Six compartment model with flow, exchange, and recirculation.
Model number: 0118
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System is composed of 6 compartments, five of them in series, with one in parallel. The system is divided into three operators with recirculation as diagrammed. Exchange is allowed in only the first operator. The second and third operators are each composed of two stirred tanks operators in series. The input function, Cin, is positioned between the first and second operators but could be positioned anywhere. A fractional clearance occurs between the output of the third operator with the remainder recirculating to the first operator. This model can be used to explore the theory of John L.Stephenson, Bull Math Biophys 10: 117-121, 1948.and Bull Math Biophys 22:1-17, 1960.
Figure: A plot of concentration as a function of time for each of the compartment outflows, where CC2 is the outflow conentration from the system before recirculating into compartment CA1. Concentrations are in mM.
CC2*(1-clear) <----------<---------------------------<---------------<---------------< Fp| OPERATOR 1 Cin OPERATOR 2 OPERATOR 3 | | _________________ | ______ _______ _______ _______ ^ v |Vp CA1(t) | CA1 v |VB1 | |VB2 | |VC1 | |VC2 | | Creturn -->| |--->(+)--->| CB1 |->| CB2 |----->| CC1 |->| CC2 |->| | PSg | |_____| |_____| |_____| |_____| | ^ | --------|-------- FLOW = Fp ml/(g*min) --> | v | | | |Visfp CA2(t) | -----------------
The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.Operator A, a single stirred tank with permeation into a nonflowing tank.
Operator B, a pair of tanks in series with inputs from A1 and from Cin:
Operator C, same as B but no other input:
Return to Operator A:
Where Vp is the volume of the plasma space, PSg is the permeability surface area product, Visfp is the ISF volume fraction in 1 gram of tissue, clear is the fractional clearance, VB is the plasma volume fraction in 1 gram of B tissue and VC is the plasma volume fraction in 1 gram of C tissue.
John L.Stephenson, Bull Math Biophys 10: 117-121, 1948. John L.Stephenson, Bull Math Biophys 22:1-17, 1960.
Single Compartment Models:
- Comp1Decay: Single Compartment with Decay,
- Comp1Flow: Single Compartment with Flow,
- Comp1FlowDecay: Single Compartment with Flow and Decay,
- Comp1Reaction: Single Compartment with One Reaction,
- Comp1FlowReaction: Single Compartment with Flow and One Reaction,
- Comp1FlowReactions2: Single Compartment with Flow and Two Reactions,
Two Compartment Models:
- Comp2Exchange: Two Compartments with Exchange,
- Comp2ExchangeReaction: Two Compartments with Exchange and One Reaction,
- Comp2FlowExchange: Two Compartments with Flow and Exchange Fit to a data set,
- Comp2FlowExchangeReaction: Two Compartments with Flow, Exchange, and One Reaction.
- Comp2FlowMMExchangeReaction: Two Compartments with Flow, Exchange using a Michaelis-Menten transporter, and One Reaction.
- Comp2FlowMRIContrast: Two Compartments with Flow, conversion of water to water spin for MRI contrast.
- Cortisol secretion: Two compartments with feedback control of precursor to cortisol and its adrenal secretion.
N>2 Compartment Models:
- Comp3FlowExch: Three compartmental model for plasma, interstitial fluid, and parenchymal cell,
- Comp6Propofol: Six compartmental model for propofol anaesthesia,
- CTEX10: N Compartments in series with Flow, emphasizes sensitivity analysis and optimization,
- CTEX10stat: CTEX10 model with statistics on inflow and outflow curves,
- CTEX20: N Compartments in series with Flow, each compartment exchanging with a compartment in parallel,
- CTEX20 5 path: Weighted sum of up to 5 paths of CTEX 20 modeled capillaries.
- CompNFlowDelay: N Compartments in series with Flow and Delay.
- Comp6_Recirc: Six compartmental recirculating model,
- Comp2x2Recirc: Dual two compartment models with recirculation and clearance,
- Uncoupled fluxes of water and solute across membrane.
- Uncoupled fluxes of water and solute across membrane w/ columns for measuring pressure.
- Transport of a hard spherical solute through a cylindrical pore.
- Washout curve simulation by sum of three decaying exponentials.
- Three reactions in series with no enzymes.
- Michaelis-Menton reactions in series.
- Enzymatic reactions in series.
- Four sequential enzymatic reactions.
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The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
[This page was last modified 02Nov16, 2:27 pm.]
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