# How to translate compartmentalized liver to analog computer? I Just want to learn to translate the figure to equations.

#### terabaaphoonmein

Joined Jul 19, 2020
111
Highly reputed source(International)-:
The compartmental analysis figure is the diagram that I want to translate to differential equations and eventually analog computer.  This is from This book. IDK about the author, but I bet that this is extremely reliable compared to the materials locally available and written by local authors. But it doesn't tell which equation it is modeling, so I am not 100% sure about it.
It has problems as well-:

It doesn't use negative for K12 And idk why is it using negative for K23.

Less reputed source-: This is pretty ambiguous, their equation and figure don't even match.

Highly reputed source(LOCAL)-:   My thoughts about sign what they should be-:

If the arrows are coming towards the block in consideration, add + sign else add - sign.
For eg-: consider x1 block, then we find x1', for that + will be what comes inside i.e K21*x2, and - will be what goes outside ie.K12*x1.

My Teacher(He hasn't written any pdfs that I know of)-:
He says "some books have written plus(in K21) while some minus I am not sure what it is actually."

#### MrAl

Joined Jun 17, 2014
10,914
Highly reputed source(International)-:
The compartmental analysis figure is the diagram that I want to translate to differential equations and eventually analog computer.  This is from This book. IDK about the author, but I bet that this is extremely reliable compared to the materials locally available and written by local authors. But it doesn't tell which equation it is modeling, so I am not 100% sure about it.
It has problems as well-:

It doesn't use negative for K12 And idk why is it using negative for K23.

Less reputed source-: This is pretty ambiguous, their equation and figure don't even match.

Highly reputed source(LOCAL)-:   My thoughts about sign what they should be-:

If the arrows are coming towards the block in consideration, add + sign else add - sign.
For eg-: consider x1 block, then we find x1', for that + will be what comes inside i.e K21*x2, and - will be what goes outside ie.K12*x1.

My Teacher(He hasn't written any pdfs that I know of)-:
He says "some books have written plus(in K21) while some minus I am not sure what it is actually."

Hello,

For any integrator you can handle it as thinking in terms of a differentiator.
So if the output of an integrator is X(t) then the input is d(X(t))/dt, or in more simple notation if the output is X then the input is dX/dt.

What seems unusual though is the circles with the "K12", "K21", etc. inside them. Are these gains or just node labels.
Gains are usually shown as rectangular blocks but it's kind of strange that we can see K12 on both the input and output of an inverter which does not make sense.
What you could try is find some other related work and see if the meaning is more obvious.
Normally if you had an integrator with feedback and the gain in the feedback is -K and the input is added to the gain -K at the input of the integrator then the equation is simply dX/dt=Vin-K with the output being X. If on the other hand the node where -K goes into the integrator is labeled "K" with it shown at the output of an inverter and the input to the inverter is also "K", then it doesnt make much sense as one or the other has to be "-K". In most cases the output of the inverting gain will be "-K" with the input being "K" or just not shown at all, so when you add it to the input it would just be "Vin+(-K)" which of course comes out to "Vin-K".

There are mistakes all over the web and the nomenclature also varies considerably you would think some of these authors went to school on another planet sometimes.

Last edited:

#### terabaaphoonmein

Joined Jul 19, 2020
111
Hello,

For any integrator you can handle it as thinking in terms of a differentiator.
So if the output of an integrator is X(t) then the input is d(X(t))/dt, or in more simple notation if the output is X then the input is dX/dt.

What seems unusual though is the circles with the "K12", "K21", etc. inside them. Are these gains or just node labels.
Gains are usually shown as rectangular blocks but it's kind of strange that we can see K12 on both the input and output of an inverter which does not make sense.
What you could try is find some other related work and see if the meaning is more obvious.
Normally if you had an integrator with feedback and the gain in the feedback is -K and the input is added to the gain -K at the input of the integrator then the equation is simply dX/dt=Vin-K with the output being X. If on the other hand the node where -K goes into the integrator is labeled "K" with it shown at the output of an inverter and the input to the inverter is also "K", then it doesnt make much sense as one or the other has to be "-K". In most cases the output of the inverting gain will be "-K" with the input being "K" or just not shown at all, so when you add it to the input it would just be "Vin+(-K)" which of course comes out to "Vin-K".

There are mistakes all over the web and the nomenclature also varies considerably you would think some of these authors went to school on another planet sometimes. This is the notation being used. So it's multiplier.

#### terabaaphoonmein

Joined Jul 19, 2020
111
Hello,

For any integrator you can handle it as thinking in terms of a differentiator.
So if the output of an integrator is X(t) then the input is d(X(t))/dt, or in more simple notation if the output is X then the input is dX/dt.

What seems unusual though is the circles with the "K12", "K21", etc. inside them. Are these gains or just node labels.
Gains are usually shown as rectangular blocks but it's kind of strange that we can see K12 on both the input and output of an inverter which does not make sense.
What you could try is find some other related work and see if the meaning is more obvious.
Normally if you had an integrator with feedback and the gain in the feedback is -K and the input is added to the gain -K at the input of the integrator then the equation is simply dX/dt=Vin-K with the output being X. If on the other hand the node where -K goes into the integrator is labeled "K" with it shown at the output of an inverter and the input to the inverter is also "K", then it doesnt make much sense as one or the other has to be "-K". In most cases the output of the inverting gain will be "-K" with the input being "K" or just not shown at all, so when you add it to the input it would just be "Vin+(-K)" which of course comes out to "Vin-K".

There are mistakes all over the web and the nomenclature also varies considerably you would think some of these authors went to school on another planet sometimes.
the problem is for analog method there's no resource. ig the book by naim a kheir contains it, but its pdfs isn't available online, neither its slides is. discrete simulation is pretty popular in india so it's available..

#### MrAl

Joined Jun 17, 2014
10,914 This is the notation being used. So it's multiplier.
Oh ok then i guess "K12" is a gain block simply used twice. That makes sense now.
So just do a block diagram calculation.