Chapter 5: Hydraulic Model of the
Cardiovascular System

A model, incorporating many of the unique characteristics of the cardiovascular system, allows the opportunity to observe the significance of each of those features. The characteristics reproduced in the model are: (1) the hydraulic system is a circle; (2) it is an elastic system, (3) it is filled with fluid producing a mean pressure; (4) there are two pumps in series between two vascular beds; (5) the pumps fill passively; (6) pump output is intermittent; (7) the pumps have atria that allow continuous, unimpeded flow to the pumps; (8) the pumps are capable of pumping out a greater volume than the system will produce; and (9) there are resistance points near the pumps' inlets as well as near their outlets.

Studying the model has an advantage over studying in vivo preparations in that the effect of altering one variable at a time can be directly observed. Furthermore, the model eliminates the possibility that some simultaneous, hidden, undetected change might have occurred that would invalidate cause and effect conclusions (Fig. 37). The model has proven to be a very effective study and teaching tool.

The Model:

Figure 38 shows the layout of the model pictured in Figure 39.

The Pumps:

The model pumps share the three unique characteristics of the heart: They are non-sucking, and therefore fill passively at their inlets, they have a pulsatile outflow, and they have atria which allow uninterrupted inflow to the intermittent, pulsatile outflow ventricles.

Figure 40 shows one of the two assembled pumps. Figure 41 shows the unassembled parts of a pump.

The atrial and ventricular pump chambers consist of a rigid side (Fig. 41 at A) and an opposing pliable silicone rubber side (Fig. 41 at B). The ventricular half of the rigid side has both an inlet and an outlet port containing inlet and outlet valves, respectively. The atrial half of the rigid side has a single port with no valve. There is a "Y" connection between the atrial port, inlet port to the ventricle and the venous line. This "Y" inlet allows venous fluid to run both into the atrium, when the inlet ventricular valve is closed during systole, and into the ventricular chamber during both ventricular diastole and atrial systole. This arrangement reproduces the "atrial effect" by allowing continuous uninterrupted flow from the veins to the intermittent outflow ventricles, thus preventing the need of overcoming inertia by starting stopped flow after each pump beat.

The impeller part of the pump also consists of a rigid side (Fig. 41 at E) and an opposing pliable rubber side (Fig. 41 at D). Each half of the rigid part has a port through which air can be forced into or sucked out of the impeller chambers. When the impeller chambers are inflated, their rubber side exerts pressure on the silicone rubber side of the ventricle or atrial chambers, thus emptying the ventricle or atrium.

A spacer (Fig. 41 at C), placed between the opposing impeller and pumping chambers, has many side holes which allow air to pass freely to and fro between the ambient air and the space between the impeller and pump ventricles. This free communication prevents any negative pressure, caused by suction used to deflate the impeller spaces, from being transmitted to the pump ventricles. Thus, the ventricles fill passively from venous pressure.

The power supply to the pumps is from compressed air and vacuum sources, delivered alternately to the impeller spaces timed in the desired sequence. An electronic regulator triggers solenoid valves to control pulse rate and the ratio of systole to diastole. The pulse rate is variable from 1 to 160 strokes per minute at an impeller pressure of one to thirty p.s.i. Reducer valves regulate peak pressure and onset to peak time. Impeller deflating suction is strong enough that passive ventricular filling is not impeded.

Simulated Vascular Network:

The major vessels are silicone tubing, while the capillary beds are made of more compliant Penrose drain material. Variable resistance points are at various sites in both arterial and venous lines. Pressure transducers connect to a direct writing recorder and pressure tubes connect to an electromagnetic flow meter. A transfusion reservoir provides opportunity to change the fluid volume within the system. Different weights placed on a plate resting on the "capillary beds" allow changes in the system compliance to be made. The system was filled with water. Hundreds of pieces of #0 silk suture material, 2 millimeters in length (found to be isobaric with water), were suspended in the water to allow visualization of the circulation.

Model Findings Correlate with Observations in Human Physiology

EXPERIMENT #1:The relationship of mean cardiovascular pressure to volume in the system

With the pumps turned off, the compliance remaining unchanged, and starting with the system full of water, at a volume of 2000 cc. at a pressure of zero, pressure was recorded as fluid was added by way of the transfusion reservoir. Figure 43 shows the non-linear relationship between the mean system pressure and the volume.

EXPERIMENT #2: The relationship of circulation rate to mean system pressure

Starting with a mean system pressure of zero, and with arbitrary settings of the resistance points, the pumps were started. Appropriate amounts of fluid were added to increase the mean system pressure by increments of 2 cm. water pressure (Fig. 44)


  1. Figure 44 shows a direct correlation between pump output and mean system pressure over the range of 0 to 20 cm. of water pressure. The greater the mean system pressure, the greater the pumps' output.

  2. At no time, over the range of pressure studied, did the ventricles fill to capacity at diastole. There was always a "pump capacity excess."

  3. At no time was there any interruption of venous flow by the intermittent closing of the inlet valves of the ventricles at systole, as the atria had been emptied during ventricular diastole.

EXPERIMENT #3: Pump rate correlation with pump output

The pump rate in the model was varied from 0 to 170 beats per minute with other variables remaining constant (Fig. 45). The mean system pressure was kept at 12 cm. water pressure, with the impeller pressure at 14 p.s.i. and the resistance kept constant.


  1. At pump rates between 0 and 20 beats/min.:
    • The pump output correlated in a linear way with the pump rate (Fig. 45, from A to halfway to B).
    • The ventricles filled to capacity at each ventricular diastole.
    • The atria filled to capacity during each ventricular systole.

  2. At pump rates between 20 and 40 beats/min.:
    • The pump rate correlated in a non-linear way with the pump output (Fig. 45, from halfway in between A and B, to B).
    • The ventricles filled slightly less than capacity at ventricular diastole.
    • The atria were filled to capacity at the end of ventricular systole.
    • Venous flow was slowed but not completely interrupted before the end of ventricular systole.

  3. Increasing the pump rate from 50 to 110 beats/min.:
    • Caused no increase in pump output (Fig. 45, B to C).
    • Was associated with progressive decrease in ventricular end-diastolic volume.
    • Caused progressive decrease in atrial diastolic volume.
    • Was unaccompanied by any interruption in venous flow.
    • The pump rate and stroke volume were reciprocals of one another.

  4. Increasing the pump rate from 110 to 170 beats/min. (Fig. 45, C to D) was accompanied by a progressive increase in residual air pressure in the ventricular impeller after ventricular systole which:
    • Progressively decreased pump output.
    • Impeded ventricular filling at ventricular diastole.
    • Caused venous flow interruption at ventricular systole.

EXPERIMENT #4: Ventricular impeller-force correlation with pump output

The ventricular impeller pressure was varied from 0 to 20 p.s.i., in increments of 2 p.s.i., while keeping other variables constant (Fig. 46). The pump rate was 80, the mean system pressure was 12 cm. water pressure and all resistances remained unchanged.


  1. At impeller pressures between 0 and 10 p.s.i. there was:
    • Linear correlation between impeller pressure and pump output (Fig. 46, from A to B).
    • The ventricles were never completely emptied at ventricular systole.
    • The ventricles were completely filled at ventricular diastole.
    • Venous flow to the pumps was interrupted at each ventricular systole.

  2. At impeller pressures between 10 and 18 p.s.i. there was:
    • No increase in the output as the pressure increased (Fig. 46, from B to C).
    • Maximal ventricular emptying at systole.
    • Sub-maximal filling of the ventricles at diastole
    • No venous flow interruption at any time.

  3. As the impeller pressure was progressively increased above 18 p.s.i. (Fig. 46, from C to D) there was progressively incomplete evacuation of compressed air in the ventricle during diastole which:
    • Progressively decreased pump output.
    • Impeded ventricular filling at diastole.
    • Caused venous flow interruption at ventricular systole.

EXPERIMENT #5: Relationship of resistance location to pump output

Resistance at a variety of sites was changed in the model's vascular network while maintaining other factors constant, with the mean system pressure at 12 cm. water pressure, pump rate at 80 beats per minute, and an impeller pressure of 16 p.s.i. There was a marked difference in response to a given resistance depending on where the resistance was placed in the model. Responses fell into two categories which became more obvious the closer the resistance was to either the inlet or outlet of a pump. Therefore, resistance was studied in two situations: near a pump inlet, where there was a large compliant bed upstream; and near a pump outlet, with no compliant bed upstream.

Relationship of Resistance Near a Pump Outlet to Pump Output (Fig. 47)

A variable resistance clamp was placed 20 cm. from the left heart homologue pump outlet (Fig. 38, #9), across which a pressure gradient could be monitored by transducers (Fig. 38, #8).


  1. As the resistance is progressively increased (Fig. 38, #9), the superimposed arterial pressure tracings, which demonstrated no gradient initially (Fig. 47 at A), separated as resistance was added (Fig. 47, from A to C).

  2. With increase in outflow resistance up to 100 mm. Hg. gradient, there was no drop in pump output (Fig. 47 at C).

  3. Further increase in gradient from 100 to 250 mm. Hg did cause a corresponding drop in flow (Fig. 47, from C to D).

  4. In the range where there was no drop in flow (Fig. 47, A to C), the left ventricle did not fill maximally, but did empty maximally, and there was no interruption of venous flow at any time during the pumping cycle.

  5. However, when the gradient became great enough that the flow slowed (Fig. 47, C to D), the left ventricle progressively emptied less completely, and the residual volume resulted in complete left ventricular filling at diastole and interruption of venous inflow at each systole.

  6. Whenever the left ventricle was being filled completely at diastole, increasing the mean system pressure caused no concomitant increase in pump output.

  7. As slowing of flow occurred (Fig. 47, C to D), there was gradual increase in a greater than previous volume in the pulmonary circuit at the expense of the systemic circuit. The greater the slowing, the more the volume equilibrium shifted to the simulated pulmonary circuit.

The Effect of Resistance Near a Pump Inlet on Pump Output: (Fig. 48)

An adjustable resistance clamp was placed 20 cm. from the left pump's inlet (Fig. 38, #7), across which a pressure gradient could be monitored using the transducers (Fig. 38, #6). The clamp was progressively closed. The resulting inflow resistance magnitude is represented by the pressure gradient between the transducers. Figure 48 shows the two superimposed pressure lines (Fig. 48, A to B) in the absence of resistance. When resistance is progressively increased, starting at B, a pressure gradient becomes evident (Fig. 48, B to C).


  1. There was a direct inverse correlation between pump output and inflow resistance to the pump (Fig. 48, B to C) over the whole range studied. This is in marked contrast to outflow resistance of the previous experiment (Fig. 47, B to C), where decrease in flow did not occur until there was pump failure.

  2. As inlet resistance increased there was progressively less filling of the ventricles at diastole. Maximal emptying did occur at each ventricular systole, and venous flow remained uninterrupted at all times.

  3. Progressive increase in left pump inflow resistance shifted the fluid equilibrium between the pulmonary and systemic circuits toward the pulmonary bed.

  4. The circuit with the greatest inflow resistance was the major determinant of the output of both.

EXPERIMENT #6: The Atrial Effect

In the model, to eliminate the atrial effect, the air pressure in the atria can be left continuously obliterating the atrial chambers, while not impinging on the connection of the venous tubes to the ventricles. By intermittently producing circulation with and without the atrial effect, its contribution to pump output was determined. At pump rates between 60 and 90 there was four times the pump output (2400 cc./min.) with the atria functioning as with no atrial effect (600 cc./min.). The output without atria progressively decreased as the rate was increased. At 130 beats per minute, flow stopped completely. It is demonstrated that atria markedly increase flow when used with pulsatile, passively filling pumps. They prevent inertia, which would otherwise occur if the inlet valves were allowed to stop venous flow at each beat.

EXPERIMENT #7: Pulsatile Flow

A branching hydraulic system was made with twenty, 3/16 inch diameter, transparent tubes, six to twelve inches in length, linked together with "Y" connectors in the configuration of a simulated vascular bed.


  1. With pulsatile flow there was flow in all parts of the system. It fairly danced with the pulsation. There were areas where flow was in one direction during most of the cycle and reversed in the other direction for the rest of it. With pulsatile flow, the distribution remained stable for a long period of time.

  2. With continuous non-pulsatile flow, the distribution started out in a diffuse manner. Very shortly, some channels had higher flow than others. Yet there was some flow in all of them. However, within a short time the 2 mm. silk particles began clustering at "Y" junctions, eventually totally blocking some and partially blocking others. Before long, almost all of the flow was in just a few channels and very little was in the others. When pulsatile flow then replaced the steady flow, the aggregates of silk were broken up, the whole bed began dancing with the pulse, and flow was again established in a diffuse manner, with flow fairly equal in all channels.

Conclusion: There is obviously a difference in the mechanism of aggregation of silk particles in this system and the mechanism that caused poor distribution with non-pulsatile flow in the animal in the previous chapter. However, this experiment does show that the simplest way to guarantee diffuse, equal distribution of fluid in a hydraulic system is to make flow pulsatile.

The Model as a Teaching Tool

An example of the teaching and learning benefit of the model is illustrated by an incident. One day I had scheduled a replacement of an aortic and mitral valve in a woman who had severe mitral and aortic stenosis. The student on my service came to me and said, "This woman is so critically ill that she may have difficulty surviving such a big operation. Maybe it would be the better part of valor to correct only one valve. Then, when she is better, go back and replace the other one." I asked him which valve he thought I should replace first. He responded that he would go to the model and put an inlet and outlet obstruction on the circuit. Then remove one and then the other and see what improvement would result from a single obstruction removal. When he only removed the inlet obstruction, the increased flow to the pump put it into power failure. When he removed only the outlet obstruction it decreased the workload of the pump, but the output didn't increase.

We would have sealed the woman's fate if we had corrected only one of the valves. She would have remained in low output failure if we had corrected the aortic valve alone; and she would have gone into acute left ventricular failure if we had relieved the mitral stenosis alone. Therefore, we replaced both valves and the patient made an excellent recovery.

The close correlation of model findings to physiological observations in man makes the model useful in understanding how the cardiovascular system works, and helps to anticipate cause and effect in human physiology.

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