Basic Science.
Consider this photograph…
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Every time this child moves the pump handle through a full sweep she will generate one stroke volume of the pump. She will produce this stroke volume at a hydrostatic pressure and at a flow velocity which is determined by the force on the pump handle. But what if her father were to operate the pump instead? He would still produce the same stroke volume, but he would produce it in a much shorter time and with a higher pressure and flow velocity than his daughter could manage. Clearly the difference is due to the power that he possesses relative to his daughter. |
(Photograph by kind permission of Oxfam – Donations can be made online!)
Haemodynamics is just the same. We can deduce the power of the heart by measuring the same variables as in the pump example here. We need to know stroke volume, hydrostatic pressure developed, flow velocity, fluid density (to calculate the mass of liquid pumped) and time taken to eject one stroke volume – the systolic flow time. Contraction of the myocardium follows the “all or nothing rule”, it will contract with all the power that it has at that moment in time, and that depends on its inotropy.
We developed a formula derived from basic haemodynamic theory to calculate the external work done by the heart in a single beat. Power is the capacity to do work and is defined as the work produced divided by time taken, or work per unit time.
To calculate myocardial power or inotropy we need to measure the potential and kinetic energy developed by the heart, which is the external cardiac work, and then divide this by the flow time, the time taken to do this much work. Potential Energy is the energy used to produce blood pressure. Kinetic Energy is the energy used to produce blood flow.
Potential Energy is the product of change of pressure and the change of volume or PE = ΔP x ΔV. The change in pressure, ΔP, is the mean blood pressure – CVP, or the pressure of the blood coming out of the heart minus the pressure that the blood came in to the heart.
Kinetic Energy for any moving mass is given by the formula KE = ½mV2, where m is the mass of the object and V its velocity.
Applying this to the heart, where the mass of blood is SV x Density, we get
Inotropy (Watts) = P.E./Flow Time + K.E./Flow Time
= BPm x SV x 10-3 + D x SV x 10-6 x Vm2 (The Smith-Madigan formula)
7.5 x FT 2 x FT
Where BPm = (mean arterial pressure – central venous pressure) in mmHg, SV = stroke volume in ml, D = density, Vm = mean velocity, FT = systolic flow time. The factors 7.5, 10-3 and 10-6 are required to convert mmHg and ml to kPa and m3 to conform to SI values. The unit of inotropy is therefore the Watt, the SI unit of power.
Except for BP and blood density which is calculated from the haemoglobin concentration, other variables are measured directly by the USCOM. The USCOM measures the velocity of blood flow every 10 milliseconds during systole. In a typical ejection time of 380ms we have 38 measures of velocity from which we can derive the mean flow velocity. (In fact the USCOM uses mean velocity to calculate Pmn, the pressure gradient across the valve, from the formula Pmn = 4 x V2.)
Inotropy can be calculated using the USCOM data and the “Inotropy 2009” computer program. The program simply plugs the data into the formula above to calculate inotropy. It also derives the Smith-Madigan Inotropy Index (SMII) by dividing the total inotropy value by the body surface area of the subject (which is also calculated by the USCOM) just as we do with cardiac index. The most recent software updates for the USCOM do all this for you – talk to your dealer if yours doesn’t do it yet. |
The USCOM and Inotropy
