Catheterization and Cardiovascular Diagnosis 2:199--210 (1976)
A SIMPLE METHOD FOR CALCULATING LEFT VENTRICULAR FUNCTIONS FROM ANGIOGRAPHIC DATA USING A PROGRAMMABLE HAND CALCULATOR John H.K. Vogel, M.D., Robert D. Swenson, and Virgil Elings, PhD The end diastolic volume and systollc ejection fraction have gained increasing acceptance as important indicators of ventricular performance. Time consuming calculations and lack of computer facilities have hindered the emergence of these calculations as a routine part of cardiac catheterization studies. The introduction of the programmable hand calculator has provided means for rapid analysis of ventricular volume data in an efficient and inexpensive manner. In this paper the step-by-step procedure for programming the hand calculator is given, as well as instructions for entering raw data and obtaining final calculations. Programs are given for both single plane and biplane cine angiographic studies. Key words: cardiac catheterization, left ventrlculography, biplane cine, single plane cine, data analysis
INTRODUCTION
The application of computer systems analysis to cardiac catheterization data has assumed increasing importance over the past ten years. The recent introduction of the programmable hand calculator is a significant development in this area. Whereas for the past three years our laboratory data were transported to a computer terminal and processed there, the same calculations are now obtained using the Hewlett-Packard HP-65 programmable hand calculator available for about $800.00. Data analysis by the large computer system required the completion of several typed key punch cards and yielded a three page print out. Patient data are keyed directly into the hand calculator. The calculated values are systematically displayed by the calculator as the program is initiated. Values are printed by the operator on a one page report. Because of its accessability and versatility the hand calculator has provided analysis of catheterization data more quickly and efficiently for this catheterization laboratory, which averages 200 patients per year. This article contains the equations used to calculate left ventricular indices and the step-by-step procedure for programming the hand calculator. In addition, instructions are given for the sequence of entering the raw data and obtaining final calculations. Programs are given for both single-plane RAO and biplane studies. From the Gobta Valley Community Hospital, Santa Barbara, California
Reprint requests to: J.H.K. Vogel, M.D., Goleta Valley Community Hospital, 351 South Patterson Avenue, Santa Barbara, CA. 931 1 1 Received Aug. 24, 1975; revision accepted, Nov. 30, 1975
199
@ 1976 Alan R. Liss, Inc., 150 F i f t h Avenue, New York, N.Y. 10011
200
Vogel. Swenson, and Elings
METHODS The elipsoid of revolution equations suggested by Dodge and associates (1) for determining ventricular volume are used* Biplane:
CV = 4/3n LM/2 X D RA0/2 X D L A 0 / 2 or 8 cv=x - 3n
ARAOXALAO
LM
-
Single Plane: In our laboratory correction factors needed for RAO and LAO measurements are determined by filming a 1 cm2 grid after the study has been performed with the grid placed at the level of the left ventricle in both planes and the image intensifiers placed at the same position as at the time of the cine angiograms. The correction factor is the ratio of the number of squares in the area of interest to their area as measured when projected on a viewer. The result is an aerial correction factor that takes into account pinpoint distortion and magnification of the x-ray system. Applying the correction factors (CFRAO,CFLAO)to the volume equations
In that the majority of patients have the longest length in the RAO view, that length has been used as LM in the calculation for the volume. Thus our working equations are Biplane:
c v = -3ng
(ARAO) (
GRAO) (ALAO) (CFLAO) LR AO
Single plane: True biplane cine angiographic left ventricular volumes are established by a regression equation proposed by Vogel and associates (2) for biplane cine angiography and the equation suggested by Gault (3) is used for the true RAO single-plane cine angiographic left ventricular volumes. Biplane:
TV = 0.895 CV - 5.1 13 ML.
Single plane:
TV = 0.81
*CV = calculated volume LM = maximum length D RAO = right anterior oblique diameter D LAO = left anterior oblique diameter A RAO = right anterior oblique area A L A O = left anterior oblique area
CV + 1.9 ML.
Calculating Left Ventricular Functions
201
Where CV is the calculated volume and TV is the true volume. The equation used for calculating the average velocity of circumferential fiber shortening (4) is* (dD - sD)
Vc,
=
t
dD
The average diameters are calculated from Dodge’s elipsoid of revolution equation. In our program, the number of frames from end diastole to end systole is entered into the calculator, and the time is computed for a camera speed of 6Ofps. Heart rate is calculated from the number of frames per beat. Cardiac index is the product of the heart rate and stroke index. Both the biplane and the single-plane programs require two magnetic cards. Table I lists the program steps for the first RAO single-plane card. To prepare this card the calculator is turned on, switched to the W/PRGM mode, and F PRGM in sequence is pressed to clear the memory. The column marked Key entry indicates the keys on the calculator that the programmer presses and the Code shown column is the resulting display of the calculator. Once the steps listed in Table I have been keyed into the calculator, a blank magnetic card is entered. The program is now permanently stored on this card. To use this card the operator follows the users instructions given in Table 11. The calculator is switched to the R U N mode, and the card is entered into the calculator. The operator then stores the patient data indicated under the Input data column in the calculator. Instead of typing the data onto computer key punch cards, the data are keyed directly into the calculator and stored in its memory by pressing STO and the appropriate register number I - 7. Once the data have been entered, it is wise to quickly recall each register before the program is initiated by pressing RCL 1 - 7 to assure that no errors have been made in entering the raw data. The Program is initiated by pressing labels A - E, in the order given in Table 11. Labels A, C , D, and E yield ESV in ml, EDV in ml, VCF in circumferencedsec, and stroke volume in ml, respectively. Label B is pressed when ESV, EDV, and stroke volume are displayed to convert these values to indices, ESV/mZ, EDV/m2, and stroke index in mYm2. The calculated values must be recorded by the operator as they are displayed. Fig. 1 shows one possible data sheet designed to correspond to the order that the data is obtained. Table 111 lists the program steps for the second single-plane card, and Table IV gives instructions for using this card. When the calculator is programmed with the second single-plane card, pressing Label A gives the systolic ejection fraction expressed as a percentage. After entering number of framedbeat and stroke index, Label B gives the heart rate in beatshin, and Label C gives the cardiac index in literdmin.
*VCF = velocity of (circumferential) fiber shortening dD = average diastolic diameter, sD = average systolic diameter t = time in seconds
202
Vogel, Swenson, and Elings
Table V lists the program steps for both biplane cards. Steps 1-80 are keyed into the calculator and recorded on a blank magnetic card. This card is programmed for the first part of the biplane analysis. F PRGM is then pressed to clear the memory, and the 16 remaining steps required for the second biplane card are keyed into the calculator. A second blank card is entered and programmed for the second part of the analysis. When the calculator is programmed with the first biplane card, following the user instructions in Table VI will yield ESV, the average systolic diameter in cm, EDV, the average diastolic diameter in cm. the stroke volume, and the systolic ejection fraction expressed as a percentage. Again in this program Label B is used to standardize values for body surface area. Note that Labels A, B, and C are used to evaluate systolic data and then reused for diastolic data. When the calculator is programmed with the second biplane card, Label A is pressed to obtain VCF. The remainder of the second biplane card can be programmed to calculate other indices as required. DISCUSSION The introduction of the Hewlett-Packard HP-65 programmable hand calculator has made it possible to readily determine the important angiographic indices in a short period of time. It is a relatively simple procedure to do the actual drawings of the silhouettes in end diastole and end systole, planimeter those areas, and obtain the correction factors. With the programmable hand calculator it is possible to process the data within 2-3 min for the final answers, thus providing useful data rapidly and avoiding the complex interplay with a large computer system or the potential for error by the multiple hand calculations. KEY FOR TABLES I-VI: CFRAO = aerial correction factor for right anterior oblique projection CFLAO = aerial correction factor for left anterior oblique projection
BSA = body surface area No. frames = the number of frames from end diastole t o end systole with a camera speed of 60 fps. Dias. ARAO or Sys. ARAO = diastolic or systolic area from left anterior oblique projection Dias. ALAO or Sys. ALAO = diastolic or systolic area from left anterior oblique projection Dias. LRAO or Sys. LRAO= diastolic or systolic length from right anterior oblique projection Dias. LLAO or Sys. LLAo = diastolic or systolic length from left anterior oblique projection
No. framedbeat = the number of framedbeat with a camera speed of 60 frames/sec. ESV = end systolic volume EDV = end diastolic volume
SV = stroke volume SI = stroke index SEF as % = systolic ejection fraction expressed as a percentage VcF = velocity of circumferential fiber shortening Sys. Dia. = average systolic diameter d x Dia. = average diastolic diameter CI = cardiac index HR = heart rate
Calculating Left Ventricular Functions
203
TABLE I.
HP-65 Program Form T,,,~, TABLE I. Calsubtm of Lett Ventricular Function by the Sinple.plane Method SWITCH TO W PRGM
mES5 f
WIGM
Page-ol
(0 CLEAR UEMORY
TO IECLXD P 4 0 G R A U lNSflT MAGNETIC CARD WITH SWITCH 511 A T W , P I W
__
204
Vogel, Swenson, and Elings
TABLE I I .
HP-65 User Instructions
STEP
INSTRUCTIONS Switch to run, inM cad I and Enter patient data
t 7 Obtain patient information
.-
wl Fig. 1.
SEF
51
sv SI
CI
SYS DIAMETER
sv
'CF
HEART RATE-
A
EDV
%
%
DIAS DIAMETER
- EDV
BIPLANE ANALYSIS
1 SEF E S V L
SINGLEPLANE ANALYSIS
AXIS
AREA
ESV
AXIS
AREA
SYSTOLIC FUNCTION DIASTOLIC FUNCTION
VENTRICULOGRAPHY
I
m
0
h)
n
206
Vogel, Swenson, and Elings
TABLE 111.
HP-65 Program Form T,,p
TABLE 111. C.leu*tiOn of L . h V m w b h r Functions by th SingCpbno Mnhod Sw1lCMlOlpDwl
PRESS f
PROl
Calculatim of
IOCLIMYEMOW
-
Page-of
__
Calculating Left Ventricular Functions
207
TABLE IV.
HP-65 User Instructions Tme TABLE IV. C.lcu*cion of L a V m * u * r Functions by thm S -i
Mmtd
- Page __
of
-
Date
Programmer
LV Singleplane 11.
CI
SEF b a r t r @
I
I INPUT
INSTRUCTIONS Leave on run, incard 2 and Jbtain patient informtion
~
ATAIUNIT! ~~
0. framed
Entr Datiemdata
eat
-~
roke index ..
_.. -
~
3btain uatimt information ~
.. .
F
mi-
~
.
.
208
Vogel, Swenson, and Elings
TABLE
v.
HP-65 Program Form ~,(l,,TABLE SWllC" TO
w
V. Calculation 01 Left Vmtriculu Functions by theBiphcMethod PRW
PRfSS
PRGM
- Page-ol
~
10 CLEAR Y t U O l "
REGISTERS
Rq No.frames
ESV
R6 ALAO EDV R 7 LRAO
-
sys. Dia.
RE
LLAO
G% Dia. R9 DRAO
sv LABELS
A EndVOl. B Im'
cA r. dia. D sv
E
E
F as % ~
0 -1 v, 2 -___
3 4
5 6 -___ 7 ___ 8 9 FLAGS 1 ___
2 -___
Calculating Left Ventricular Functions
209
TABLE VI.
HP-65 User Instructions T
, TABLE ~ ~ ~VI. CIkuIMbn of L d t Vmmicutu Fvrrtiola by tha E
i y.thod
Page __ ol __ Date
Programmer
LV Biplane 11: Vd
I
I
I
Obtain patient information
i l + - - I Z - - : Enter diastolic data
1
Obtain patient information
Enter ularlated values
t
--+-I
I
i
+ t i Obtain patimt intornution
____
I
210
Vogel,
Swenson, and Elings
REFERENCES 1. Dodge HT, Sandler H, BaUew DW et al: The use of biplane angiocardiography for the measurement of the left ventricular volumes in man. Am Heart J 60:762. 1%0.
2. Vogel JHK, Morgan JA and Strahl CL: Left ventricular dysfunction in chronic constrictive pencarditis. Chest 59:484, 1971. 3. Gault JH: Angiographic estimation of left ventricular volume. Cath Cardiovasc Diag 1:7, 1975. 4. Gault JH, Ross, J Jr. and Braunwald E: The contractile state of the left ventricle in man: instantaneous tension-velocity-length relationship in patients with and without disease of left ventricular myocardium. Cir Res 22:451.1%8.
A SIMPLE METHOD FOR CALCULATING LEFT VENTRICULAR FUNCTIONS FROM ANGIOGRAPHIC DATA USING A PROGRAMMABLE HAND CALCULATOR John H.K. Vogel, M.D., Robert D. Swenson, and Virgil Elings, PhD The end diastolic volume and systollc ejection fraction have gained increasing acceptance as important indicators of ventricular performance. Time consuming calculations and lack of computer facilities have hindered the emergence of these calculations as a routine part of cardiac catheterization studies. The introduction of the programmable hand calculator has provided means for rapid analysis of ventricular volume data in an efficient and inexpensive manner. In this paper the step-by-step procedure for programming the hand calculator is given, as well as instructions for entering raw data and obtaining final calculations. Programs are given for both single plane and biplane cine angiographic studies. Key words: cardiac catheterization, left ventrlculography, biplane cine, single plane cine, data analysis
INTRODUCTION
The application of computer systems analysis to cardiac catheterization data has assumed increasing importance over the past ten years. The recent introduction of the programmable hand calculator is a significant development in this area. Whereas for the past three years our laboratory data were transported to a computer terminal and processed there, the same calculations are now obtained using the Hewlett-Packard HP-65 programmable hand calculator available for about $800.00. Data analysis by the large computer system required the completion of several typed key punch cards and yielded a three page print out. Patient data are keyed directly into the hand calculator. The calculated values are systematically displayed by the calculator as the program is initiated. Values are printed by the operator on a one page report. Because of its accessability and versatility the hand calculator has provided analysis of catheterization data more quickly and efficiently for this catheterization laboratory, which averages 200 patients per year. This article contains the equations used to calculate left ventricular indices and the step-by-step procedure for programming the hand calculator. In addition, instructions are given for the sequence of entering the raw data and obtaining final calculations. Programs are given for both single-plane RAO and biplane studies. From the Gobta Valley Community Hospital, Santa Barbara, California
Reprint requests to: J.H.K. Vogel, M.D., Goleta Valley Community Hospital, 351 South Patterson Avenue, Santa Barbara, CA. 931 1 1 Received Aug. 24, 1975; revision accepted, Nov. 30, 1975
199
@ 1976 Alan R. Liss, Inc., 150 F i f t h Avenue, New York, N.Y. 10011
200
Vogel. Swenson, and Elings
METHODS The elipsoid of revolution equations suggested by Dodge and associates (1) for determining ventricular volume are used* Biplane:
CV = 4/3n LM/2 X D RA0/2 X D L A 0 / 2 or 8 cv=x - 3n
ARAOXALAO
LM
-
Single Plane: In our laboratory correction factors needed for RAO and LAO measurements are determined by filming a 1 cm2 grid after the study has been performed with the grid placed at the level of the left ventricle in both planes and the image intensifiers placed at the same position as at the time of the cine angiograms. The correction factor is the ratio of the number of squares in the area of interest to their area as measured when projected on a viewer. The result is an aerial correction factor that takes into account pinpoint distortion and magnification of the x-ray system. Applying the correction factors (CFRAO,CFLAO)to the volume equations
In that the majority of patients have the longest length in the RAO view, that length has been used as LM in the calculation for the volume. Thus our working equations are Biplane:
c v = -3ng
(ARAO) (
GRAO) (ALAO) (CFLAO) LR AO
Single plane: True biplane cine angiographic left ventricular volumes are established by a regression equation proposed by Vogel and associates (2) for biplane cine angiography and the equation suggested by Gault (3) is used for the true RAO single-plane cine angiographic left ventricular volumes. Biplane:
TV = 0.895 CV - 5.1 13 ML.
Single plane:
TV = 0.81
*CV = calculated volume LM = maximum length D RAO = right anterior oblique diameter D LAO = left anterior oblique diameter A RAO = right anterior oblique area A L A O = left anterior oblique area
CV + 1.9 ML.
Calculating Left Ventricular Functions
201
Where CV is the calculated volume and TV is the true volume. The equation used for calculating the average velocity of circumferential fiber shortening (4) is* (dD - sD)
Vc,
=
t
dD
The average diameters are calculated from Dodge’s elipsoid of revolution equation. In our program, the number of frames from end diastole to end systole is entered into the calculator, and the time is computed for a camera speed of 6Ofps. Heart rate is calculated from the number of frames per beat. Cardiac index is the product of the heart rate and stroke index. Both the biplane and the single-plane programs require two magnetic cards. Table I lists the program steps for the first RAO single-plane card. To prepare this card the calculator is turned on, switched to the W/PRGM mode, and F PRGM in sequence is pressed to clear the memory. The column marked Key entry indicates the keys on the calculator that the programmer presses and the Code shown column is the resulting display of the calculator. Once the steps listed in Table I have been keyed into the calculator, a blank magnetic card is entered. The program is now permanently stored on this card. To use this card the operator follows the users instructions given in Table 11. The calculator is switched to the R U N mode, and the card is entered into the calculator. The operator then stores the patient data indicated under the Input data column in the calculator. Instead of typing the data onto computer key punch cards, the data are keyed directly into the calculator and stored in its memory by pressing STO and the appropriate register number I - 7. Once the data have been entered, it is wise to quickly recall each register before the program is initiated by pressing RCL 1 - 7 to assure that no errors have been made in entering the raw data. The Program is initiated by pressing labels A - E, in the order given in Table 11. Labels A, C , D, and E yield ESV in ml, EDV in ml, VCF in circumferencedsec, and stroke volume in ml, respectively. Label B is pressed when ESV, EDV, and stroke volume are displayed to convert these values to indices, ESV/mZ, EDV/m2, and stroke index in mYm2. The calculated values must be recorded by the operator as they are displayed. Fig. 1 shows one possible data sheet designed to correspond to the order that the data is obtained. Table 111 lists the program steps for the second single-plane card, and Table IV gives instructions for using this card. When the calculator is programmed with the second single-plane card, pressing Label A gives the systolic ejection fraction expressed as a percentage. After entering number of framedbeat and stroke index, Label B gives the heart rate in beatshin, and Label C gives the cardiac index in literdmin.
*VCF = velocity of (circumferential) fiber shortening dD = average diastolic diameter, sD = average systolic diameter t = time in seconds
202
Vogel, Swenson, and Elings
Table V lists the program steps for both biplane cards. Steps 1-80 are keyed into the calculator and recorded on a blank magnetic card. This card is programmed for the first part of the biplane analysis. F PRGM is then pressed to clear the memory, and the 16 remaining steps required for the second biplane card are keyed into the calculator. A second blank card is entered and programmed for the second part of the analysis. When the calculator is programmed with the first biplane card, following the user instructions in Table VI will yield ESV, the average systolic diameter in cm, EDV, the average diastolic diameter in cm. the stroke volume, and the systolic ejection fraction expressed as a percentage. Again in this program Label B is used to standardize values for body surface area. Note that Labels A, B, and C are used to evaluate systolic data and then reused for diastolic data. When the calculator is programmed with the second biplane card, Label A is pressed to obtain VCF. The remainder of the second biplane card can be programmed to calculate other indices as required. DISCUSSION The introduction of the Hewlett-Packard HP-65 programmable hand calculator has made it possible to readily determine the important angiographic indices in a short period of time. It is a relatively simple procedure to do the actual drawings of the silhouettes in end diastole and end systole, planimeter those areas, and obtain the correction factors. With the programmable hand calculator it is possible to process the data within 2-3 min for the final answers, thus providing useful data rapidly and avoiding the complex interplay with a large computer system or the potential for error by the multiple hand calculations. KEY FOR TABLES I-VI: CFRAO = aerial correction factor for right anterior oblique projection CFLAO = aerial correction factor for left anterior oblique projection
BSA = body surface area No. frames = the number of frames from end diastole t o end systole with a camera speed of 60 fps. Dias. ARAO or Sys. ARAO = diastolic or systolic area from left anterior oblique projection Dias. ALAO or Sys. ALAO = diastolic or systolic area from left anterior oblique projection Dias. LRAO or Sys. LRAO= diastolic or systolic length from right anterior oblique projection Dias. LLAO or Sys. LLAo = diastolic or systolic length from left anterior oblique projection
No. framedbeat = the number of framedbeat with a camera speed of 60 frames/sec. ESV = end systolic volume EDV = end diastolic volume
SV = stroke volume SI = stroke index SEF as % = systolic ejection fraction expressed as a percentage VcF = velocity of circumferential fiber shortening Sys. Dia. = average systolic diameter d x Dia. = average diastolic diameter CI = cardiac index HR = heart rate
Calculating Left Ventricular Functions
203
TABLE I.
HP-65 Program Form T,,,~, TABLE I. Calsubtm of Lett Ventricular Function by the Sinple.plane Method SWITCH TO W PRGM
mES5 f
WIGM
Page-ol
(0 CLEAR UEMORY
TO IECLXD P 4 0 G R A U lNSflT MAGNETIC CARD WITH SWITCH 511 A T W , P I W
__
204
Vogel, Swenson, and Elings
TABLE I I .
HP-65 User Instructions
STEP
INSTRUCTIONS Switch to run, inM cad I and Enter patient data
t 7 Obtain patient information
.-
wl Fig. 1.
SEF
51
sv SI
CI
SYS DIAMETER
sv
'CF
HEART RATE-
A
EDV
%
%
DIAS DIAMETER
- EDV
BIPLANE ANALYSIS
1 SEF E S V L
SINGLEPLANE ANALYSIS
AXIS
AREA
ESV
AXIS
AREA
SYSTOLIC FUNCTION DIASTOLIC FUNCTION
VENTRICULOGRAPHY
I
m
0
h)
n
206
Vogel, Swenson, and Elings
TABLE 111.
HP-65 Program Form T,,p
TABLE 111. C.leu*tiOn of L . h V m w b h r Functions by th SingCpbno Mnhod Sw1lCMlOlpDwl
PRESS f
PROl
Calculatim of
IOCLIMYEMOW
-
Page-of
__
Calculating Left Ventricular Functions
207
TABLE IV.
HP-65 User Instructions Tme TABLE IV. C.lcu*cion of L a V m * u * r Functions by thm S -i
Mmtd
- Page __
of
-
Date
Programmer
LV Singleplane 11.
CI
SEF b a r t r @
I
I INPUT
INSTRUCTIONS Leave on run, incard 2 and Jbtain patient informtion
~
ATAIUNIT! ~~
0. framed
Entr Datiemdata
eat
-~
roke index ..
_.. -
~
3btain uatimt information ~
.. .
F
mi-
~
.
.
208
Vogel, Swenson, and Elings
TABLE
v.
HP-65 Program Form ~,(l,,TABLE SWllC" TO
w
V. Calculation 01 Left Vmtriculu Functions by theBiphcMethod PRW
PRfSS
PRGM
- Page-ol
~
10 CLEAR Y t U O l "
REGISTERS
Rq No.frames
ESV
R6 ALAO EDV R 7 LRAO
-
sys. Dia.
RE
LLAO
G% Dia. R9 DRAO
sv LABELS
A EndVOl. B Im'
cA r. dia. D sv
E
E
F as % ~
0 -1 v, 2 -___
3 4
5 6 -___ 7 ___ 8 9 FLAGS 1 ___
2 -___
Calculating Left Ventricular Functions
209
TABLE VI.
HP-65 User Instructions T
, TABLE ~ ~ ~VI. CIkuIMbn of L d t Vmmicutu Fvrrtiola by tha E
i y.thod
Page __ ol __ Date
Programmer
LV Biplane 11: Vd
I
I
I
Obtain patient information
i l + - - I Z - - : Enter diastolic data
1
Obtain patient information
Enter ularlated values
t
--+-I
I
i
+ t i Obtain patimt intornution
____
I
210
Vogel,
Swenson, and Elings
REFERENCES 1. Dodge HT, Sandler H, BaUew DW et al: The use of biplane angiocardiography for the measurement of the left ventricular volumes in man. Am Heart J 60:762. 1%0.
2. Vogel JHK, Morgan JA and Strahl CL: Left ventricular dysfunction in chronic constrictive pencarditis. Chest 59:484, 1971. 3. Gault JH: Angiographic estimation of left ventricular volume. Cath Cardiovasc Diag 1:7, 1975. 4. Gault JH, Ross, J Jr. and Braunwald E: The contractile state of the left ventricle in man: instantaneous tension-velocity-length relationship in patients with and without disease of left ventricular myocardium. Cir Res 22:451.1%8.
