Dynamic Fluid Volume Model

The original ACAT model was developed with a constant volume for each intestinal component. With the Dynamic Fluid Volume model, you can simulate changes in intestinal volume based on fluid intake, absorption, and secretion. The model assumes constant fluid secretion, first-order water absorption, and first-order emptying rates between compartments. Equation 1-1 is the equation for the calculation of the change in volume versus time.

Equation 1-1: Change in fluid volume versus time

where:

Variable	Definition
	The volume of the fluid in the j^thintestinal compartment.
	The volume of the fluid in the previous intestinal compartment (i.e. j-1).
	Time.
	The water secretion rate(s) in the j^thintestinal compartment.
	The water absorption rate(s) in the j^thintestinal compartment.
	The transit rate of the j^th intestinal compartment.
	The transit rate of the previous intestinal compartment (i.e. j-1).

You can edit the absorption rate and the secretion rate for each individual compartment.

Because concentration = mass/volume, dynamic volume also impacts the calculation of drug concentration in the model. Equation 1-2 is the equation for the calculation of the change in concentration due to volume.

Equation 1-2: Change in drug concentration due to fluid volume versus time

where:

Variable	Definition
	Time.
	The total concentration of the drug in the j^th intestinal compartment at time t.
	The volume of fluid in the j^th intestinal compartment.
	The mass of drug in the j^th intestinal compartment.

GastroPlus® includes four default volume profiles for the Dynamic Fluid Volume model. Because no reliable MRI measurements currently exist for the fed state, these four volume profiles are available only for the fasted state. The ACAT physiologies for these profiles are named as shown below.

“Human - Dyn Vol 100% Mudie - Fasted.” This profile is based on the stomach and small intestine fluid volumes in the fasted state ¹ .

“Human - Dyn Vol 200% Mudie - Fasted.”

“Human - Dyn Vol 300% Mudie - Fasted.”

“Human - Dyn Vol 400% Mudie - Fasted.”

The last three profiles that are listed represent 200%, 300%, and 400% of the MRI fluid volume measurements, respectively.

You can change the % fluid volume in the small intestine and colon to generate new Dynamic Fluid Volume models. If you change the % fluid volume, then GastroPlus® tries to re-balance secretion rates to keep the same initial volume and final volume under the assumption that the first-order water secretion rate is constant. The balance equations assume a steady state solution to Equation 1-1. Equation 1-3 is the equation for the calculation of the secretion rate for the new Dynamic Fluid Volume model.

Equation 1-3: Secretion rate for a new Dynamic Fluid Volume model

where:

Variable	Definition
	The volume of the fluid in the j^th intestinal compartment.
	The volume of the fluid in the previous intestinal compartment (i.e. j-1).
	Time.
	The new secretion rate in the j^th intestinal compartment.
	The gut compartment.
	The water absorption rate(s) in the j^th intestinal compartment.
	The transit rate of the j^th intestinal compartment.
	The new fluid volume in the j^th intestinal compartment.
	The transit rate of the previous intestinal compartment (i.e. j-1).
	The new fluid volume in the previous intestinal compartment (i.e. j-1).

Mudie, D.M., Murray, K., et al. (2014). “Quantification of gastrointestinal liquid volumes and distribution following a 240 mL dose of water in the fasted state.” Mol. Pharm. 11(9): 3039-3047.