MODEL NUMBER: 0089 MODEL NAME: Myo_Dyn_Resp_wFit SHORT DESCRIPTION: This model describes the dynamic response of a vessel after a step increase in intraluminal pressure. ----------------------------------------------------------------------------- M Y O G E N I C D Y N A M I C R E S P O N S E M O D E L ----------------------------------------------------------------------------- FIGURE: DETAILED DESCRIPTION: // This model describes the dynamic response of a vessel after a step // increase in intraluminal pressure. It has been well documented that an // initial passive distension occurs which is then followed by a // vasoconstriction to a vessel diameter below that of the initial diameter // at low pressure. We have previously developed a model of the myogenic // response in the resistance vessels which differentiates and defines the // passive and active diameter responses to pressure (see Ref 1 below). // Briefly, the passive and active tensions must balance the circumferential // tension generated by the pressure difference across the vessel wall. So: // Ttot = Tpass + Tact // where Ttot is the pressure generated circumferential tension governed by // the Law of Laplace: // P * D // Ttot = ------- // 2 // where P is the intraluminal pressure and D is the vessel diameter. The // passive tension is nonlinear with respect to D and has been approximated // here with an exponential: // Tpass = Cp1 * exp ( Cp2 * (( D/Dp100 ) - 1) ) // where Cp1 is the passive tension at an intraluminal pressure of 100 mmHg, // Cp2 describes the steepness of the exponential and Dp100 is the diameter // of the vessel in a passive state at 100 mmHg. The active tension can be // further broken down into two components: A, the degree of activation of // the VSM (range from 0 to 1) and Tactmax, the active tension generated by // the VSM in a maximally activated state. The maximally active tension is // given by: // _ _ // | _ _ 2 | // | | (D/Dp100) - Ca2 | | // Tactmax = Ca1 * exp < - | ----------------- | > // | |_ Ca3 _| | // |_ _| // where Ca1 is the peak active tension, Ca2 is the diameter of the peak // active tension normalized by the passive vessel diameter at 100 mmHg, // and Ca3 is the width of the Gaussian normalized by Dp100. The VSM // activation is approximated by a sigmoidal function and is given by: // A = 1 / ( 1 + exp ( -Cmyo*Ttot + Ctone ) ) // where Cmyo determines the sensitivity of the VSM activation to // circumferential tension and Ctone is the base level of tone that is in // a vessel without any stimuli. This previous formulation produces the // steady state diameter as a function of pressure for a vessel defined by // the parameters Cp1, Cp2, Dp100, Ca1, Ca2, Ca3, Cmyo and Ctone. In order // to model the dynamic response we assume that: // dD 1 Dc // ---- = ------ * ---- * ( T - Ttarget ) // dt taud Tc // and // dA 1 // ---- = ------ * ( Atarget - A ) // dt taua // where taud and taua are the time constants of the response, Dc and // Tc are the control diameter and total vessel wall tension for scaling // purposes, and Ttarget and Atarget are the steady state tension and // activation based on the current diameter, D, pressure, P, vessel wall // tension, T, and VSM activation, A. The expressions for Ttarget and // Atarget are given by: // _ _ // | (2*T/P) | // Ttarget = C1p * exp< C2p * --------- - 1 > // |_ Dp100 _| // _ _ _ 2 _ // | | (2*T/P)/Dp100 - C2a | | // + A * C1a * exp< - |--------------------- | > // |_ |_ C3a _| _| // and // Atarget = 1 / ( 1 + exp ( -Cmyo*(D*P/2) + Ctone ) ) // In this model the model parameters C1p, C2p, C1a, C2a, C3a, Cmyo and // Ctone have been set to those optimized to fit the experimental data of // Davis and Sikes (see Ref 3 and Regulatory Vessel model on the Physiome // site). An additional parameter set has been developed where taud and // taua in addition to the previous parameters and taud and have been // optimized in a two step process to fit the dynamic data of Sun et al. // (see Ref 2). The time constants were first optimized to fit the data // and then the parameters C1p, C2p, C1a, Cmyo and Ctone were optimized // at the new taud and taua values. This process was repeated yeilding a // very good fit to the eperimental data. To see this fit load the // Opt_2_Hill parameter set and run the model. The fit and data will be // displayed on the Fit_2_Hill plotpage. SHORTCOMINGS/GENERAL COMMENTS: - Specific inadequacies or next level steps KEY WORDS: vascular smooth muscle, Data, intraluminal pressure, circulatory vessel, myogenic response, Cardiovascular system, Blood flow, Autoregulation, arteriole, Acive contraction, pressure REFERENCES: Carlson BE and Secomb TW: A theoretical model for the myogenic response based on the length-tension characteristics of vascular smooth muscle Microcirc 12:327-338, 2005 Hill MA, Zou H, Davis MJ, Potocnik SJ and Price S: Transient increases in diameter and [Ca2+]i are not obligatory for myogenic constriction Am J Physiol Heart Circ Physiol 278:345-352, 2000 Sun D, Huang A, Koller A, Kaley G: Flow-dependent dilation and myogenic constriction interact to establish the resistance of skeletal muscle arterioles, Microcirc 2:289-295, 1995 REVISION HISTORY: Original Author : BCarlson Date: 07/12/07 Revised by: BEJ Date:19jun11 : Update comment format COPYRIGHT AND REQUEST FOR ACKNOWLEDGMENT OF USE: Copyright (C) 1999-2011 University of Washington. From the National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061. Academic use is unrestricted. Software may be copied so long as this copyright notice is included. This software was developed with support from NIH grant HL073598. Please cite this grant in any publication for which this software is used and send an email with the citation and, if possible, a PDF file of the paper to: staff@physiome.org.

Control activation b4 step change

Maximally active tension parameter

Target SS T for current state

Control diameter b4 step change

Reference vessel diameter

Step function

Myogenic VSM activation parameter

Control intraluminal pressure

Vessel wall tension

Target SS A for current state

Intraluminal pressure

Passive tension parameter

Maximally active tension parameter

Basal tone VSM activation parameter

Control tension b4 step change

Vessel diameter

VSM activation in vessel wall

Passive diameter time constant

Maximally active tension parameter

VSM activation time constant

Passive tension parameter

Control diameter b4 step change

Control activation b4 step change