Physiologically based pharmacokinetic (PBPK) models have beenshown to be useful in predicting drug distribution throughout thebody.

You will be examining the distribution of a model drug, Elheats.Elheats is broken down in the liver into Cirekram. Cirekram hasmany detrimental effects in the body, and therefore, it isdesirable to track and document both compounds after ingestion ofthe drug.

ELHEATS DISTRIBUTION:

STOMACH:

Elheats is ingested orally, and you can approximate the startingcompartment as the stomach itself-no Elheats is absorbed ormetabolized between the mouth and the stomach.

The initial dose of interest is 25g/kg, which is consumed with100mL of fluid. Assume the standard adult mass of 69.4kg, andneglect any other stomach contents.

Elheats dissolves into the fluid in the stomach very quickly(assume immediately), and thestomach can be considered to bewell-mixed. The rate of stomach emptying is dependent

upon the volume of the stomach contents, with a rate constantks= 0.045 min-1(this a first-order rate constant).

Hint: Since the concentration of Elheats in the stomach isconstant, and it is only the rate at which it leaves that varies,try to end up with an equation to describe the

stomach contents volume at any time (dVs/dt).

GI TRACT:

The GI Tract is approximately 2.40L in total water volume.Elheats leaves the stomach and enters the GI tract. The GI tractalso receives input from the blood (the CENTRAL

COMPARTMENT), which carries both Elheats and Cirekram. Thevolumetric flow rate of blood is 900mL/min. From the GI tract, itenters the first compartment of the liver (see

below). The volumetric flow rate of material leaving the GItract to the liver is 900mL/min.

LIVER:

The liver is approximately 1.08L in total water volume. Elheatsis metabolized intoCirekram in the liver, so unlike the remainderof the compartments, the liver cannot beconsidered to bewell-mixed. To deal with this, consider the liver as 5 separatecompartments. Material enters the liver (L1) from the GI tract (asabove), where it is mixed with blood from the central compartment(entering the liver at 450mL/min).

One reaction occurs to metabolize Elheats into Cirekram. (ForDeliverable 1, consider thisreaction to be a consumption/generationterm that is dependent upon the concentration of Elheats and theconcentration of Cirekram. Use r1(units of mass/(vol*time)).)

Another reaction occurs to metabolize Cirekram into an innocuouscompound, whose distribution we are not interested in at thispoint. (For Deliverable 1, consider this reaction to be aconsumption term that is dependent upon the concentration ofCirekram. Use r2 (units of mass/(vol*time)).)

The L1liver compartment empties at a volumetric flow rate of1350mL/min into the L2 liver compartment, where the same reactionsoccur. The L2 liver compartment empties into the L3 livercompartment, at the same volumetric flow rate, and with the samereactions. This continues for the L4 compartment. For the L5compartment, the output is directly to the bloodstream (the centralcompartment). Note that by separating the liver into 5compartments, we are able to capture the spatial nature of thereaction rates and the dependence on concentration more accurately.Each liver compartment itself can be considered to be well-mixedwithout requiring the physiologically inaccurate assumption thatthe entire liver is well-mixed.

CENTRAL COMPARTMENT (BLOODSTREAM)

The central compartment is a catch-all for every other part ofthe human body (excluding the stomach, GI Tract, liver, andmuscle), which we lump together with the carrying bloodstream tocall the central compartment. The central compartment as definedhere has a total water volume of 11.56L. The central compartmentreceives blood carrying Elheats and Cirekram from the L5compartment of the liver (at a volumetric flow rate of 1350mL/min)and from the muscles (950mL/min), and delivers blood to the muscles(950mL/min), liver (450mL/min), and GI tract (900mL/min). Noreactions occur in the central compartment.

MUSCLES

The muscles compartment has a total water volume of 25.76L.Although you are not required to do so here, you could decouple anyentity from the central compartment in the

same way that the muscles are decoupled. The muscles receiveElheats and Cirekram from the central compartment at a volumetricflow rate of 950mL/min, and return the blood to

the central compartment after mixing well in the muscles at arate of 950mL/min. There are no reactions that occur in themuscles.

ANSWER THE QUESTIONS BELOW

Problem 1A: From the information given above, create twoschematics that show the

distribution paths of Elheats and Cirekram (one schematiceach-they should be similar,but not identical). Your schematics maytake any form, but you may wish to review Figure1 of Zhuang and Lufor an example. You may, however, find it easier to simplify theirrepresentation and draw a simple flow diagram that shows the pathof distribution.

Problem 1B:

From the information given above, generate a list of ordinarydifferential equations that you would use to develop a PBPK modelof Elheats and Cirekram. Submit the list of equations as well asall of your work to develop those equations. You may use eithernumerical values (with units) or parameters (e.g. Vc) in theseequations. If you choose to use parameters, make sure to define theparameters somewhere easily accessible in your submission.

Hint: Label each compartment with a number or letter, and labeleach mass flow stream.Then use a system boundary around eachcompartment to calculate the concentration of Elheats or Cirekram(one equation for each) in that compartment. Recall thatconcentration is mass/volume, and volume is constant for eachnon-stomach compartment.