatory failure related to sepsis [10,11].
∗ Corresponding author at: Department of Engineering, East Carolina University, Greenville, NC, USA. Tel.: +1 252 737 1750. E-mail addresses:
[email protected] (S. Kim),
[email protected] (M. Aboy),
[email protected] (J. McNames). 1746-8094/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.bspc.2013.01.008
Another study concluded that PPV can be used to predict whether or not volume expansion will increase cardiac output in postoperative patients who have undergone coronary artery bypass grafting [12]. Several recent studies have shown that the perioperative or intraoperative fluid management guided by dynamic parameters such as PPV may improve the postoperative outcome of patients receiving surgery [13–16]. Although both stroke volume variation (SVV) and PPV have been shown to be sensitive predictors of fluid responsiveness and several studies have found a good correlation between two metrics, our study is focused on the development of an automatic algorithm for PPV estimation. A significant advantage of PPV is that it can be accurately computed from the ABP signal alone. The respiratory variations of stroke volume (SV) need to be estimated by measurement of aortic blood flow velocity or using the velocity-time integral. While there has been some work on trying to estimate SVV from pulse contour analysis, leading experts including Pinsky have advised to be cautious in the clinical use of SVV until there is more data to validate the estimated surrogate metric [17]. Creating a novel algorithm for SVV estimation based on ABP alone is surely a very interesting (and challenging) problem but not the focus of our study. The standard method for calculating PPV often requires simultaneous recording of arterial and airway pressure [5]. Then, pulse pressure (PP) is manually calculated on a beat-to-beat basis as the difference between systolic and diastolic arterial pressure. Maximal PP (PPmax ) and minimal PP (PPmin ) are calculated over a single
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S. Kim et al. / Biomedical Signal Processing and Control 8 (2013) 333–340
respiratory cycle, which is determined from the airway pressure signal. Pulse pressure variations PPV are calculated in terms of PPmax and PPmin and expressed as a percentage, PPV(%) = 100 ×
PPmax − PPmin . (PPmax + PPmin )/2
(i)
as w(i) . The state trajectories before resampling are denoted as x˜ n (i) and as xn after resampling. 2.2. State-space model
(1)
Recently, Cannesson et al. proposed a novel method to use respiratory variations in the pulse oximetry plethysmographic waveform amplitude so that one can calculate PPV noninvasively [6,18]. However, there are few publicly available algorithms to automatically estimate PPV accurately and reliably. Initially the PICCO system (Pulsion Medical Systems, Germany) was the only commercial monitoring system with the capability of automatic PPV determination. Later on, Philips Medical Systems adopted our beat detection-based PPV estimation algorithm, which was made publicly available by the authors [19], and built a system which can display PPV in real-time on the Philips Intellivue MP70 monitors (Intellivue MP70, Philips Medical Systems). Its accuracy against the gold standard obtained by manual annotations were independently assessed by Cannesson [20]. A limitation of our previously described algorithm adopted by Philips is that it may not work adequately during abrupt hemodynamic changes and this may limit its applicability in operating room environments. An enhanced automatic algorithm for PPV estimation during abrupt hemodynamic changes was recently proposed to address this potential limitation [21]. Automatic beat detection algorithms have been proposed in [22]. Both of our previous PPV estimation algorithms [21,19] utilize the automatic beat detection algorithms to calculate the pulse pressure in each cardiac cycle. In the current work, we propose an alternative approach to avoid heuristic beat detection algorithms entirely. This novel automatic algorithm can be used to obtain the pulse pressure variation (PPV) from ABP signals during abrupt hemodynamic changes. Our newly proposed algorithm is the first reliable PPV method based on a statistical state-space model for arterial blood pressure signals and optimal estimation methods, which eliminates the need for the use of heuristics and empirical parameter determination. A primitive version of our automatic PPV tracking algorithm has been proposed in [23]. It was based on the state-space model in [24] and the conventional sequential Monte Carlo method in [25]. However, the reliability and accuracy of this primitive PPV tracking algorithm were not so impressive. The current PPV tracking algorithm addresses this problem by incorporating a novel state-space model and a new sequential Monte Carlo method. The objectives of the paper are to provide a detailed description of the proposed PPV tracking algorithm and to demonstrate the potential of the proposed algorithm as an accurate and reliable PPV tracker based on real ABP signals.
The proposed automatic PPV estimator utilizes our recently developed sequential Monte Carlo estimation method which is based on the state-space model approach [25]. The state-space model is a mathematical expression to describe the evolution of any physical system’s unobservable state xn and its relation to measurement y n , where the state xn is a vector of parameters representing the system’s condition. The state-space method is a technique to estimate the state xn as a function of measurement y n utilizing the state-space model. The typical state-space model can be expressed as, xn+1 = f (xn ) + un
(2)
y n = h (xn ) + vn
(3)
where (2) is a process model, (3) a measurement model, f(·) and h(·) functions of the state xn , and un and vn uncorrelated white noises with variances q and r. A designer needs to incorporate prior domain knowledge of a system into the state-space model and define the functions f(·) and h(·). The flexibility and versatility of the state-space method are attributable to these two functions, which can be either linear or nonlinear. 2.2.1. Measurement model The measurement model of the ABP signal is shown in Eqs. (4)–(7), where n is the respiratory signal, n the amplitudemodulated cardiac signal, k,n the amplitude modulation factor of the kth cardiac harmonic partial, k,n the kth cardiac harmonic parr c tial, n the instantaneous respiratory angle, n the instantaneous r cardiac angle, f n the instantaneous respiratory rate, Nhr the number of respiratory partials, Nhc the number of cardiac partials, and vn the white Gaussian measurement noise with variance r. This measurement model permits the respiratory signal k,n to modulate each of the cardiac harmonics k,n differently. The new measurement model is motivated by our observation of the asymmetric upper and lower envelopes of ABP signals after the respiratory signal is removed. Nc
y n = n + n + vn = n +
k,n k,n + vn
(4)
k=1 Nr
n =
h
r
r
r 1,k,n cos k n + r 2,k,n sin k n
(5)
k=1 Nr
2. Algorithm description
h
k,n = 1 +
h
r
r
m1,k,j,n cos j n + m2,k,j,n sin j n
(6)
j=1
2.1. Notation Nc
We have adopted the notation used in [26] with minor modifications. We use boldface to denote random processes, normal face for deterministic parameters and functions, upper case letters for matrices, lower case letters for vectors and scalars, superscripts in parenthesis for particle indices, upper-case superscripts for nonlinear/linear indication, and subscripts for time indices. For example, the nonlinear portion of the state vector for the ith state trajectory N,(i) (i.e., particle) is denoted as xn where n represents the discrete time index and (i) denotes the ith particle. The unnormalized parti˜ (i) and the normalized particle weights cle weights are denoted as w
k,n =
h
c
c
c 1,k,n cos k n + c 2,k,n sin k n
(7)
k=1
2.2.2. Process model The process model describes the evolution of each element of the state xn . In our application, xn includes the instantaneous respir c ratory and cardiac angles n and n , the instantaneous mean cardiac c
frequency f n , the instantaneous cardiac frequency f cn , and the sinusoidal coefficients { r 1,k,n , r 2,k,n , c 1,k,n , c 2,k,n , m1,k,n , m2,k,n }, that
S. Kim et al. / Biomedical Signal Processing and Control 8 (2013) 333–340
c n+1 c f n+1
f cn+1
r
= 2(n + 1)Ts f =
c n
=g
=
+ 2Ts f cn
c fn
(8)
c fn
+u
+˛
c −fn
+ uf c ,n
(11)
mk,n+1 = mk,n + um,n
(14)
where f r is the constant respiratory frequency,
f cn
the instan-
⎧ f − (f − fmax ) ⎪ ⎨ max
fmax < f
f
fmin < f ≤ fmax
fmin + (fmin − f )
f ≤ fmin .
(15)
MAM-PF
Initialization for i = 1, . . ., Np do N,(i)
N ∼0 (x0 )
Sample x0
N,(i)
|x0
end for for i = 1, . . .,Np do (i)
N,(i)
N,(i)
p y 0 |x0
L,(i)
, x0
(i)
(i)
& z 0 = x0
end for ∗ (i) i∗ = argmax˛0 & xˆ 0 = xi0 i
for n = 1, . . ., NT do for i = 1, . . ., Np do MAP Estimation Particle Propagation N,(i) xn ∼qn
k∗
=
N,(i) N,(i) xn |xn−1 , y n
(k) argmax˛n−1 p k
N,(i)
R v,n =
en eTn (k∗ )
− Hn
N,(i) N,(k) xn |xn−1
N,(i)
(k∗ )
(i)
(i)
L
N,(i)
xˆ n = xˆ n|0:n , xn
T
N,(i)
C n|0:n Fn xn
N,(i)
˛n = ˛n−1 p y n |xn
T
L,(k∗ )
+ Q Lu
N,(i)
, xˆ n|0:n−1 p xn (i)
(k∗ )
(i)
&z 0:n = z 0:n−1 , xˆ n
N,(k∗ )
|xn−1
end for Update MAP State Estimate ∗ (i) i∗ = argmax˛n & xˆ 0:n = z i0:n i
end for
2.3. Maximum a-posterior marginalized PF The sequential Monte Carlo method (SMCM) is a computational Bayesian approach to estimation of an unknown state xn recursively given measurement y n and the state-space model [26,28]. The SMCM estimates the posterior mean of the state E [p (x0:n |y 0:n )] (i) as a weighted sum of random samples x0:n , which can be expressed as, E [p (x0:n |y 0:n )] =
Np
(i)
(i)
x0:n w 0:n
(16)
(i)
where x0:n = { x0 , . . ., xn } and w 0:n is the random sample weight. The SMCM is better known as particle filters (PFs) since the random samples are often referred to as particles. More details can be found in [26]. Earlier we proposed a multiharmonic tracking method based on the conventional SMCM, that is the marginalized particle filter (MPF) [25]. Recently we have developed a novel SMCM that can overcome the limitations of the conventional SMCM such as sampling degeneracy and impoverishment issues. It also addresses properly the multi-modality issue of the posterior distribution p( f n | y 0:n ) where f n is the fundamental frequency of a multiharmonic signal. The proposed SMCM is called, maximum aposteriori adaptive marginalized particle filter (MAM-PF). The detail of the algorithm is provided in Algorithm 1. The MAM-PF ABP tracker continuously estimates the parameters of the process model shown in (8)–(14). The number of parameters to track is 4Nhr + 2Ncc + 1. Obtaining accurate estimation of those parameters is the first step toward PPV estimation.
Nc
xˆ n|0:n−1 & en = y n − yˆ n|0:n−1
Given the estimated signal parameters in (8)–(14), it is possible to estimate the upper envelope, e,n , and lower envelope, e,n , of ABP signals by following steps below,
L,(k∗ )
N,(i) xn
(k∗ )
C n|0:n−1
2.4. ABP signal envelope estimation
Marginalized Sequential Estimation Measurement Update yˆ n|0:n−1 = Hn xn
L,(k∗ )
L
&ˆxn|0:n = xˆ n|0:n−1 +
i=1
The range of instantaneous mean frequencies is assumed to be known as domain knowledge.
˛0 = 0 x0
ˆ v,n +R
c
taneous cardiac frequency, Ts the sampling period, f n the instantaneous mean cardiac frequency, ˛ the autoregressive coefficient, and ur,n , uc,n , and um,n the process noises with variances qr , qc , and qm . Since this process model is for ABP signals of patients with full mechanical support, the respiratory frequency f r has a r known constant value and the respiratory angle n is proportional to an integer multiple of it. The clipping function g[·] limits the range of instantaneous mean frequencies, which can be written as,
L,(i)
N,(i)
T
L N,(i) ˆ v,n = R ˆ v,n & xˆ L,(i) R xˆ n|0:n n+1|0:n = Fn x n (i)
(13)
L,(i)
C n+1|0:n = Fn xn
N,(i)
(R e,n )−1
(i)
f ,n
xˆ 0:−1 = E x0
C n|0:n = I − K n Hn xn
(10)
c
c k,n+1 = c k,n + uc,n
Algorithm 1.
N,(i)
T
Time Update
(12)
⎪ ⎩
K n en
(k∗ )
C n|0:n−1 Hn xn
(k∗ )
(9)
r k,n+1 = r k,n + ur,n
g[f ] =
K n = C n|0:n−1 Hn xn
f cn
N,(i)
R e,n = Hn xn
represent the morphology of the ABP signal. The process model can be expressed as, r n+1
335
(k∗ ) C n|0:n−1 Hn
ˆ v,n = ˇR ˆ v,n−1 + (1 − ˇ)R v,n R
N,(i) xn
T
c max,n
= argmax
h
c min,n
= argmin
k=1 Nc
+
k,n c 1,k,n cos k + c 2,k,n sin k
h
k=1
k,n c 1,k,n cos k + c 2,k,n sin k
Pulse Pressure (mmHg)
Blood Pressure (mmHg)
336
S. Kim et al. / Biomedical Signal Processing and Control 8 (2013) 333–340
Original Estimate
100
Nc
r
min,n = argmin
1 + k,n
Nr
100
105
110
115
120
PPmax
50
125
max,k,n =
45
(21)
r
r
r
m1,k,j,n cos j max,n + m2,k,j,n sin j max,n
Nr
min,k,n =
40
max,k,n − min,k,n
(22)
j=1
PP
PPmin
h
k=1
80 60
h
h
r
m1,k,j,n cos j min,n + m2,k,j,n sin j min,n
(23)
j=1
35 100
105
110
115
120
125
Time (s)
Nc
Fig. 1. Top: original ABP signal (red) and its estimate (green) with automatically computed envelopes (blue). Bottom: automatically computed PP signal (red) and its envelopes (blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
c
c
c
max,k,n = c 1,k,n cos k max,n + c 2,k,n sin k max,n
c
min,k,n = c 1,k,n cos k min,n + c 2,k,n sin k min,n
e,n = n +
max,k,n − min,k,n
(24)
k=1
ε,n =
k,n max,k,n
1 + max,k,n
Nc
h
1 + min,k,n
max,k,n − min,k,n
(25)
k=1
Nc
h
ε,n =
h
(17)
where 1 + k,n is equal to k,n and ε,n and ε,n are the continuous estimates of the PPmax and PPmin , respectively. The blue lines in the bottom plot in Fig. 1 represent the upper, ε,n , and lower, ε,n , envelopes of the PP signal obtained by following the steps described above.
k=1
2.6. Pulse pressure variation calculation Nc
h
k,n min,k,n
(18)
k=1
where arg max x f(x) and arg min x f(x) are operators to obtain the value of x for which f(x) attains its maximum and minimum values, respectively. The top plot in Fig. 1 shows a five respiratory cycle period of an ABP signal y n (thick red), its estimate yˆ n (thin green), and its estimated envelopes e,n and e,n (blue). 2.5. Pulse pressure signal envelope estimation The pulse pressure (PP) signal is the difference between the upper envelope, e,n , and lower envelope, e,n , of the ABP signal. This PP signal oscillates roughly at the respiratory rate as shown in the bottom plot in Fig. 1. This oscillation is due to the respiratory effect on the variation of systemic ABP under full ventilation support [10]. Within each respiratory cycle PP reaches its maximum (PPmax ) and minimum (PPmin ) values, which are two critical parameters to compute the PPV. Traditionally, the PPmax and PPmin values have been computed only once per each respiratory cycle. Given the estimated signal parameters in (8)–(14), however, we can compute the continuous equivalents of PPmax and PPmin . They are the upper, ε,n , and lower, ε,n , envelopes of the PP signal. The upper envelope, ε,n , is the continuous estimate of PPmax and the lower envelope, ε,n , that of PPmin . The ε,n and ε,n estimation steps can be written as follows:
Given the ε,n and ε,n values, it is straightforward to calculate the PPV. It can be computed as follows: PPV(%) = 100 ×
εmax − εmin (εmax + εmin )/2
(26)
This new PPV is different from the traditional PPV described in (1) because the new one is continuous in time while the traditional one can be obtained only once per each respiratory cycle. Fig. 2 illustrates an example of the automatically computed continuous PPV (thick green) and the manually obtained discrete PPV (thin red) of a real 10 min ABP signal. Each hollow white dot represents a traditional “discrete” PPV, which can be obtained once per each respiratory cycle.
35 Automatic Manual 30
PPV Index (%)
e,n = n +
A Measurement Window (5 Respiratory Cycles)
25
20
15 Nr
k,n =
h
m1,k,j,n cos j + m2,k,j,n sin j
(19)
j=1
10 0
100
200
300
400
500
600
Time (s) Nc
r max,n
= argmax
h
k=1
1 + k,n
max,k,n − min,k,n
(20)
Fig. 2. Automatic PPV (green) and manual PPV (red) over the entire ABP signal duration (10 min). One PPV measurement is computed from each measurement window, which is a time period of 5 respiratory cycles. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
S. Kim et al. / Biomedical Signal Processing and Control 8 (2013) 333–340
3. Algorithm assessment 3.1. Database for algorithm assessment The Massachusetts General Hospital (MGH) waveform database on PhysioNet is a comprehensive collection of electronic recordings of hemodynamic and electrocardiographic waveforms patients in critical care units [29,30]. It consists of recordings from 250 patients representing a broad spectrum of physiologic and pathophysiologic states. The typical recording includes arterial blood pressure (ABP) signals in addition to seven other types of waveforms. By visually inspecting the spectrogram of ABP signals we identified 26 patients whose respiratory rate remained constant at least for 10 consecutive minutes. We used the constant respiratory rate shown in spectrogram as an indicator of full respiratory support. Fig. 3 shows the spectrogram of one of the 26 ABP signals. The total duration of the 26 ABP signals was a little bit over 4 h (260 min). The original sample rate fs of the signals was 360 Hz, but they were downsampled by a factor of 9, so that the final sample rate fs was 40 Hz. Typically the constant respiratory rate f r of subjects under full ventilation support is easily accessible medical information since it is precisely controlled by the ventilator. However, the MGH database does not provide this information. Therefore, we estimated f r of each of the 26 ABP signals by following three steps. First, a given ABP signal was lowpass-filtered at 1 Hz to remove all cardiac components. Second, multiple synthetic cosine signals cos(2nTs f) were generated by sweeping the frequency f from 0.01 Hz to 1 Hz. Finally, we calculated cross-correlation between the lowpass-filtered ABP signal and synthetic cosine signals to find the best match and chose the frequency of the best matched synthetic cosine signal as the estimate of the constant respiratory rate. In the present study, it was necessary to perform this offline analysis. However, it should be noticed that normally this type of offline analysis would not be necessary because f r is known. The number of cardiac components Nc was 10 and that of respiratory components Nr was 3. The number of particles was 250. Table 1 lists the parameter values used for the PPV estimator.
337
Table 1 Summary of user-specified design parameters for the PPV tracker. Name
Symbol
Value
No. particles No. cardiac components No. respiratory components Minimum heart rate Maximum heart rate Measurement noise variance Cardiac frequency variance Respiratory amplitude variance Modulation factor amplitude variance Cardiac amplitude variance Initial respiratory amplitude Initial modulation factor amplitude Initial cardiac amplitude
Np Nc Nr c fmin c fmax r qf c qa , qb qc , qd qe , qf ua , ub uc , ud ue , uf
250 10 3 50/60 Hz 150/60 Hz var (y)/1e3 7e−6 Ts 1e−5 Ts 1e−9 Ts 1e−6 Ts std (y)/1e2 std (y)/1e2 std (y)
We had to exclude 3 ABP signals out of the 26 ABP signals from our study because it was not possible to annotate their PP signals due to a high noise level or abnormal cardiac activity. 3.3. Statistical analysis We took 5 PPV measurements per subject separately by 2 min. Each PPV measurement is an averaged value over 5 respiratory cycles. Fig. 2 shows the measurement windows. The proposed PPV tracking algorithm was assessed by calculating the agreement (mean ± standard deviation) between PPVauto and PPVmanu measurements and using Bland-Altman analysis. A Bland-Altman plot is a statistical and visualization method that is often used in the assessment of PPV estimation algorithms in order to determine the agreement between two different PPV estimates across the PPV range. It shows the difference PPV between PPVauto and PPVmanu on the y-axis and the PPVmanu on the xaxis. It shows the overall accuracy of estimation and estimation bias or trend versus PPVmanu . We used it to compare the current standard using manual annotations with our automatic estimation algorithm. 4. Results
3.2. Manual PPV annotations (current standard) We manually detected the peaks and troughs of the ABP signals and calculated the PPV indices (gold standard) as defined in (1). They are referred to as manual PPV indices PPVmanu . PPVauto represents PPV indices obtained using the proposed PPV tracking algorithm.
Fig. 4 depicts the Bland-Altman plot of the 23 subjects. There are 5 PPV measurements available per each subject. Most (98%) of PPVauto measurements were in agreement with PPVmanu measurements within ±5% accuracy, and 100% within ±7% accuracy. Table 2 lists the mean ± standard deviation of 5 PPVmanu and PPVauto measurements for each subject. The second column is for PPVmanu and the third column for PPVauto . Figs. 5 and 6 exemplify a case where signal features that are not physiological in nature are automatically filtered out resulting in more accurate PPV estimation than manual annotation. The top plot in Fig. 5 illustrates 6 respiratory cycles of the ABP
PPVmanu−PPVauto (%)
15 10 5 0 −5 −10 −15
0
10
20
30
PPVmanu (%) Fig. 3. Spectrogram of one of the 26 ABP signals from subjects under full ventilation support.
Fig. 4. Bland-Altman plot of the 23 subjects.
40
S. Kim et al. / Biomedical Signal Processing and Control 8 (2013) 333–340
Table 2 Summary of the mean and standard deviation of the PPVmanu and PPVauto measurements. Subject
PPVmanu (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
23.2 23.0 13.7 12.3 36.3 8.7 18.2 6.3 9.6 15.9 5.3 3.1 31.8 15.3 33.9 4.6 20.4 9.8 9.6 11.9 8.7 21.7 20.9
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
PPVauto (%)
1.0 0.3 0.8 1.1 5.9 1.8 2.6 1.3 1.7 0.8 1.0 0.2 1.6 2.8 1.1 1.1 2.3 0.8 2.1 0.5 1.8 1.9 2.1
23.6 22.8 14.3 9.1 33.9 9.5 18.8 6.2 7.1 14.8 5.5 4.0 31.5 13.1 34.3 3.4 20.1 11.9 11.2 10.3 11.9 18.9 20.0
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
1.0 1.6 1.2 3.1 6.7 2.0 1.7 0.8 0.8 0.8 0.7 0.3 0.8 1.8 1.8 1.0 2.7 2.2 1.4 1.2 1.9 1.2 0.7
Blood Pressure (mmHg) PPV Index (%)
Original Estimate
100 50 390 80
395
400
405
410 Manual Automatic
60 40 20 0 390
395
400 Time (s)
405
Original Estimate
150 100 50 395
396
397
398
399
400
401
402
80 60 40 395
PPmax
PPmin PPmin
PPmax 396
397
398 399 Time (s)
Manual Automatic 400
401
402
Fig. 6. Top: original ABP signal (red) with its manually annotated envelopes (black) and signal estimate (green) with its automatically computed envelopes (purple). Bottom: manual PP signal (red) and automatic PP signal (green) where the manual PP signal decreases momentarily due to an irregular and abnormal heart beat in the ABP signal. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
signal (red) of Subject 3 and its estimate (green). It also shows the manually annotated signal envelopes (black) and the automated computed signal envelopes (purple). The bottom plot in Fig. 5 depicts the PPVmanu and PPVauto over the same period. Around 399 s, the PPVmanu value (red) abruptly increases up to 78% while the PPVauto value (green) remains at 20%. Around 403 s, the PPVmanu value returns to 20%. Fig. 6 focuses on the time period marked with the black rectangular box in Fig. 5. The top plot in Fig. 6 shows that the heart beat between 398 s and 399 s is irregular and abnormal. As a result, the corresponding PPmanu shown in the bottom plot reaches a very small minimum value (PPmin,manu : 38%) between 398 s and 399 s. However, the automatically computed minimum PP value (PPmin,auto ) over the same period is as high as 70%. This discrepancy between the manual annotation and the proposed automatic method results from the capability of the MAM-PF algorithm, which estimates the ABP signal based on the state-space model. While the original heart beat 398 s and 399 s in Fig. 6 is abnormal in a physiological sense, the estimated heart beat over the
150
Pulse Presusre (mmHg) Blood Pressure (mmHg)
338
410
Fig. 5. Top: original ABP signal (red) with its manually annotated envelopes (black) and signal estimate (green) with its automatically computed envelopes (purple). Bottom: manual PPV indices (red) and automatic PPV indices (green) where one of the manual PPV indices has an abnormally high value. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
same time period shows the physiologically expected morphology and location of the heart beat.
5. Discussion 5.1. Significance Despite the availability of a commercial device for PPV monitoring, the PICCO PPV system (PICCO Pulsion Medical Systems, Munich, Germany), the need for additional independent PPV estimation algorithms is significant for several reasons. Some studies have suggested that the PICCO PPV algorithm may not work well in certain situations [31]. Our validation results in previous studies indicate that the PICCO system may not work well during abrupt hemodynamic changes [21]. Secondly, the novel PPV algorithm presented in this paper is based on a sound statistical model for ABP and plethysmogram signals and it can be implemented and used to accurately estimate PPV in data already collected and archived. Finally, we provide a detailed description to ensure that other researchers and medical manufacturers can implement it, use it for research purposes, and independently validate the results obtained using commercial PPV monitoring systems. We provide a thorough description designed to ensure reproducibility so that both medical manufactures such as Philips and Pulsion or independent researchers can implement it as part of their commercial systems. It is important to note that the proposed algorithm is a completely new design from our previously described algorithms [19]. Our previous algorithm was made publicly available by the authors and due to its performance has been adopted by Philips Medical Systems. Currently, our previously published PPV algorithm is displayed in real-time on the Philips Intellivue MP70 monitors (Intellivue MP70, Philips Medical Systems) and has been used in numerous studies related to PPV and fluid responsiveness. Its ability to monitor fluid responsiveness in the operating room and its accuracy against the current standard obtained by manual annotations were assessed by Cannesson [20]. PPV is considered the best predictor of fluid responsiveness in this setting. However, previously it was not possible to conveniently monitor this measure in the operating room or in the intensive care unit because it had to be manually calculated. Thus, the automatic PPV estimation technique
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has potential clinical application for fluid management optimization in the operating room [20]. As stated earlier, a potential limitation of our previously described algorithm adopted by Philips in their Intellivue MP70 monitors is that it may not work adequately during abrupt hemodynamic changes or significant artifact [21]. In this paper, we provide a detailed description of a novel algorithm based on a state-space model that has been designed to be a robust PPV estimator during abrupt hemodynamic changes and signal artifacts. The underlying statistical model results in automatic filtering of signal artifacts and does not require the use of algorithm heuristics or empirically determined algorithm parameters.
5.2. Algorithm’s advantages The major design difference between the proposed algorithm and previously published algorithms in [19,21] is the fact that the proposed method is based on a statistical state-space model and estimation of the cardiovascular pressure pressure signal. The state-space modeling stage results in an algorithm that is more robust to hemodynamic changes and artifacts. As shown in Figs. 5–6 the statistical state-space signal model and associated model parameter estimation algorithm automatically filter out noise and artifact that cannot be captured with the model. Since the statistical signal model is based on cardiovascular physiology and pathophysiology, signal features that are not physiological in nature are automatically filtered out. Additionally, the model is general enough to accurately model both arterial blood pressure signals and plethysmogram signals. Consequently, it can also be used to calculate the plethysmogram variability index (PVI). It is important to note that the instantaneous mean cardiac frequency, c f n , is modeled as a random walk process in (10) although the cardiac frequency is known to be modulated by the respiratory frequency. In order for the state-space model to be more accurate in a physic ological sense, the process model of f n has to be a function of the respiratory frequency, f r . However, the MAM-PF ABP tracker with the current state-space model is capable of capturing this modulation effect of the respiratory frequency on the cardiac frequency. Fig. 7 illustrates an estimated cardiac frequency (top) and its spectrogram (bottom). Since the estimated cardiac frequency fluctuates due to the modulation effect of the respiratory frequency, its spectrogram clearly shows the respiratory component at 0.2 Hz.
Fig. 7. Top: estimated cardiac frequency with fluctuations due the modulation effect of the respiratory rate. Bottom: spectrogram of the estimated cardiac frequency showing the respiratory component at 0.2 Hz.
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5.3. Study limitations The algorithm’s assessment was based on only 23 subjects with pre-recorded ABP data. Additionally, for each subject five PPV estimates were used in the assessment study. This assessment was designed to be an engineering algorithm validation against current standard manual annotations, and not a clinical validation study. Consequently, a clinical validation study assessing the ability of the proposed algorithm to monitor fluid responsiveness in the operating room in situations involving abrupt hemodynamic changes still needs to be conducted. This would require the proposed algorithm to be first adopted as part of a commercial system as was the case with our previous automatic PPV algorithm [19]. The measurement noise, vn , in Eqs. (3) and (4) is additive white Gaussian noise, which is not correlated with either the instantaneous cardiac frequency, f cn , or the instantaneous respiratory rate, f rn . In handling real data, however, situations can occur where the noise becomes colored and/or correlated with f cn or f rn . It may be worth investigating whether the performance of the proposed method noticeably degrades in the presence of colored and correlated noises. However, a thorough characterization study with synthetic data would be required, which is beyond the scope of the current work. 6. Summary We proposed a novel automatic PPV estimation algorithm based on a statistical state-space model inspired by the underlying cardiovascular and respiratory physiology. This algorithm uses our recently developed SMCM (MAM-PF) for optimal parameter estimation. The assessment results indicate good agreement against the gold standard PPV (98% within ±5% of the current standard). The algorithm was designed to work during abrupt hemodynamic changes and signal artifact. Acknowledgement This work is partially supported by funding from Thrasher Research Fund and the Medical Research Fund of Oregon. We are grateful for their financial support. References [1] E. Søreide, C.D. Deakin, Pre-hospital fluid therapy in the critically injured patient – a clinical update, Injury, International Journal of the Care of the Injured 36 (9) (2005) 1001–1010. [2] H. Solus-Biguenet, M. Fleyfel, B. Tavernier, E. Kipnis, J. Onimus, E. Robin, G. Lebuffe, C. Decoene, F.R. Pruvot, B. Vallet, Non-invasive prediction of fluid responsiveness during major hepatic surgery, British Journal of Anaesthesia 97 (6) (2006) 808–816. [3] M. Feissel, F. Michard, J. Faller, J. Teboul, The respiratory variation in inferior vena cava diameter as a guide to fluid therapy, Intensive Care Medicine 30 (9(Mar)) (2004) 1117–1124. [4] D.A. Reuter, T.W. Felbinger, E. Kilger, C. Schmidt, P. Lamm, A.E. Goetz, Optimizing fluid therapy in mechanically ventilated patients after cardiac surgery by on-line monitoring of left ventricular stroke volume variations comparison with aortic systolic pressure variations, British Journal of Anaesthesia 88 (1) (2002) 124–126. [5] F. Michard, D. Chemla, C. Richard, M. Wysocki, M.R. Pinsky, Y. Lecarpentier, J.L. Teboul, Clinical use of respiratory changes in arterial pulse pressure to monitor the hemodynamic effects of peep, American Journal of Respiratory and Critical Care Medicine 159 (3(Mar)) (1999) 935–939. [6] M. Cannesson, Y. Attof, P. Rosamel, O. Desebbe, P. Joseph, O. Metton, O. Bastien, J.-J. Lehot, Respiratory variations in pulse oximetry plethysmographic waveform amplitude to predict fluid responsiveness in the operating room, Anesthesiology 106 (6(Jun)) (2007) 1105–1111, http://dx.doi.org/10.1097/01.anes.0000267593.72744.20. [7] F. Michard, Changes in arterial pressure during mechanical ventilation, Anesthesiology 103 (2(Aug)) (2005) 419–428. [8] B. Tavernier, O. Makhotine, G. Lebuffe, J. Dupont, P. Scherpereel, Systolic pressure variation as a guide to fluid therapy in patients with sepsis-induced hypotension, Anesthesiology 89 (6(Dec)) (1998) 1313–1321.
340
S. Kim et al. / Biomedical Signal Processing and Control 8 (2013) 333–340
[9] J. Coyle, R. Teplick, M. Long, J. Davison, Respiratory variations in systemic arterial pressure as an indicator of volume status, Anesthesiology 59 (1983) A53. [10] F. Michard, S. Boussat, D. Chemla, N. Anguel, A. Mercat, Y. Lecarpentier, C. Richard, M.R. Pinsky, J.L. Teboul, Relation between respiratory changes in arterial pulse pressure and fluid responsiveness in septic patients with acute circulatory failure, American Journal of Respiratory and Critical Care Medicine 162 (1(Jul)) (2000) 134–138. [11] F. Michard, L. Ruscio, J.L. Teboul, Clinical prediction of fluid responsiveness in acute circulatory failure related to sepsis, Intensive Care Medicine 27 (7(Jul)) (2001) 1238. [12] A. Kramer, D. Zygun, H. Hawes, P. Easton, A. Ferland, Pulse pressure variation predicts fluid responsiveness following coronary artery bypass surgery, Chest 126 (5(Nov)) (2004) 1563–1568, http://dx.doi.org/10.1378/chest.126.5.1563. [13] F. Michard, M.R. Lopes, J.-O.C. Auler, Pulse pressure variation: beyond the fluid management of patients with shock, Critical Care 11 (3) (2007) 131, http://dx.doi.org/10.1186/cc5905. [14] M. Kobayashi, M. Ko, T. Kimura, E. Meguro, Y. Hayakawa, T. Irinoda, A. Takagane, Perioperative monitoring of fluid responsiveness after esophageal surgery using stroke volume variation, Expert Reviews in Medical Devices 5 (3(May)) (2008) 311–316, http://dx.doi.org/10.1586/17434440.5.3.311. [15] M. Buettner, W. Schummer, E. Huettemann, S. Schenke, N. van Hout, S.G. Sakka, Influence of systolic-pressure-variation-guided intraoperative fluid management on organ function and oxygen transport, British Journal of Anaesthesia 101 (2(Aug)) (2008) 194–199, http://dx.doi.org/10.1093/bja/aen126. [16] M.R. Lopes, M.A. Oliveira, V.O.S. Pereira, I.P.B. Lemos, J.O.C. Auler, F. Michard, Goal-directed fluid management based on pulse pressure variation monitoring during high-risk surgery: a pilot randomized controlled trial, Critical Care 11 (5) (2007) R100, http://dx.doi.org/10.1186/cc6117. [17] M.R. Pinsky, Probing the limits of arterial pulse contour analysis to predict preload responsiveness, Anesthesia & Analgesia 96 (5(May)) (2003) 1245–1247. [18] M. Cannesson, C. Besnard, P.G. Durand, J. Bohé, D. Jacques, Relation between respiratory variations in pulse oximetry plethysmographic waveform amplitude and arterial pulse pressure in ventilated patients, Critical Care 9 (5(Oct)) (2005) R562–R568, http://dx.doi.org/10.1186/cc3799. [19] M. Aboy, J. McNames, T. Thong, C. Phillips, M. Ellenby, B. Goldstein, A novel algorithm to estimate the pulse pressure variation index, IEEE Transactions on Biomedical Engineering 51 (2004) 2198–2203.
[20] M. Cannesson, J. Slieker, O. Desebbe, C. Bauer, P. Chiari, R. Hénaine, J.-J. Lehot, The ability of a novel algorithm for automatic estimation of the respiratory variations in arterial pulse pressure to monitor fluid responsiveness in the operating room, Anesthesia & Analgesia 106 (4(Apr)) (2008) 1195–1200, http://dx.doi.org/10.1213/01.ane.0000297291.01615.5c, table of contents. [21] M. Aboy, C. Crespo, and D. Austin,;1; An enhanced automatic algorithm for estimation of respiratory variations in arterial pulse presssure during periods of abrupt hemodynamic changes. IEEE Transactions on Biomedical Engineering 56(10(Oct)) (2009) 2537–2545. [22] M. Aboy, J. McNames, T. Thong, D. Tsunami, M.S. Ellenby, B. Goldstein, An automatic beat detection algorithm for pressure signals, IEEE Transactions on Biomedical Engineering 52 (10(Oct)) (2005) 1662–1670. [23] S. Kim, M. Aboy, J. McNames, Pulse pressure variation estimation using a sequential monte carlo method, in: 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Minneapolis, MI, USA, Sep. 2009, 2009. [24] J. McNames, M. Aboy, Statistical modeling of cardiovascular signals and parameter estimation based on the extended kalman filter, IEEE Transactions on Biomedical Engineering 55 (1(Jan)) (2008) 119–129. [25] S. Kim, L. Holmstrom, J. McNames, Multiharmonic Tracking Using Marginalized Particle Filters, in: Proceedings of 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2008, Aug, pp. 29–33. [26] O. Cappé, S. Godsill, E. Moulines, An overview of existing methods and recent advances in sequential Monte Carlo, Proceedings of the IEEE, IEEE-INST Electrical Electronics Engineers, Inc. 95 (5(May)) (2007) 899–924. [28] A. Doucet, S. Godsill, C. Andrieu, On sequential Monte Carlo sampling methods for Bayesian filtering, Statistics and Computing 10 (3(Jul)) (2000) 197–208. [29] A.L. Goldberger, L.A.N. Amaral, L. Glass, J.M. Hausdorff, P.C. Ivanov, R.G. Mark, J.E. Mietus, G.B. Moody, C.-K. Peng, H.E. Stanley, PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals, Circulation 101 (23) (2000) e215–e220 (June 13), circulation Electronic Pages: http://circ.ahajournals.org/cgi/content/full/101/23/e215 [30] G.B. Moody, R.G. Mark, A database to support development and evaluation of intelligent intensive care monitoring, Computers in Cardiology 23 (1996) 657–660. [31] C. Wiesenack, C. Fiegl, A. Keyser, C. Prasser, C. Keyl, Assessment of fluid responsiveness in mechanically ventilated cardiac surgical patients, European Journal of Anaesthesiology 22 (9(Sep)) (2005) 658–665.
