A NONINVASIVEMETHODOF ESTIMATINGMEAN PULMONARYARTERYPRESSUREIN THE PNEUMATIC TOTAL ARTIFICIALHEART

Vonesh MJ, Cork RC, Mylrea KC. A noninvasive method of estimating mean pulmonary artery pressure in the pneumatic total artificial heart. J Clin Monit 1991;7:294-303

Michaeld. Vonesh, MSEE,* Randall C. Cork, MD, PhD,~" and Kenneth C. Mylrea, PhD, PE~:

ABSTRACT,Accurate hemodynamic monitoring is essential for

the clinical management o f the recipient of a total artificial heart (TAH). The high incidence of pulmonary congestive disorders in this population complicates this already formidable task. Lack of diagnostic pulmonary artery pressure (PAP) information is recognized as a fundamental source of these problems. Because conventional methods o f obtaining hemodynamic information are difficult to implement in T A H recipients, improvement o f T A H case management depends on the development o f innovative monitoring strategies. Noninvasive monitoring techniques have been developed for three (right atrial pressure, left atrial pressure, and aortic pressure) of the four auxiliary circulatory pressures used to quantify hemodynamic performance. Development o f the fourth, for PAP, was the subject of this work. We developed a noninvasive, in vitro method o f estimating mean PAP in the Jarvik-7 T A H (Symbion, Inc, Salt Lake City, UT) recipient. This information was obtained by analyzing the relationship between the pneumatic right drive pressure (RDP) and PAP waveforms produced by aJarvik-7 (70 ml) connected to a Donovan mock circulation and driven by a Utahdrive System IIIe Controller (Symbion, Inc, Salt Lake City, UT). Total artificial heart driver parameters (i.e., heart rate, percent systole, and vacuum) were manipulated to produce a range o f ventricular filling volumes (FV), from 40 to 60 ml, for three distinct states o f the pulmonary vasculature: hypotensive, normal, and hypertensive. A unique multiple-linear regression equation was derived for each FV from the R D P - P A P relationship exhibited under these conditions. Comparison of computed estimates of PAP with actual measurements showed overall average correlations o f greater than 0.92, with a standard error of the estimate o f less than 1.9 m m Hg. The mean difference between actual and computed PAP measurements was - 0 . 0 3 - 2.0 Hg. Estimations were accurate within 8.5% of true PAP values. Additional experimentation revealed that while the R D P - P A P relationships are dependent on FV, they are independent of the manner in which FV was obtained. Estimates proved useful over the clinical operating range of the pneumatic heart driver, as well as over the normal physiologic range o f PAP in the human. This method is readily applicable to a computer-based monitoring implementation, although its effectiveness needs to be demonstrated in vivo. KEY WORDS.Heart: total artificial. Monitoring: pressure, pul-

monary arterial.

From the +Department of Cardiology, Northwestern University Medical School, Evanston, IL; the -['Department of Anesthesiology, Arizona Health Sciences Center, Tucson, AZ; and the :~Department of Electrical and Computer Engineering, University of Arizona College of Engineering, Tucson, AZ. Received May 30, 1989, and in revised form Nov 5, 1990. Accepted for publication Nov 26, 1990. Address correspondence to Dr Cork, Department of Anesthesiology, Arizona Health Sciences Center, Tucson, AZ 85724. 294 Copyright © 1991 by Little, Brown and Company

N o n o n i n v a s i v e m e t h o d exists for e s t i m a t i n g p u l m o n a r y a r t e r y p r e s s u r e (PAP) in t h e J a r v i k - 7 total artificial heart ( T A H ) ( S y m b i o n , Inc, Salt Lake City, U T ) . A l t h o u g h arterial grafts specially o u t f i t t e d w i t h i n d w e l l i n g catheters are available for this p u r p o s e , t h e y are f r a u g h t w i t h p r o b l e m s such as infection, t h r o m b o e m b o l i f o r m a t i o n , catheter clotting, and difficulties associated w i t h fabrication a n d calibration, [1,2]. C o n v e n t i o n a l t r a n s c u t a n e o u s pressure catheters (e.g., S w a n - G a n z )

295

Vonesh et ah Estimating Pulmonary Artery Pressure in the T A H

Inflow Valve

Drive Line Pressure (DLP) Waveform

f--- OutflOo~tf~:l:Graf t , ,u.--~ ,

Isovolumetric Contraction /

, 1, m Blood ~1

Housing--J' ~ ~ ~ J ~ _ _ Base--/----Y / /// ~x/ ,/~--Drive

\

I I Ejection I ~ Ft" EmptyPoint

o,-_

D,a0 a0m

:' 1 D I

i

r¢

_iu

Nipple

"---Airand Intermediate Diaphragms Line

Fig I. Schematic of the Jarvik-7 TAH.

:

• Diastole

Systole

cannot be used to measure PAP in T A H recipients due to the obstruction they would present to the prosthetic valves regulating blood flow through the right ventricle. As a consequence, accurate determination and close regulation of the pressure-flow relationships in the pulmonary vasculature are not possible. This is a genuine problem given the high incidence of pulmonary hypertension, pulmonary edema, and acute respiratory distress syndrome frequently encountered in TAH recipients [3-5]. The goal of this research was to develop a noninvasive method of estimating mean PAP in the Jarvik-7 T A H (Fig 1), valid over a wide range of physiologic conditions. Noninvasive monitoring techniques have been developed for three (right atrial pressure [RAP], left atrial pressure [LAP], and aortic pressure [AOP]) of the four auxiliary circulatory pressures used to quantify hemodynamic performance. Development of the fourth, for PAP, was the subject of this work. Noninvasive monitoring is feasible in the pneumatic T A H because considerable hemodynamic information is transduced across the elastic pumping diaphragm of the artificial ventricle to the driving medium: air [6-9]. Analysis of the driving medium characteristics (e. g., air pressure and flow) allows indirect determination of hemodynamic information on a cycle-to-cycle basis (Figs 2 and 3). Our method of estimating mean PAP uses information within the right drive pressure (RDP) waveform. By analyzing the ventricular RDP waveform for cardiac cycles of known filling volume (FV) and toad conditions, we were able to derive a multiple linear regression equation relating RDP waveform characteristics to mean PAP. A unique regression equation was identified for each FV. This equation was found to be accurate

I 80

I

I

I

240

I

I

CompleteFillPoint

I

I

400 560 Time (sec)

I

I

720

Fig 2. The Jarvik-7 drive line pressure waveform annotated with the hemodynamic information used in this report.

I

50-

;'

40-

1

I Integration line

)i

FV = A r e a u n d e r c u r v e

! ,

I

._1

I

30-

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rr

.g

20-

LL 10-

1 , I

I! I

i

I

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0.2

I 0.3

i

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i

i

i

Seconds

Fig 3. Diastolic airflow waveform of the Jarvik-7 TAH.

(i.e., >90%) over the physiologic conditions simulated in this experiment and independent of the driver parameters used to control T A H performance. This method holds promise for improving future clinical TAH hemodynamic monitoring schemes. MATERIALS AND METHODS

The relationship between RDP and mean PAP was investigated in a two-part experimental protocol imple-

296 Journal of Ctinical Monitoring Vol 7 No 4 October 199t

Pulmonary Artery Pressure 25

-

I

A

Mock Circulation

Pressure Module

L

[I

22.5 -"rE E v

]

PAP

Jarvik-7 TAH 20

--

(t} u)

"¢ 13.

17,5--

15

--

COMDU and Driver Unit

I 80

I

I 240

I

I

I

I

400 560 Time (sec)

I

I

Data Acquisition System

720

Fig 5. Schematic of the experimental setup.

Fig 4. PAP waveform indicating systolic (A) and diastolic (B) pressures.

mented in the laboratory of the University of Arizona Artificial Heart Department. All experiments were conducted using a water-filled Donovan mock circulation (Symbion, Inc, Tempe, AZ) to which a Jarvik-7 (70 ml) TAH was connected. The TAH was pneumatically driven by a Utahdrive System IIIE Controller unit (Symbion, Inc, Salt Lake City, UT), and its hemodynamic performance was monitored by C O M D U software (version 1.110) residing in a Compaq PC (Houston, TX). Auxiliary monitoring equipment used for this research included Gould pressure transducers and Hewlett-Packard (Waltham, MA) pressure modules (no. 78553A) and monitor (no. 78534A). Continuous pressure measurements were obtained from the four mock circulation compartments (right atrium, left atrium, aorta, and pulmonary artery) via catheters placed into these chambers. Continuous analog signals of PAP (Fig 4), RDP, and trigger (TRIG) were interfaced to an IBM-AT computer via an analog-to-digital data acquisition system (Metrabyte DASH-16, Metrabyte, Inc, Taunton, MA). Right drive pressure and TRIG signals were generated by the pneu-

matic drive system. A schematic of the experimental setup is given in Figure 5. A computer program written with ASYST software (version 1.56, MacMillan Software Company, New York, NY) was used for data acquisition and preliminary waveform analysis. Data acquisition was initiated on reception of the TRIG signal, at which time 32 Sequential cardiac cycles of PAP and RDP waveform data were sampled at 500 Hz and subsequently averaged using a nonweighted algorithm. Averaged RDP and PAP waveforms were archived, along with records of RAP, LAP, AOP, C O M D U estimates of cardiac output and FV, and the settings of the pneumatic drive system, heart rate (HR), percent systole (SYS), and diastolic vacuum (VAC). Statistical analysis of the data was performed on the University's DEC VAX mainframe computer. We used SPSSX software (version 3.0, SPSS Inc, Chicago, IL) to perform the stepwise multiple linear regression, residual, t-test, and other statistical analyses [10] described below. Experimental conditions simulated the clinical situation as closely as possible. Pneumatic driver parameters (HR, SYS, and VAC) were kept within the normal din-

Table 1. Experimental Driver Parameters

Parameter

Units

Clinical Range

Mean

SD

HR SYS VAC

Cycles/min % mm Hg

115-155 40-65 0-20

135.25 56.27 1.48

9.05 6.65 2.12

Vonesh et al: Estimating Pulmonary Artery Pressure in the T A H

297

Table 2. Mock Circulation Pressures (ram ttg)

Variable

Physiologic Range

Mean

SD

AOP RAP LAP Hypotensive PAP Normal PAP Hypertensive PAP

70-105 0-8 4-14 1-12 13-20 21-30

81.95 7.89 12.57 10.55 15.76 24.86

3.12 2.19 2.67 3.43 2.09 2.27

Table 3. Filling Volumes Used in Experiment (ml)

FV

% Ventricle Full

Mean

SD

30 35 40 45 50 55 60

43 50 57 64 71 79 86

30.40 35.10 39.99 45.33 49.89 54.33 59.72

1.25 1.06 3.75 1.12 4.16 1.18 1.41

ical range o f the Jarvik-7 T A H (Table 1). With the exception o f the pulmonary circuit, the mock circulation emulated normal circulatory conditions. The pulmonary circuit was configured to mimic three different conditions o f the pulmonary circulation: hypotension, normotension, and hypertension (Table 2). Part 1

The first part o f the experiment was devised to establish a relationship between the RDP and PAP waveforms for cardiac cycles o f k n o w n FV. Filling volume was chosen as a way o f categorizing these relationships, because it is often used as the primary method o f adjusting the clinical performance oftheJarvik-7 TAH. For stable circulatory conditions, FV is a function o f both pneumatic driver parameters (HR, SYS, and VAC) and physiologic considerations, such as venous return, ventricular preload, and vascular resistance. Filling volume can thus be thought o f as a single parameter representing the net effect o f both driver and circulatory factors on T A H performance. Right drive pressure and PAP data were collected for seven different FVs (Table 3) under each o f the three afterload conditions. For each FV, an optimal RDP was identified as that point at which incomplete filling and complete ejection o f the ventricular contents occurred. Adhering to this protocol allowed filling and ejection waveforms to meet the same evaluation criteria applied to a T A H recipient in the clinical environment. Once the optimal RDP was identified, the RDP was reduced by 10 m m Hg. Waveform data were collected at this RDP and at 10 incremental

(2.5 m m Hg) steps o f RDP above this point. In this manner, the T A H was driven at a range o f pressures about the optimal RDP point for a given FV. This protocol resulted in 7 data sets composed o f 30 digitized R D P - P A P waveform pairs. Data were used to derive a stepwise multiple-linear regression equation defining the R D P - P A P relationships for each o f the 7 FV data sets. Twelve primary variables and 30 secondary variables (42 variables) were used as the independent measures characterizing the RDP waveforms (Fig 2 and Tables 4 and 5). The dependent variable was mean PAP, which was estimated as the average value o f the PAP waveform over 1 cardiac cycle. Initially, all 42 independent variables were included in the multiple linear regression equation. Following analysis o f the t-ratios and beta-weights o f the resulting coefficients, the number o f independent variables used in the regression equation was restricted to 4. It was found that the first 4 independent variables included in the regression equations (i.e., those with the 4 highest beta-weights o f their coefficients) had an average t-ratio o f 7.51, indicating a strong likelihood for inclusion in the regression equation (i.e., p < 0.001). The remaining 38 independent variables had lower beta-weights (indicating that they had less influence on the dependent variable) and yielded t-ratios o f less than 2 in magnitude (indicating a lack o f significance for inclusion in the equation at thep = 0.05 level). By including only 4 independent terms in the multiple linear regression equation, we were able to reduce equation size without a significant (p < 0.05) loss o f correlation to mean PAP. N o forcing through 0 was attempted.

298 Journal of Clinical Monitoring Vol 7 No 4 October t991

Table 4. Primary Variables Characterizing Drive Line Pressure

A

Ventricular end-diastolic pressure Outflow valve opening pressure Minimum ventricular plateau pressure End of valve motion pressure End-ejection pressure End-systolic ventricular pressure Mean RDP between points B and E Mean RDP between points B and F Mean RDP between points C and E Mean RDP between points C and F Mean RDP between points D and E Mean RDP between points D and F

B

C D E F RM1 RM2 RM3 RM4 RM5 RM6 See Figure 2.

Table 5. Secondary Waveform Variables Used in Regression Equations

B-A C-A D-A E-A F-A A/B A/C A/D AlE A/F

B-C D-C E-C F-C

D-B E-B F-B

B/C B/D B/E B/F

C/D C/E C/F

E-D F-D

F-E

used in part 1 o f the experiment were repeated for the 3 additional trials o f the low, normal, and high FV cases. In the second part o f the experiment, however, 3 different combinations o f driver parameters (HR, SYS, and VAC) were identified and used for each FV trial. This protocol yielded 3 data sets, corresponding to the 40, 50, and 60 ml FV cases, composed o f three groups (i.e., 3 different driver parameter sets) o f 30 R D P - P A P waveform couplets each. The regression equations derived in part 1 were applied to the data sets collected in part 2 to estimate true PAP. By using the original regression equations with new data sets, a measurement o f FV influence on the overall accuracy o f the equations was obtained. As in part 1, regression and residual statistics were calculated on these data. Student's t-tests were performed to compare the regression and residual statistics obtained in each half. RESULTS

D/E D/F

E/F

See Figure 2 and Table 4.

Residual statistics were computed to quantify the ability o f RDP waveform characteristics to estimate mean PAP. The difference between actual and estimated mean PAP (residual) was calculated for each data set. From these values, a residual mean (bias) and standard deviation (precision) were computed. Additionally, the accuracy o f this method was computed by dividing the bias by the actual PAP and multiplying this result by 100. Part 2

The second part o f this experiment was designed to test whether the R D P - P A P relationships determined in the first half were independent o f the manner in which the individual FVs were obtained. For steady-state circulatory conditions, FV can be realized through many different combinations o f HR, SYS, and/or VAC. Consequently, it is necessary to ascertain whether the driver parameters determining a particular FV play a significant role in the R D P - P A P relationship. Low (40 ml), normal (50 ml), and high (60 ml) FV cases were isolated for additional testing because they are representative o f the FV range typically encountered in the clinical environment. Data collection procedures

Part 1

Part 1 o f this experiment hypothesized the existence o f a relationship between RDP and PAP for discrete FVs. Regression and residual statistics were computed to quantify this relationship. The results o f these analyses are presented below. Regression statistics estimate the degree o f relationship between dependent and independent variables assessing the fraction of the variance o f the dependent variable attributable to variations in the independent variables. Stepwise regression analyses o f the data from part 1 yielded 7 unique multiple-linear regression equations relating RDP to PAP. Thirty data points were used for each regression analysis. For each FV category, these data points were representative o f the R D P - P A P relationship over a range o f RDPs (25 m m Hg) and PAPs (hypotensive to hypertensive) states. The regression equations computed by SPSSX are mathematically expressed in the form REGRESSION EQUATIONS.

4

Dependent variable = E B[i] * independent variable[i] + C i~1

where the dependent variable is mean PAP, the independent variables are the characteristics o f the RDP waveform, B is the SPSSX computed correlation coefficient, and C is a computed constant. The 4 independent variables, their corresponding correlation coefficients, and the constant used in each o f the 7 original

Vonesh et ah Estimating Pulmonary Artery Pressure in the T A H

299

Table 6. Multiple Linear Regression Equations

FV

Vat1: Coeff

Var2: Coeff

Var3: Coeff

Var4: Coeff

Const

30 35 40 45 50 55 60

RM5:2.44 A: 2.36 A: 4.23 A: 3:45 A: 3.40 B: 0.91 B: 0.65

F-C: - 2.23 RM3:0.85 A/D: - 15.22 A/D: -123.6 A/B: -474.3 C-A: -0.33 E - D : - 0.51

C-A: F-C: E-D: F-D: A/F: C/D: C/D:

E/F: C/F: D-C: B-C: E/F: D/E: A/B:

19.05 88.92 - 13.35 10.87 8.13 2.09 24.85

- 1.67 -3.13 0.15 -0.67 391.8 -48.81 - 40.44

- 38.25 - 124.7 - 0.92 0.53 3.93 30.22 14.78

See Tables 4 and 5 and Figure 2 for variable (Var) definitions. Abbreviations: Coeff, regression coefficient; Const, regression constant.

Table 7. Part 1 Regression Statistics

Computed vs. Actual PAP (mmHg)

FV

N

r

SE of Estimate (mm Hg)

30 35 40 45 50 55 60

30 30 30 30 30 30 30

0.99 0.99 0.99 0.98 0.98 0.98 0.98

0.85 0.66 0.83 1.15 1.32 1.24 1.13

1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.99

1.05

1.00 (0.03)

Slope

Intercept (mm Hg) 0.00 0.00 0.00 0.00 0.00 0.00 0.00

24-

R = 0.99

"~ 22"

Z ' ' "

< 0.001

E

Average

(0.02) (0.02) (0.03) (0.04) (0.03) (0.04) (0.02)

(0.37) (0.38) (0.55) (0.65) (0.67) (0.71) (0.54)

.~E 20" a. 18" n< 12"

g 10" ~"

0.00 (0.55)

,,

=

0

NOTE: N u m b e r s in parentheses represent standard errors.

equations are presented in Table 6. Table 7 contains the regression statistics for the 7 regression equations. Typical regression plots for evaluating the regression equations at 40, 50, and 60 ml FV are depicted in Figures 6, 7, and 8, respectively.

b

14"

|

|

4

f

8

FV = 40ml !

!

!

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!

|

!

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=

12 16 20 24 Computed PAP (mmHg)

|

I

28

I

32

Fig 6. Case regression plot, 40 ml FV: estimated versus actual mean PAP.

Computed vs. Actual PAP (mmHg) 35-

RESIDUAL STATISTICS. Residual statistics quantify the similarity b e t w e e n a value and an a p p r o x i m a t i o n to this value. Analysis o f residual statistics thus provides insight into the ability o f an estimation technique. Bias, precision, and accuracy statistics for the 7 regression equations are c o m p i l e d in Table 8.

'a0-

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a. 20=

ls"o 10" =

5" 0" -5

In part 2 o f the experiment, w e hypothesized that the validity o f the derived regression equations w o u l d be independent o f the m a n n e r in w h i c h a given FV was obtained. Regression and residual statistics were c o m puted f r o m the extended testing o f the 40, 50, and 60 ml FV equations to evaluate this hypothesis. Results o f these analyses are presented in Table 9. C o m p a r i s o n s o f the average regression and residual statistics f r o m each half o f the experiment are tabulated in Table 10, along with the results o f t-tests p e r f o r m e d on these groups.

.

E 25E

¢9

Part 2

R = 0.98

2

FV = 50ml

l'ol'21'41'61'sioi2i4d6isiod23"4 Computed PAP (mmHg)

Fig 7. Case regression plot, 50 ml FV: estimated versus actual mean PAP.

300 Journal of Clinical Monitoring Vol 7 No 4 October 1991

DISCUSSION

Computed vs. Actual PAP (mmHg)

.--.40- R = 0.98 ~35"E p < ~

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12

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24

28

32

36

Computed PAP (mmHg) Fig 8. Case regression plot, 60 ml FV: estimated versus actual mean PAP.

Noninvasive hemodynamic monitoring of TAH perf o r m a n c e can be a c c o m p l i s h e d t h r o u g h analysis o f p n e u m a t i c d r i v e line variables. F o r e x a m p l e , p n e u m a t i c d r i v e line pressure o f t h e J a r v i k - 7 T A H p r o v i d e s insight into the m e c h a n i c s o f v e n t r i c u l a r o p e r a t i o n , as well as i n t r a v e n t r i c u l a r pressures (Fig 2) [7,8,11,12]. A d d i t i o n a l d i a g n o s t i c i n f o r m a t i o n is available t h r o u g h the c o m p u terized e v a l u a t i o n o f the air e x h a u s t p a t t e r n s in the d r i v e lines d u r i n g diastole (Fig 3). D u r i n g the diastolic phase o f the cardiac cycle, each milliliter o f b l o o d passively e n t e r i n g the v e n t r i c u l a r b l o o d c o m p a r t m e n t displaces a milliliter o f air f r o m the v e n t r i c u l a r air c h a m b e r [13]. Since p r e s s u r e is c o n s t a n t d u r i n g this phase, the v o l u m e o f b l o o d e n t e r i n g the T A H d u r i n g diastole m a y be quantified b y m e a s u r i n g the q u a n t i t y o f air exiting the

Table 8. Part 1 Residual Statistics FV

N

30 35 40 45 50 55 60 AVG

30 30 30 30 30 30 30

Mean Residual (Bias in mm Hg)

SD o f Residual (Precision in m m Hg)

Accuracy (%)

SD o f Accuracy

0.00 0.00 -0.07 0.00 0.08 0.00 -0.12 -0.02

0.84 0.65 1.19 1.13 1.51 1.45 1.31 1.15

4.14 3.02 11.64 5.20 8.34 7.25 7.66 6.75

3.74 3.21 8.62 3.45 8.01 5.77 6.90 5.67

Table 9. Part 2 Regression and Residual Statistics Regression SE of

Residual

FV

N

r

Estimate (mm Hg)

40 50 60

90 90 90

0.93 0.98 0.86

I. 95 1.23 2.34

0.00 0.00 - 0.09

2.12 1.29 2.34

10.29 6.12 8.99

7.05 5.70 6.87

0.92

1.84

- 0.03

1.92

8.47

6.54

Average

Bias (mm Hg)

Precision (ram Hg)

Accuracy (%)

SD of Accuracy (%)

Table 10. Comparison of Average Regression and Residual Statistics From Parts t and 2 Parameter

Part 1

Part 1

Part 2

FV (ml) cvaluated r SE of Regression Estimate (mm Hg) Bias (mm Hg) Precision (mm Hg) Accuracy (%)

All 0.99 1.05 - 0.02 1.15 6.75

40, 50, 60 0.98 a 1.09" - 0.04 ~ 1.3# 9.21

40, 50, 60 0.92 bc 1.84 bc - 0.03 bc 1.92 bc 8.47 c

~No significant difference between part 1 (all) versus part 1 (40, 50, 60) at p < 0.01. bNo significant difference between part 1 (all) versus part 2 (40, 50, 60) at p < 0.01. CNo significant difference between part I (40, 50, 60) versus part 2 (40, 50, 60) at p < 0.01.

Vonesh et al: Estimating Pulmonary Artery Pressure in the T A H

drive line over this period of time. This measurement allows the calculation of ventricular FV and, by multiplication with driver HR and appropriate empiric constants, an estimate o f cardiac output. The hemodynamic data furnished via the interpretation of the drive line air pressure and air flow waveforms constitute the bulk of the information currently available for diagnostic use. This monitoring scheme has been proven to be an accurate, noninvasive means of obtaining vital hemodynamic information [7,8,1411. Nevertheless, in its present configuration, the current monitoring approach does not fully use all the information available, and requires the human operator to assimilate an enormous amount of data to properly regulate T A H performance [15]. To augment present T A H monitoring capabilities, several investigators have established relationships between the currently monitored parameters (filling rate, FV, cardiac output, drive line pressure, HR, etc.) and variables that provide significant information but that are not presently monitored (atrial pressures, central venous pressures, etc.). Hemodynamic information available through this work includes AOP [1], LAP [1,2,5], and RAP or central venous pressure (CVP) [1,5]. Noninvasive monitoring techniques have been developed for three (RAP, LAP, and AOP) of the four auxiliary circulatory pressures used to quantify hemodynamic performance. Development of the fourth, for PAP, was the subject of this work. Our method of estimating mean PAP from characteristics of the RDP waveform provides a noninvasive means o f acquiring essential hemodynamic information. This method is clinically important because information can be made available without the use of indwelling transducers, prosthesis modification, or additional surgical intervention. This method proved valid, in a simulated environment, over the normal clinical operating range of the Jarvik-7 T A H driver, as well as the normal physiologic range of mean PAP for the human T A H recipient. Part 1

Table 6 indicates that a R D P - P A P relationship does exist and can be defined by a unique 5-term multiple linear regression equation for T A H cardiac cycles of known FV. The average correlation coefficient (r) for the 7 regression equations was greater than 0.98 (Table 7). Since correlation coefficients of 1.00 signify a perfect correlation between independent and dependent variables, the values of the correlation indices obtained in this experiment suggest that the R D P - P A P relationship defined by the regression equations is particularly

301

strong. This contention is supported by the modest mean estimation error (1.05 m m Hg; from Table 7) attributable to the derived regression equations. The acceptably small estimation error, together with the high degree of correlation between RDP and PAP, suggests that this method may be accurate enough to provide clinically useful information. The residual statistics contained in Table 8 further support the notion that a relationship between RDP and PAP exists, and that this relationship may be exploited to estimate PAP. Mean residual (bias) values averaged close to 0.00 ( - 0 . 0 2 m m Hg), indicating that predicting PAP via the regression equations provided a very close, although slightly negative, average approximation to true PAP values. Mean standard deviation of the residual (precision) values were also relatively small (1.15 mm Hg). As expected, values of the standard error of the regression estimate were similar to precision values. On the average, this method was shown to be capable of estimating PAP with accuracies within +-7% o f the true PAP. t-Testing revealed no significant differences (at p < 0.01) between true PAP and estimated PAP. These facts are significant for two reasons: they establish the existence of a relationship between RDP and PAP for discrete FVs of the T A H and they suggest that the original regression equations are accurate over a wide range of operational and physiologic conditions. Part 2

The R D P - P A P relationships established by this research are wholly dependent on FV, but are independent of h o w the FV was obtained. In part 2 of the experiment, the original multiple-linear regression equations derived for FV cases of 40, 50, and 60 ml were each tested on additional sets of data collected according to the same protocol used in part 1. The primary difference between the testing data and the original data was the manner in which the FVs were obtained. The driver parameters manipulated to acquire the three FVs of the test cases were substantially different from those used in the original cases, as well as from each other. Comparing the statistics describing the part 1 data (Tables 7 and 8) with those describing the part 2 data (Table 9) provides insight as to how FV influences regression equation performance. Comparison of coefficient values reveals that, as expected, there is an average decrease ( - 7 . 0 7 % ) in the overall correlation index of the regression equations when tested under varying conditions. Similar comparisons of the average percent change between part 1 and part 2 data reveals that standard error increased 75%, bias increased 50%, precision increased 67%, and estimation accuracy decreased 26%.

302 Journal of Clinical Monitoring Vol 7 No 4 October 1991

A decrease in the effectiveness o f this method between part 1 and part 2 is to be expected. Thus, the important question involves the extent o f this difference and its implications. Table 10 compares the average regression and residual values obtained for all FV cases o f part 1, the 40, 50, and 60 ml FV subset of part 1, and all o f part 2. Grouped t-tests performed between each o f these categories revealed that there were no significant (p < 0.01) differences between any o f the groups for correlation indices (r), standard error, bias, or precision. A significant difference between the accuracy o f the estimates between part 1 (all) and part 2 was found. There were, however, no significant differences in accuracy between the part 1 subset (40, 50, and 60 ml FV cases) and part 2 estimation (also composed o f 40, 50, and 60 ml FV cases). It should be noted that a significant difference between the accuracy o f part 1 (all) and its subset (40, 50, and 60 ml FV cases) was also evident. As in part 1, there were no significant differences between true and estimated PAP at p < 0.01. These data imply that despite the apparently large percentage discrepancies between part 1 and part 2 estimations, no statistically significant differences exist between performance indicators for equivalent FVs in those 2 groups. This means that the regression equations derived in part 1 remain valid, independent o f the manner in which FV was obtained. The data in Table 9 imply that the best performance indicators are available for cases having 50-mt (normal) FVs. These indicators diminished as the FV approached maximum (60 ml) or minimum (40 ml) values. Because the Jarvik-7 is normally operated for FVs constituting 70 to 80% (50-55 ml) o f the total FV capacity, these results suggest that higher correlations can be obtained by operating in the " n o r m a l " FV region. Possible causes o f this phenomenon include regurgitation mechanisms occurring at extreme FV cases and the empiric optimization o f the C O M D U software for normal FV operation. The method developed in this research may find similar success in estimating A O P from characteristics o f the left pneumatic drive pressure (LDP) waveform. These conclusions are based on the hemodynamic similarity o f the R D P - P A P and L D P - A O P systems. Although past methods o f A O P determination have proven to be entirely adequate, this method may be easier to integrate into the current T A H monitoring instrumentation. This method is readily adaptable to a computerbased, automated monitoring implementation. In a simple software confuguration, FV estimates from the C O M D U program can be used to index a look-up table containing a series o f unique regression equations for a

range o f FVs. Appropriate RDP waveform descriptors can be identified (via an automated algorithm applied to the C O M D U - g e n e r a t e d RDP waveform) and plugged into the regression equation indexed by the FV. Mean PAP can be subsequently estimated, displayed, and used for diagnostic or control purposes. N o clinical implementation o f this method, however, is feasible without thorough verification in an animal (calf) model. The terms comprising the regression equations (i.e., independent variables, correlation coefficients, and constants) that define the R D P - P A P relationship will no doubt change with different circulatory models, pneumatic heart drivers, and refinements o f the T A H itself. Nevertheless, the primary tenet o f this research, that a unique, empiric relationship exists between RDP and PAP for T A H cardiac cycles o f k n o w n FV (regardless o f how FV was obtained), will, in all likelihood, remain true. For this reason, this method holds promise for improving T A H monitoring. The authors wish to acknowledge the valuable assistance given by Marilyn Cleavinger and Rich .Smith in the Artificial Heart Department at University Medical Center and by Ronald Hilwig, DVM, Veterinary Sciences, University of Arizona.

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CORRECTION There was a mistake in the labeling o f Figure 3 in the article "Accuracy o f End-Tidal Carbon Dioxide Tension Analyzers," which appeared in the April issue (Raemer DB, Calalang I. J Clin Monit 1991;7:195-208). In Figure 3A, the top curve, which was labeled C-IR, should have been labeled D-IR, and the b o t t o m curve, labeled D-IR, should have been C-IR. In Figure 3B, the top curve, labeled D - I R , should have been labeled C-IR, and the b o t t o m curve should have been labeled D-IR. We apologize for this error.

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