How can I take blood pressure into the cardiac output formula?

Question

I wanted to know if there is some kind of formula that can help me calculate the cardiac output.

So, lets say we have a standing person. The StrokVolume should be around 100 cm2 for the average adult, and let's say for simplicities sake the pulse is 50. This person should have a CO of ~ 5L/minute.

If he lost a liter, his blood pressure would go down and his heart rate up, yet CO would go down, or if this person meets his superstar and has a vasovagal response his blood pressure would also go down and his heart rate up, and his CO would again be low leading to lightheadedness bc he won't pump 5L and only 4.5/min and now his brain now gets 10% less blood.

What I need is a correlation between Blood Pressure and cardiac output. Does blood pressure change the stroke volume? If yes - I would like to know how so I can take this into account. (e.g. for every % lost in BP his SV will go down .5%, even a graph showing the correlation will help)

Answer 1

For calculation of Bp and CO,

Bp = CO * TPR

CO = SV * HR

Where tpr is total peripheral resistance, HR is heart rate(bpm), SV is stroke volume

SV = End diastolic vol - end systolic vol

Now, there isn't any direct graphs for relation between BP and SV, theoretically we can see BP varies linearly with SV. However more important are changes which are observed with alterations, Important to understand is about Frank Starling Law, simply stated it tells volume of ejected blood in systole depends on initial fibre stretch of ventricular fibres(or otherwise stated venous return or blood that was present at end diastolic volume(EDV))

Now SV = EDV - ESV, and as per frank starling law, SV should depend on EDV but actually it means contractility of heart fibres has increased, (more elastic energy stored provided upto a physiologic limit)

Also EDV depends on blood returning to heart which is Venous return(VR) (it is just opposite end of CO) (ESV depends on contractility of heart, TPR, but I don't think we have graphs for actually stating that)

So, CO = VR

(Our circulatory system is a closed circuit, here we are counting changes in osmotic, hydrostatic pressure, etc. in pathologic conditions, however above equation will still hold true for changes, until compensatory mechanisms start to act(see below))

It means if BP is to be defined,

Bp = CO * TPR

it is Blood flow(CO) times Resistence of vessel(TPR)[which follows ohm's law normally]

and now since above we have shown how CO depends on VR which also relates to SV, hence BP and SV dependent linearly(upto physiological limits)

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Look at graph below:

Solid lines intersect at physiologic operating point.

1. Lets think about CO (red) left shift -

• increased inotropy (more blood pumped as contractility increased)
• decreased TPR (it will be easier to pump more for decreased amount of resistance/afterload)

(changes occur in tandem)

What it leads to- increased CO at a lesser VR(see intersection of bold dashed red and solid blue lines)

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2. Lets think about VR(blue) upward shift

• increased venous return

What it leads to- increased CO with increased VR(see intersection of bold dashed blue and solid red lines)

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Now let us finally see relation between left ventricular pressure(which actually will decide systolic BP) and left ventricular volume.(i.e roughly relation between BP and SV)

• firstly understand systolic BP will be highest point between aortic valve opening and closing.
• Diastolic will be when aortic valve just opens

1. Afterload(TPR) increased leads to increased aortic pressure, which causes lesser amount of blood to be pumped because valve closes earlier, so lesser SV

2. Contractility increased leads in more blood being pumped, SV increased

3. Increased preload, causes increased SV (frank staring law, because increase VR causes more fibre stretch and increased contractility)

Note: Above graph tells about changes at level of heart, now local organ CO will depend on organ needs and local factors like vasodilation, vasocontriction, hormonal changes will also play ultimately all maintaining tissue perfusion.

Although for accounting local factors you need to search for graphs of perfusion for each organ separately, following table may be useful. Use it in conjunction with above information which forms the global relation for BP and SV.

Refer to this table for CO % of various organs, from Guyton and Hall(12ed pg 192)

For muscle part of calculation assume blood flow to skeletal muscles average - 3 to 4 ml/min/100g of muscle [Guyton and hall Pg 243]

Source of graphs

1. 1st graph
2. 2nd graph First Aid Step 1, 30th ed, pg 287