########## NAME
dae
########## METADATA
time_unit = s
########## MACROS
########## STATES
// ODEs
d/dt(Pca) = Qdiff/Ca
d/dt(Qao) = Plao/Lao

// DAEs
0 = Qheart - Qdiff - Qao
0 = Pca + Pra - Prao - Plao

// Initial conditions
Pca(0)		   = 0
Qao(0)         = 0
Qdiff(0)       = 0
Plao(0)        = 0

########## PARAMETERS
Ca =  1.1
Ra = 0.1
Rao = 1.2
Lao = 0.0005

########## VARIABLES
// Define function for heart beats
k_syst = 0.4
Qheart = ceil(max(0,k_syst-fmod(time,T)/T))  * 300.*sin((CONSTANT_PI*(fmod(time,T)/T))/k_syst)
            
Pra = Ra*Qdiff
Prao = Rao*Qao

########## FUNCTIONS
########## EVENTS

########## OUTPUTS
########## INPUTS
T = T_in @ 1 // @ 1 means that T has the value 1 if T_in is not given as input

########## FEATURES
Aortic pressure = Pca + Pra [mmHg]

// Extra features to better understand the model:
Flow input Qheart = Qheart [ml/s]
Qdiff = Qdiff  [ml/s]
Qao = Qao   [ml/s]
Pca = Pca  [mmHg]
Plao = Plao  [mmHg]
KCL = Qheart - Qdiff - Qao [ml/s]
KVL = Pca + Pra - Prao - Plao [mmHg]