// Cardiovascular system - Constrained-Frank-Starling-Baroceptor
// Set up for cardiac function curves
// Contractility (cardiac function) is increased progressively

IndVars: CNT
DepVars: Va,Vv,CVP,MAP,COL,HR,SV
Params:

//Fixed parameter values & compliances
  Vblood = 3.5
  SVR = 17
  CPLv = 0.45
  CPLratio = 20
  CPLa = CPLv/CPLratio

//Unstressed volumes and pressures
//At MCP, Vv/CPLv = Va/CPLa and Va + Vv = Vblood
  Vblood = 3.5
  Va0 = Vblood/(CPLratio + 1)
  Vv0 =  Vblood-Va0
  MCP = Va0/CPLa

//Calculate desired normal volumes and pressures when stressed
//xa and xv are scaling factors that let the normal pressures change with compliance
//Empirically force one third of blood to be in the arterial compartment when stressed
  xa = 3
  PaS = xa/CPLa
  VaS = Vblood*1/3
  xv = 0.06
  PvS = xv/CPLv
  VvS = Vblood*2/3

//Calculated pressures - venous
//A line with point through (Vv0,MCP)
  slopeCVP = (MCP-PvS)/(Vv0-VvS)
  interCVP =  MCP-slopeCVP*Vv0
  CVPtemp = slopeCVP*Vv+interCVP
  CVP = IFLTZERO(CVPtemp,0,CVPtemp)

//Calculated pressures - arterial
//A line with point through (Va0,MCP)
  slopeMAP = (PaS-MCP)/(VaS-Va0)
  interMAP =  MCP - slopeMAP*Va0
  MAPtemp = slopeMAP*Va+interMAP
  MAP = IFLTZERO(MAPtemp-MCP,MCP,MAPtemp)

//HR control
//Constrain HR to be between 0 and 220
  MAPset = 100
  HRgain = 1.8
  MAPdelta = MAPset-MAP
  HRtemp = MAPset + MAPdelta*HRgain
  HR = IFLTZERO(HRtemp,0,IFLTZERO(220-HRTEMP,220,HRTEMP))

//Calculate stroke volume from CVP and Contractility
//A logistic curve
  kc = 0.00001
  SVlim = 5.1
  SV50 = 2.55
  nSV = 1.9
  SVtemp = ((Svlim*CVP^nSV)/(SV50^nSV+CVP^nSV))*kc*CNT
  SV = IFLTZERO(SVtemp,0,SVtemp)

//Cardiac output
//Constrain CVP to be positive
  COL = SV*HR
  CORtemp1 = (MAP)/SVR
  CORtemp2 = (MAP-CVP)/SVR
  COR = IFLTZERO(CVP,CORtemp1,CORtemp2)

//Differential equations for volume changes
  Vv' = COR-COL
  Va' = COL-COR

//Parameter values
  0<CNT<3000

//Initial conditions
  t=0
  Vv = Vv0
  Va = Va0