Europ. J. Intensive Care Medicine 1,175-183 (1975) © by Springer-Verlag 1975
A Computer Model and a Mechanical Model of the Circulation and their Use in the Evaluation of Indices of Myocardial Blood Flow H. J. Testa, B. R. Pullan, D. J. Rowlands Departments of Medical Physics and Cardiology, Royal Infirmary, Manchester, England
Abstract. Computer and mechanical models of the circulation have been made to study isotopic techniques of determining indices of myocardial blood flow. Parameters in the program and dimensions in the mechanical model have been scaled to represent the human circulation. Single rapid injections of 1311 labelled human serum albumen were given into the venous line of the mechanical model and records obtained from collimated scintillation detectors positioned over the heart, lung and brain. Similar injections and recordings were simulated in the computer model. Two indices of myocardial flow have been studied. The first, described by Mena et al. is the ratio of the half time of the downslope of the left ventricular curve to the half time of the downslope of the brain curve. This index distinguished myocardial flows of 0,5% and 10% of total cardiac output but was also affected by changes in cerebral flow. A new index is proposed in which the half time of the left ventricular curve downslope is related to the half time of the downslope of the lung curve. This index can distinguish myocardial flows of 0,5% and 10% total flow but is not affected by changes in cerebral flow.
Key words: 131I albumen, External scintillation detection, Coronary flow.
Introduction A number of methods for measuring indices of myocardial blood flow have been described (1-3). Detailed evaluation of these in animals and humans is difficult since the procedure of measurement disturbs the subject. For this reason two models of the cardiopulmonary system have been employed in which complete control of the parameters describing the system can be achieved. A computer model was initially developed, but because this represents an oversimplification of the system a further, more realistic simulation was produced by means of a mechanical analogue of the cardiopulmonary circulation. Using these models two different myocardial flow indices have been investigated. The first was the index described by Mena et al., (4) in which the half time of the downslope of the left ventricular curve is compared with the half time of the downslope of the b rain curve, following systemic venous injection of isotope. Both the ventricular cavity and the coronary vascular bed are in the field of view of an external detector placed over the heart. Thus the observed curve is a composite of the activity-time curves from the left ventricular cavity and left ventricular myocardium.
Although these curves overlap, the bolus of labelled material passes through the coronary vascular bed more slowly than the left ventricular cavity. The coronary flow would thus have greater influence on the overall heart curve during its latter part (downslope). It is assumed that the downslope of a curve recorded over the brain would be similar to the downslope of the left ventricular cavity curve and therefore the observed difference in rate of fall of the heart curve, over that observed in a simultaneously recorded brain curve would be due to the passage of a fraction of the radioactive bolus through the coronary vascular bed. They defined a coronary flow index as
T1/z Left Ventricle T1/2 Brain
, where T1/2 Left Ventricle is the
half time of downslope of the curve recorded from the praecordium and T1/2 Brain is the half time of the downslope of the curve recorded from the brain. Theoretically it is difficult to accept that the brain dilution curve can be used as an approximation to the left ventricular dilution curve. Mean transit times for vascular systems in series are additive, and as a consequence the
176
European Journal of Intensive Care Medicine, Vol. 1, No. 4 (1975)
,,,¢ ,t
I
t
/ s"
4¢
Iv"
;
fi
5"0
iGo
l;o
RECIPROCAL OF TIME INTERVAL 0.2
0.04
0.02
0.01
TIME INTERVAL
Fig. 1. The functional components of the circulatory system. 1, injection site; 2, right heart; 3, 3 t, lungs; 4, left heart; 5, myocardium; 6, brain; 7, systemic circulation
Fig. 2. The half times of the left heart and brain curve downslopes plotted against the time interval used to compute the drop in activity in each compartment. - Upper curve, brain half times; lower curve left heart half times
mean transit time of the dilution curve recorded over the brain is greater than the mean transit time of the curve recorded over the left ventricle. Thus the recorded brain curve does not accurately reflect the left ventricular cavity curve. Also, it has been shown that, at high cardiac outputs, the dilution curves measured over the brain are prolonged (relative to the heart curves) by the cerebral circulation (4). This problem could possibly be reduced by recording over the lung instead of the brain. The theoretical advantage of this is that the tracer dilution curve of radioactive bolus will be only minimally changed in its brief passage from the pulmonary vascular bed into the left ventricle. Thus a more appropriate ratio to consider
where V (I) is the volume of the compartment and F is the flow through it. I is a compartment index variable. The amount of tracer entering the same compartment during the same time interval At will be equal to the amount leaving the previous compartments and for a simple serial system
might be T1/2 Left Ventricle and this is the new index T1/2 Lung proposed.
C o m p u t e r M o d e l o f the C i r c u l a t i o n
Basic Algorithms A model of the circulatory system can be obtained by representing each functional part of the system by a compartment. These compartments, when linked as shown in Fig. 1, represent the circulatory pathway which will be used in this analysis. The complete computer program used need not be given, but the basic algorithms are given below. Assuming that the quantity of tracer in compartment (1) at a given time is Q (I), and that it is uniformly distributed throughout the compartments, the amount of tracer, AQ, leaving the compartment in an interval of time, At, is given by
A Q - Q (I) xFAt V (I)
(1)
A Q - Q (I-1) xFAt
(2)
V0-1) If an initial tracer dose Q is injected into compartment (1), and it is assumed that there is instantaneous homogeneous mixing, the program can then cycle through each compartment in turn computing the quantity or concentration of tracer per unit time. The program has been written in Focal (a Digital Equipment Corporation computer language) and the main algorithm is described as follows: Q(I) = Q ( I ) + D ( I - 1 )
(3)
D (I) = Q (I) FAt
(4)
V 0) Q (I) = Q (I) - D (I)
(5)
where D = the drop in the amount of tracer in a compartment (At = time interval). Applying this algorithm to each compartment and joining them as a circuit it is possible to study the effects of variations of the different parameters describing the system. Since the value of Q is a non-linear function of time, accurate answers from equation (3), (4) and (5) are only produced when the time interval, At, is vanishingly small. To demonstrate the effect of varying the time interval, the half time of clearance for typical curves was computed for a series of different time intervals. Fig. 2 shows the
H. J. Testa e t al. : Models of Circulation: Indices of Myocardial Blood Flow
---'--~LUNG COMPARTMENT ~A
Parameters and Methods
CYCLEI
cYCLe, I . I A I
1
cYcLE, I c l . l A I
177
LEFT"EA.T
COMPARTMENT
Fig. 3. Algorithm for the time delay between lung and left heart
half time of the left heart slope and brain slope plotted against the time interval At, and indicates that for the values of flow and volume encountered in these experiments there is no apparent error when the time interval is less than 0.02 (units of computer time). Throughout these experiments a time interval of 0.006 was used. In order that the effect of time delays which occur between the compartments, can be taken into account, part of the program allows the user to insert delays where necessary. The principle on which the algorithm used to insert the delay between any two compartments depends, is illustrated in Fig. 3. This shows a time delay inserted between compartments representing the lung and the left ventricle. For each cycle of the program the output from the lung is stored in one of a series of subcompartments. The length of the series determines the delay period. Each cycle transfers the lung output data to the first subcompartment of the delay and moves along all existing data. When the number of cycles executed is equal to the number of sub-compartments in series, the last sub-compartment contains the initial lung output. Thus the next cycle will cause this value to be placed in the left ventricular compartment. Fig. 3 shows a three sub-compartment delay in which the output A of the lung from cycle 1 enters the left heart compartment after a further 3 cycles.
Assumed values for parameters in the program are scaled approximately to represent the human circulation and have values similar to those of the hydraulic model to be described later in this paper. The left and right ventricular volumes were 11 ml, the myocardial vascular volume was 17 nil, the brain vascular volume was 20 ml, and lung vascular volumes of 8 ml and 14 ml were used. The smaller lung vascular volume was included to simulate the reduced pulmonary blood volume in certain disease states. The total vascular volume was 250 ml. The total flow through the system was varied between t70 and 350 ml/min. To investigate Mena's Index, two series of experiments were performed, arbitrarily divided into those in which the flow through the brain was greater than 30% of the total system flow (Range 33 to 46%, mean 40.1% S. D. 5.1) and those in which the flow through the brain was less than or equal to 30% of the total flow (Range 17% to 30%, mean 22% S. D. 5.3). In each series, three different values of myocardial flow (0%, 5% and 10% of the total output) were assigned. For each value of cerebral flow and for each value of myocardial flow, two lung volumes (8 ml and 14 ml) and six different values of total flow (between 170 and 350 ml/min.) were used. To investigate the proposed index the same procedure was followed, using lung curves in place of brain curves. In addition, to assess possible differences from thehuman circulation produced by having a single lung in the model, all the experiments were repeated using two lungs in parallel. The ratio of flows in the lungs was varied between 1 : 1 and 9 : 1. In every case lung curves were recorded from both lungs. Typical curves are shown in Fig. 4. In all cases, the downslopes of (i) curves given by the sum of the heart (left ventricle) curves and the myocardial curves (ii) the brain curves and (rio the lung curves were expressed as their respective half times. The sum of left ventricular cavity and myocardial curves was taken to model the praecordial curve in Mena's method, though
.
=,
t t I,
6 MYOCARDIAL FLOW PERCENT TOTAL OUTPUT
Fig. 6. Myocardial flow index obtained with only one lung in the circuit
K
ii
1
io
MYOCARDIAL FLOW PERCENT TOTAL OUTPUT
Fig. 7. Myocardial flow index with two lungs in parallel in the circuit
H. J. Testa et al. : Models of Circulation: Indices of Myocardial Blood Flow
GLASS BEADS
179
NYOCARDIUM
Fig. 8. Heart model: schematic representation m separated halves
(b) The proposed Index. Fig. 6 summarises the results for the myocardial flow index T1/2 Left Ventricle. A StuT 1/2 Lung dent's test between the groups without flow and the groups with myocardial flows of 5% shows that there is a statistically significant difference between them. (Student's t = 8.69 Degrees of freedom = 10, p < 0.001.) There is also a statistically significant difference between the groups with a myocardial flow of 5 and 10% of the total output respectively (Student's t = 6.53, Degrees o f freedom = 10j p < 0.001). Where two lungs are used values for the myocardial flow index are only consistent when T1/z Lung is obtained from the lung with the higher blood flow. In every case therefore the higher flow lung is used. The results are summarised in Fig. 7. A Student's t test between the group without myocardial flow and that with a myocardial flow of 5% of the total flow shows a statistically significant difference (Student's t = 7.97, Degrees of freedom = 10, p < 0.001). Similar results are obtained when comparing the groups with 5 and 10% of the total flow (Student's t = 4.88, Degrees of freedom = 10, p < 0.001).
Mechanical Model of the Circulation This model consists of a heart, lung and brain, made of perspex and connected by means of surgical rubber and plastic tubing. The heart (Fig. 8), has two 11 ml chambers, surrounded by a coronary bed made of glass beads such that the ratio of the total volume of the model's coronary bed to the volume of glass beads is the same as the ratio of the volume of blood in the coronary bed to the volume of the cardiac muscle [approximately l : 1 (5)]. Two calibrated rotometer flowmeters connected in the outflow of the coronary circulation were used to measure coronary blood flow. The arterial and vencus circulation of the lungs were represented by glass balls, and the capillary circulation by cotton wool. The brain was made in the same way as the lung, except that it was filled with a
Fig. 9. Schematic diagram of the hydraulic model of the circulation
range of sizes of glass balls. A roller pump, the speed of which could be varied to produce different rates of flow was connected between the heart and the lung. A schematic diagram o f the model is shown in Fig. 9. An additional tube with another calibrated flowmeter was added in parallel to the principal vein returning to the heart to simulate an arm vein so that the flow at the place o f injection could be kept constant. A glass bottle was used as a reservoir to model the systemic circulation. The fraction of flow through the brain was controlled by a clamp in pipe A. The model was filled with a 10% solution of "Decon" (decontamination agent) to prevent tracer sticking to the walls of the system.
Method of Investigation of Myocardial Flow Indices using Mechanical Model A radio active tracer was used with this model and was detected using two external scintillation detectors with 3.8 cm diameter and 2.5 cm thick thallium-activated sodium iodide crystals recessed 5.5 cm in a lead cylinder of internal diameter 3.5 cm. The detectors were connected to spectrometers, which in turn were coupled to ratemeters, and chart recorders and positioned over the heart and lung or brain according to the experiment. A roller pump was set to deliver the required flow, representing the total flow. The myocardial and venous (or place of injection) flow rates were adjusted to the desired values. The spectrometers were adjusted to detect 131I. Counters were positioned over the heart and over the lung or brain (as required). 50/~C of 1311human serum albumin (H.S.A. 131i) were rapidly administered into the injection site of the system and two simultaneous time-concentration curves were recorded, one over the heart and the other over the lung or brain. The pump output was measured by collecting
180
European Journal of Intensive Care Medicine, Vol. 1, No. 4 (1975)
u
~
Lu ~" 10, w _l
×
=
.59 x + 5.54 cc =0.99
J MYOCARDIAL FLOW PERCENTAGE OF TOTAL FLOW
Fig. 10. Relation between the half time of the left ventricular downslope and myocardial flow
Fig. 11. (b) 131I H.S,A. curve recorded over the lung
Fig. 11. (c)
Fig. 11. (a) 1311 H.S.A. curve recorded over the heart
131I H.S.A. curve recorded over the brain
H. J. Testa et al. : Models of Circulation: Indices of Myocardial Blood Flow fluid from the return pipe to the reservoir in a measuring cylinder over a known time interval. The whole system was then drained and the total volume measured. The recorded curves were plotted on semilogarithmic graph paper and the half times o f the descending slopes were calculated. A preliminary experiment was performed to determine the influence of myocardial flow on tile slope of the curve recorded over the left chamber o f the heart. Myocardial flow was fixed at 0, 2.5, 6, 8.6 and 13% o f the total output o f the pump which delivered a constant overall flow o f 300 ml per minute. After this preliminary experiment a series of experiments was performed to compare the myocardial flow index described b y Mena et al. with the myocardial flow index proposed in this paper. In the first set o f experiments time-concentration curves were obtained over heart and brain after an injection of H.S.A. 1311 to reproduce the same experimental conditions as used b y Mena et al. The values for flow through the brain (as a percentage o f the total flow) were exactly the same as those used in the study o f the computer model. Likewise an arbitrary division was made into those studies where the brain flow was greater than 30% o f the total flow and those where it was 30% or less. In each series different values o f myocardial flow (expressed as a percentage o f total flow) were used. The volume o f the lung was also varied to give an 8 ml or 14 ml capacity.
Table 1. Myocardial flow indices
Tl/2 Left Ventricle
! 81
In the second set of experiments, the detectors were set up over the heart and lung. As in the first set several values o f myocardial and total flow were used, together with two different values o f lung volumes as above. The total flow was varied between 170 and 350 ml/min. An injection of H.S.A. 1311 was made using the technique described previously. The recorded curves were plotted on semilogarithmic graph paper, and the half times o f the downslopes o f the left heart curves and o f the lung or brain curves were calculated. All curves had single exponential downslopes before the onset o f recirculation and the best straight line was fitted b y eye. The myocardial flow index described b y Mena T1/2 Left Ventricle
, and the myocardial flow index d ~ -
T1/2 Brain cribed in this paper, T1/2 Left Ventricle, were obtained T1[2 Lung for each o f the above sets o f conditions.
Results o f Evaluation o f Indices The results o f the preliminary experiment in which the half time o f the left heart curve downslope is compared with myocardial blood flow are shown in Fig. 10. Fig. 11 shows typical curve recorded over the heart, the lung and the brain.
(calculated with a computer model) for different myocardial flows and two
T1/2 Brain
levels of brain flow Myocardial Flow % Total Flow
0 5 10
Brain Flow over 30% total flow
Student's t Test under 30% total flow
Mean
S.D.
Mean
S.D.
0.30 0.51 0.64
0.04 0.03 0.07
0.19 0.28 0.40
0.02 0.02 0.05
S.T.
D.F.
P
A Computer Model and a Mechanical Model of the Circulation and their Use in the Evaluation of Indices of Myocardial Blood Flow H. J. Testa, B. R. Pullan, D. J. Rowlands Departments of Medical Physics and Cardiology, Royal Infirmary, Manchester, England
Abstract. Computer and mechanical models of the circulation have been made to study isotopic techniques of determining indices of myocardial blood flow. Parameters in the program and dimensions in the mechanical model have been scaled to represent the human circulation. Single rapid injections of 1311 labelled human serum albumen were given into the venous line of the mechanical model and records obtained from collimated scintillation detectors positioned over the heart, lung and brain. Similar injections and recordings were simulated in the computer model. Two indices of myocardial flow have been studied. The first, described by Mena et al. is the ratio of the half time of the downslope of the left ventricular curve to the half time of the downslope of the brain curve. This index distinguished myocardial flows of 0,5% and 10% of total cardiac output but was also affected by changes in cerebral flow. A new index is proposed in which the half time of the left ventricular curve downslope is related to the half time of the downslope of the lung curve. This index can distinguish myocardial flows of 0,5% and 10% total flow but is not affected by changes in cerebral flow.
Key words: 131I albumen, External scintillation detection, Coronary flow.
Introduction A number of methods for measuring indices of myocardial blood flow have been described (1-3). Detailed evaluation of these in animals and humans is difficult since the procedure of measurement disturbs the subject. For this reason two models of the cardiopulmonary system have been employed in which complete control of the parameters describing the system can be achieved. A computer model was initially developed, but because this represents an oversimplification of the system a further, more realistic simulation was produced by means of a mechanical analogue of the cardiopulmonary circulation. Using these models two different myocardial flow indices have been investigated. The first was the index described by Mena et al., (4) in which the half time of the downslope of the left ventricular curve is compared with the half time of the downslope of the b rain curve, following systemic venous injection of isotope. Both the ventricular cavity and the coronary vascular bed are in the field of view of an external detector placed over the heart. Thus the observed curve is a composite of the activity-time curves from the left ventricular cavity and left ventricular myocardium.
Although these curves overlap, the bolus of labelled material passes through the coronary vascular bed more slowly than the left ventricular cavity. The coronary flow would thus have greater influence on the overall heart curve during its latter part (downslope). It is assumed that the downslope of a curve recorded over the brain would be similar to the downslope of the left ventricular cavity curve and therefore the observed difference in rate of fall of the heart curve, over that observed in a simultaneously recorded brain curve would be due to the passage of a fraction of the radioactive bolus through the coronary vascular bed. They defined a coronary flow index as
T1/z Left Ventricle T1/2 Brain
, where T1/2 Left Ventricle is the
half time of downslope of the curve recorded from the praecordium and T1/2 Brain is the half time of the downslope of the curve recorded from the brain. Theoretically it is difficult to accept that the brain dilution curve can be used as an approximation to the left ventricular dilution curve. Mean transit times for vascular systems in series are additive, and as a consequence the
176
European Journal of Intensive Care Medicine, Vol. 1, No. 4 (1975)
,,,¢ ,t
I
t
/ s"
4¢
Iv"
;
fi
5"0
iGo
l;o
RECIPROCAL OF TIME INTERVAL 0.2
0.04
0.02
0.01
TIME INTERVAL
Fig. 1. The functional components of the circulatory system. 1, injection site; 2, right heart; 3, 3 t, lungs; 4, left heart; 5, myocardium; 6, brain; 7, systemic circulation
Fig. 2. The half times of the left heart and brain curve downslopes plotted against the time interval used to compute the drop in activity in each compartment. - Upper curve, brain half times; lower curve left heart half times
mean transit time of the dilution curve recorded over the brain is greater than the mean transit time of the curve recorded over the left ventricle. Thus the recorded brain curve does not accurately reflect the left ventricular cavity curve. Also, it has been shown that, at high cardiac outputs, the dilution curves measured over the brain are prolonged (relative to the heart curves) by the cerebral circulation (4). This problem could possibly be reduced by recording over the lung instead of the brain. The theoretical advantage of this is that the tracer dilution curve of radioactive bolus will be only minimally changed in its brief passage from the pulmonary vascular bed into the left ventricle. Thus a more appropriate ratio to consider
where V (I) is the volume of the compartment and F is the flow through it. I is a compartment index variable. The amount of tracer entering the same compartment during the same time interval At will be equal to the amount leaving the previous compartments and for a simple serial system
might be T1/2 Left Ventricle and this is the new index T1/2 Lung proposed.
C o m p u t e r M o d e l o f the C i r c u l a t i o n
Basic Algorithms A model of the circulatory system can be obtained by representing each functional part of the system by a compartment. These compartments, when linked as shown in Fig. 1, represent the circulatory pathway which will be used in this analysis. The complete computer program used need not be given, but the basic algorithms are given below. Assuming that the quantity of tracer in compartment (1) at a given time is Q (I), and that it is uniformly distributed throughout the compartments, the amount of tracer, AQ, leaving the compartment in an interval of time, At, is given by
A Q - Q (I) xFAt V (I)
(1)
A Q - Q (I-1) xFAt
(2)
V0-1) If an initial tracer dose Q is injected into compartment (1), and it is assumed that there is instantaneous homogeneous mixing, the program can then cycle through each compartment in turn computing the quantity or concentration of tracer per unit time. The program has been written in Focal (a Digital Equipment Corporation computer language) and the main algorithm is described as follows: Q(I) = Q ( I ) + D ( I - 1 )
(3)
D (I) = Q (I) FAt
(4)
V 0) Q (I) = Q (I) - D (I)
(5)
where D = the drop in the amount of tracer in a compartment (At = time interval). Applying this algorithm to each compartment and joining them as a circuit it is possible to study the effects of variations of the different parameters describing the system. Since the value of Q is a non-linear function of time, accurate answers from equation (3), (4) and (5) are only produced when the time interval, At, is vanishingly small. To demonstrate the effect of varying the time interval, the half time of clearance for typical curves was computed for a series of different time intervals. Fig. 2 shows the
H. J. Testa e t al. : Models of Circulation: Indices of Myocardial Blood Flow
---'--~LUNG COMPARTMENT ~A
Parameters and Methods
CYCLEI
cYCLe, I . I A I
1
cYcLE, I c l . l A I
177
LEFT"EA.T
COMPARTMENT
Fig. 3. Algorithm for the time delay between lung and left heart
half time of the left heart slope and brain slope plotted against the time interval At, and indicates that for the values of flow and volume encountered in these experiments there is no apparent error when the time interval is less than 0.02 (units of computer time). Throughout these experiments a time interval of 0.006 was used. In order that the effect of time delays which occur between the compartments, can be taken into account, part of the program allows the user to insert delays where necessary. The principle on which the algorithm used to insert the delay between any two compartments depends, is illustrated in Fig. 3. This shows a time delay inserted between compartments representing the lung and the left ventricle. For each cycle of the program the output from the lung is stored in one of a series of subcompartments. The length of the series determines the delay period. Each cycle transfers the lung output data to the first subcompartment of the delay and moves along all existing data. When the number of cycles executed is equal to the number of sub-compartments in series, the last sub-compartment contains the initial lung output. Thus the next cycle will cause this value to be placed in the left ventricular compartment. Fig. 3 shows a three sub-compartment delay in which the output A of the lung from cycle 1 enters the left heart compartment after a further 3 cycles.
Assumed values for parameters in the program are scaled approximately to represent the human circulation and have values similar to those of the hydraulic model to be described later in this paper. The left and right ventricular volumes were 11 ml, the myocardial vascular volume was 17 nil, the brain vascular volume was 20 ml, and lung vascular volumes of 8 ml and 14 ml were used. The smaller lung vascular volume was included to simulate the reduced pulmonary blood volume in certain disease states. The total vascular volume was 250 ml. The total flow through the system was varied between t70 and 350 ml/min. To investigate Mena's Index, two series of experiments were performed, arbitrarily divided into those in which the flow through the brain was greater than 30% of the total system flow (Range 33 to 46%, mean 40.1% S. D. 5.1) and those in which the flow through the brain was less than or equal to 30% of the total flow (Range 17% to 30%, mean 22% S. D. 5.3). In each series, three different values of myocardial flow (0%, 5% and 10% of the total output) were assigned. For each value of cerebral flow and for each value of myocardial flow, two lung volumes (8 ml and 14 ml) and six different values of total flow (between 170 and 350 ml/min.) were used. To investigate the proposed index the same procedure was followed, using lung curves in place of brain curves. In addition, to assess possible differences from thehuman circulation produced by having a single lung in the model, all the experiments were repeated using two lungs in parallel. The ratio of flows in the lungs was varied between 1 : 1 and 9 : 1. In every case lung curves were recorded from both lungs. Typical curves are shown in Fig. 4. In all cases, the downslopes of (i) curves given by the sum of the heart (left ventricle) curves and the myocardial curves (ii) the brain curves and (rio the lung curves were expressed as their respective half times. The sum of left ventricular cavity and myocardial curves was taken to model the praecordial curve in Mena's method, though
.
=,
t t I,
6 MYOCARDIAL FLOW PERCENT TOTAL OUTPUT
Fig. 6. Myocardial flow index obtained with only one lung in the circuit
K
ii
1
io
MYOCARDIAL FLOW PERCENT TOTAL OUTPUT
Fig. 7. Myocardial flow index with two lungs in parallel in the circuit
H. J. Testa et al. : Models of Circulation: Indices of Myocardial Blood Flow
GLASS BEADS
179
NYOCARDIUM
Fig. 8. Heart model: schematic representation m separated halves
(b) The proposed Index. Fig. 6 summarises the results for the myocardial flow index T1/2 Left Ventricle. A StuT 1/2 Lung dent's test between the groups without flow and the groups with myocardial flows of 5% shows that there is a statistically significant difference between them. (Student's t = 8.69 Degrees of freedom = 10, p < 0.001.) There is also a statistically significant difference between the groups with a myocardial flow of 5 and 10% of the total output respectively (Student's t = 6.53, Degrees o f freedom = 10j p < 0.001). Where two lungs are used values for the myocardial flow index are only consistent when T1/z Lung is obtained from the lung with the higher blood flow. In every case therefore the higher flow lung is used. The results are summarised in Fig. 7. A Student's t test between the group without myocardial flow and that with a myocardial flow of 5% of the total flow shows a statistically significant difference (Student's t = 7.97, Degrees of freedom = 10, p < 0.001). Similar results are obtained when comparing the groups with 5 and 10% of the total flow (Student's t = 4.88, Degrees of freedom = 10, p < 0.001).
Mechanical Model of the Circulation This model consists of a heart, lung and brain, made of perspex and connected by means of surgical rubber and plastic tubing. The heart (Fig. 8), has two 11 ml chambers, surrounded by a coronary bed made of glass beads such that the ratio of the total volume of the model's coronary bed to the volume of glass beads is the same as the ratio of the volume of blood in the coronary bed to the volume of the cardiac muscle [approximately l : 1 (5)]. Two calibrated rotometer flowmeters connected in the outflow of the coronary circulation were used to measure coronary blood flow. The arterial and vencus circulation of the lungs were represented by glass balls, and the capillary circulation by cotton wool. The brain was made in the same way as the lung, except that it was filled with a
Fig. 9. Schematic diagram of the hydraulic model of the circulation
range of sizes of glass balls. A roller pump, the speed of which could be varied to produce different rates of flow was connected between the heart and the lung. A schematic diagram o f the model is shown in Fig. 9. An additional tube with another calibrated flowmeter was added in parallel to the principal vein returning to the heart to simulate an arm vein so that the flow at the place o f injection could be kept constant. A glass bottle was used as a reservoir to model the systemic circulation. The fraction of flow through the brain was controlled by a clamp in pipe A. The model was filled with a 10% solution of "Decon" (decontamination agent) to prevent tracer sticking to the walls of the system.
Method of Investigation of Myocardial Flow Indices using Mechanical Model A radio active tracer was used with this model and was detected using two external scintillation detectors with 3.8 cm diameter and 2.5 cm thick thallium-activated sodium iodide crystals recessed 5.5 cm in a lead cylinder of internal diameter 3.5 cm. The detectors were connected to spectrometers, which in turn were coupled to ratemeters, and chart recorders and positioned over the heart and lung or brain according to the experiment. A roller pump was set to deliver the required flow, representing the total flow. The myocardial and venous (or place of injection) flow rates were adjusted to the desired values. The spectrometers were adjusted to detect 131I. Counters were positioned over the heart and over the lung or brain (as required). 50/~C of 1311human serum albumin (H.S.A. 131i) were rapidly administered into the injection site of the system and two simultaneous time-concentration curves were recorded, one over the heart and the other over the lung or brain. The pump output was measured by collecting
180
European Journal of Intensive Care Medicine, Vol. 1, No. 4 (1975)
u
~
Lu ~" 10, w _l
×
=
.59 x + 5.54 cc =0.99
J MYOCARDIAL FLOW PERCENTAGE OF TOTAL FLOW
Fig. 10. Relation between the half time of the left ventricular downslope and myocardial flow
Fig. 11. (b) 131I H.S,A. curve recorded over the lung
Fig. 11. (c)
Fig. 11. (a) 1311 H.S.A. curve recorded over the heart
131I H.S.A. curve recorded over the brain
H. J. Testa et al. : Models of Circulation: Indices of Myocardial Blood Flow fluid from the return pipe to the reservoir in a measuring cylinder over a known time interval. The whole system was then drained and the total volume measured. The recorded curves were plotted on semilogarithmic graph paper and the half times o f the descending slopes were calculated. A preliminary experiment was performed to determine the influence of myocardial flow on tile slope of the curve recorded over the left chamber o f the heart. Myocardial flow was fixed at 0, 2.5, 6, 8.6 and 13% o f the total output o f the pump which delivered a constant overall flow o f 300 ml per minute. After this preliminary experiment a series of experiments was performed to compare the myocardial flow index described b y Mena et al. with the myocardial flow index proposed in this paper. In the first set o f experiments time-concentration curves were obtained over heart and brain after an injection of H.S.A. 1311 to reproduce the same experimental conditions as used b y Mena et al. The values for flow through the brain (as a percentage o f the total flow) were exactly the same as those used in the study o f the computer model. Likewise an arbitrary division was made into those studies where the brain flow was greater than 30% o f the total flow and those where it was 30% or less. In each series different values o f myocardial flow (expressed as a percentage o f total flow) were used. The volume o f the lung was also varied to give an 8 ml or 14 ml capacity.
Table 1. Myocardial flow indices
Tl/2 Left Ventricle
! 81
In the second set of experiments, the detectors were set up over the heart and lung. As in the first set several values o f myocardial and total flow were used, together with two different values o f lung volumes as above. The total flow was varied between 170 and 350 ml/min. An injection of H.S.A. 1311 was made using the technique described previously. The recorded curves were plotted on semilogarithmic graph paper, and the half times o f the downslopes o f the left heart curves and o f the lung or brain curves were calculated. All curves had single exponential downslopes before the onset o f recirculation and the best straight line was fitted b y eye. The myocardial flow index described b y Mena T1/2 Left Ventricle
, and the myocardial flow index d ~ -
T1/2 Brain cribed in this paper, T1/2 Left Ventricle, were obtained T1[2 Lung for each o f the above sets o f conditions.
Results o f Evaluation o f Indices The results o f the preliminary experiment in which the half time o f the left heart curve downslope is compared with myocardial blood flow are shown in Fig. 10. Fig. 11 shows typical curve recorded over the heart, the lung and the brain.
(calculated with a computer model) for different myocardial flows and two
T1/2 Brain
levels of brain flow Myocardial Flow % Total Flow
0 5 10
Brain Flow over 30% total flow
Student's t Test under 30% total flow
Mean
S.D.
Mean
S.D.
0.30 0.51 0.64
0.04 0.03 0.07
0.19 0.28 0.40
0.02 0.02 0.05
S.T.
D.F.
P
