Simbiology: intratumoral volume

Hello, I would like to simulate the drug concentration vs time within the tumor after intratumoral delivery. The drug is tagged with a fluorophore and I will use the concentrations coverted from fluorescence data obtained over time as the inputs. This will be a simple one-compartment model with the tumor volume = compartment volume. Because the tumor volume changes over time (V will be measured and calculated), how do I set to normalize dC/dt against the changing volume at each time point?

Answer 1

[Jeremy Huard]

Hi Kelly,

compartments have a 'Constant' property that can be set to false to allow the volume to change during the course of a simulation.

A non-constant compartment can have its volume modified by rules or events. If this volume is defined by a time-dependent algebraic equation, you can use a repeated assignment. If its dynamic is defined by an ODE instead, you can (and must) use a rate rule to define this equation.

Here is an example of a volume defined by a repeated assignment:

m = sbiomodel('m1')
v = addcompartment(m,'v',10,'Constant',false,'Unit','liter')
p = addparameter(m,'p','Unit','liter')
r = addrule(m,'v = 100 * p','repeatedAssignment')
s = addspecies(v,'s',50,'Unit','milligram/liter')

I hope this helps.

Best regards,

Jérémy

[Kelly P]

Thank you for your response. I am not sure if the volume is defined by an algebraic equation or an ODE. I only have a set of volume values measured in vivo. Can I input these as a separate set of data (in addition to the concentration and time data)?

If this is a simple first order elimination model governed by Mass Action kinetics, how would the equation with volume correction look like?

[Jeremy Huard]

Hi Kelly,

I am a bit confused. I was assuming that you wanted to simulate the model only and that you had en equation to describe the tumor growth.

Can you give me more context? Are you trying to fit your model to experimental data?

Best,

Jérémy

[Kelly P]

Hello Jeremy,

Sorry for the confusion. I would like to fit the model to experimental data to estimate the parameters (k elimination, kon/koff between the drug species and the delivery platform within the compartment). Then use these parameters to optimize the model and simulate a dosing regimen based on desirable free drug AUC. I have tumor growth data (measured volumes) but do not have an equation to describe it.

Thank you,

Kelly

[Jeremy Huard]

Hi Kelly,

thanks for the clarification. I have a remark though: if your plan is to simulate different dosing regimens which will affect the tumor growth, your model should contain this dependency somehow. Do you agree?

You could use a simple model for the tumour growth and include a term for the drug effect (reduction of tumour volume). As an example, it could look like this

But this is just an example, there are multiple Tumor Growth Inhibition models described in the literature that could be used.

With this type of equation, the goal would now be to consider V as a measurement and estimate the parameters describing its dynamics.

I hope this helps.

Best,

Jérémy