Modelica Day Jiří Kofránek. Univerzita Karlova v Praze, 1. lékařská fakulta, Laboratoř biokybernetiky a počítačové podpory výuky

Transkript

1 Modelica Day 2015 Jiří Kofránek Univerzita Karlova v Praze, 1. lékařská fakulta, Laboratoř biokybernetiky a počítačové podpory výuky

2 Naše cesta k Modelice Jiří Kofránek Modelica pro simulace

3 Formalizace fyziologických vztahů Annual Review of Physiology 1972 A.C. Guyton

4 Functional block Divider Formalizace fyziologických vztahů??!! Integrator Multiplier PPA PLA Summator PCP PCP=0.55 PLA+0.45 PPA

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30 RPF - Renal plasma flow [ml/min] GKf - Glomerular filtration coeffitient [ml/min/torr] 7 GKf RAP RAP - Renal artery pressure [torr] 1 RAP PAff - Afferent artery pressure [torr] RBF - Renal blood flow [ml/min] 4 RBF PAf f PAff=RBF*AffC GP = RAP - PAff GP - Glomerulal pressure [torr] GP GKf GKf - Glomerular filtration coeffitient [ml/min/torr] Grafické zobrazení matematických vztahů? NETP - Net pressure gradient in glomerulus [torr] GFR = NETP*GKf GFR - Glomerular filtration rate [ml/min] Ne! 1 GFR 2 AffC AffC - Afferent artery conductance [ml/min/torr] 3 GFR - Glomerular filtration rate [ml/min] TubC - Tubule conductance [ml/min/torr] PTP - Proximal tubule pressure [torr] TubC PTP = GFR/TubC AVeCOP - Average colloid osmotic pressure [torr] NetP = GP - PTP - AVECOP GFRold - GFRnew Solve f (z) z f(z) = 0 Algebraic Constraint 5 RPF 6 APr APr - Afferent protein concentration [g/ml] 1160 B - Landis-Pappenheimer coeffitient [torr/g/ml]1 Grafické zobrazení GFR - Glomerular filtration rate [ml/min] FF - Filtration fraction [relative number] transformace FF = GFR/RPF u 2 vstupních hodnot na výstupní (APr)^2 B * (Apr)^2 ACOP - Afferent colloid osmotic pressure [torr] 320 A - Landis-Pappenheimer coeffitient [torr/g/ml] A*Apr ACOP = A*Apr + B*(APr)^2 1 EPr - Efferent protein concentration [g/ml] u FF EPr = APr / (1-FF) (EPr)^2 B * (Epr)^2 ECOP - Efferent colloid osmotic pressure [torr] A*Epr ECOP = A*Epr + B*(EPr)^2 ACOP+ECOP 2 AVeCOP = (ACOP+ECOP)/2 Matlab/Simulink simulation chip: G L O M E R U L A R F I L T R A T I O N

31 Softwarové nástroje pro tvorbu modelů 6.25 Normal proximal tubule conductance [ml/min/torr] 0.07 Plasma protein cnoncentration [g/ml] 16 Normal glomerular filtration coeffitient [ml/min/torr] RAP AffC TubC RBF RPF APr GKf G L O M E R U L A R F I L T R A T I O N INPUTS : RAP - Renal artery pressure[torr] Affc - Afferent artery conductance [mll/min/torr] TubC - Proximal tubule conductaqnce [ml/min/torr] RBF - Renal blood flow [ml/min] RPF - Renal plasma flow APr - Plasma protein concentration (in afferent artery) [g/ml] GKf - Glomerular filtration coeffitient [ml/min/torr] OUTPUT : GFR - Glomerular filtration rate [ml/min] Calculation of glomerular filtration rate1 GFR 0.8 Normal Na proximal fractional reabsorbtion PNa GFR LogA2 PrxFNaNorm Log Pd C M Y O G E N I C R E S P O N S E 200 Venous conductance [ml/min/torr] 7 Vena renalis pressure [torr] 0.44 Hematocrit AffC EffC RenVenC AP VP Hct Clamp R E N A L P E R F U S I O N INPUTS : AffC - Afferent artery conductance [ml/min/torr] EffC Efferent artery conductance [ml/min/torr] RenVenC - Renal venous conductance [ml/min/torr] AP - Arterial pressure [torr] VP - Vena renalis pressure [torr] Hct - Hematocrit [relative number] Clamp - Renal artery pressure drop caused by renal artery clamp [torr] OUTPUTS : RAP - Renal artery pressure [torr] RBF - Renal blood flow rate[ml/min] RPF - Renal plasma flow rate[ml/min] RAP RBF RPF RAP INPUT : RAP - Renal artery pressure [torr] OUTPUT : AffC - Myogenic effect [ x Normal] AffMyo1 Calculation of the myogenic response to changes in renal perfusion pressure (afferent conductance responds to changes in perfusion pressure, with pressure increases causing vasoconstriction) Calculation of renal artery pressure and renal blood flow rate Renal artery pressure clamp drop [torr] A F F E R E N T A R T E R Y AffMyo INPUTS : AffMyo - Myogenic effect [ x Nomal] AffC MDSig - Macula densa feedback signal [ x Normal] MDSig AffNorm - Normal conductance in afferent artery [ml/min/torr] OUTPUT : AffC - Vascular conductance [ml/min/torr] Calculates conductance of afferent artery Af f Norm 30 Normal conductance of Afferent artery [ml/min/torr] Matlab/Simulink

32 Kauzální modelovací nástroje Je jednoznačně definován postup výpočtu 200 Venous conductance [ml/min/torr] Normal proximal tubule conductance [ml/min/torr] 0.07 Plasma protein cnoncentration 16 [g/ml] Normal glomerular filtration coeffitient [ml/min/torr] R E N A L P E R F U S I O N AffC INPUTS : EffC AffC - Afferent artery conductance [ml/min/torr] EffC Efferent artery conductance [ml/min/torr] RenVenC RenVenC - Renal venous conductance [ml/min/torr] AP - Arterial pressure [torr] VP - Vena renalis pressure [torr] AP Hct - Hematocrit [relative number] Clamp - Renal artery pressure drop VP caused by renal artery clamp [torr] RAP RBF RAP G L O M E R U L A R F I L T R A T I O N AffC INPUTS : RAP - Renal artery pressure[torr] TubC Affc - Afferent artery conductance [mll/min/torr] TubC - Proximal tubule conductaqnce [ml/min/torr] RBF RBF - Renal blood flow [ml/min] GFR RPF - Renal plasma flow RPF APr - Plasma protein concentration (in afferent artery) [g/ml] GKf - Glomerular filtration coeffitient [ml/min/torr] APr OUTPUT : GFR - Glomerular filtration rate [ml/min] GKf Calculation of glomerular filtration rate1 0.8 Normal Na proximal fractional reabsorbtion M Y O G E N I C R E S P O N S E INPUT : RAP RAP - Renal artery pressure [torr] AffMyo OUTPUT : AffC - Myogenic effect [ x Normal] Calculation of the myogenic response to changes in renal perfusion pressure (afferent conductance responds to changes in perfusion pressure, with pressure increases causing vasoconstriction) 1182 N A T R I U M - P R O X I M A L T U B U L E PNa MDNaFlow INPUTS : PNa - Plasma sodium concentration [mmol/ml] GFR - GLomerulal filtration rate [ml/min] GFR LogA2 - Logarithm of plasma angiotensin concentration [pg/ml] PrxFNaNorm - Normal value of sodium proximal PdxNaReab fractional reabsorbtion [relative number] LogA2 OUTPUTS : MDNaFlow - Sodium outflow [mmol/min] PdxNaReab - Proximal sodium reabsorbrtion [mmol/l] PrxFNa - Proximal fractional sodium reabsorbtion PrxFNa PrxFNaNorm [relative number] Calculation of proximal tubule sodium reabsorbtion Vena renalis pressure [torr] Hct 0.44 Clamp Hematocrit OUTPUTS : RAP - Renal artery pressure [torr] RBF - Renal blood flow rate[ml/min] RPF - Renal plasma flow rate[ml/min] RPF Calculation of renal artery pressure and renal blood flow rate Renal artery pressure clamp drop [torr] Kauzální modelování A F F E R E N T A R T E R Y AffMyo INPUTS : AffMyo - Myogenic effect [ x Nomal] AffC MDSig - Macula densa feedback signal [ x Normal] MDSig AffNorm - Normal conductance in afferent artery [ml/min/torr] OUTPUT : AffC - Vascular conductance [ml/min/torr] Af f Norm 30 Normal conductance Model v Simulinku vyjadřuje spíše způsob výpočtu než strukturu modelované reality AP EffC ZNAE A R T E R I A L P R E S S U R E INPUTS : ZNAE - ECF sodium content [mmol] AP LogA2 loga2 - Logarithm of plasma angiotensin concentration [pg/ml] AP APNorm - Normal value of arterial pressurel [torr] OUTPUT : 100 APNorm AP Arterial pressure [torr] APNorm [torr] Control of arterial pressure by angiotensin and extracellular sodium content LogA2 Scope1 Scope A N G I O T E N S I N PRA A2 INPUTS : PRA - Plasma renin activity [ Units/ml] CEAct - Converting enzyme activity [x Normal] CEAct A2Inf Angiotensin 2 infusion rate [ng/min] LogA2 OUTPUTS : loga2 A2 - Plasma angiotensin 2 concentration [ pg/ml] A2Inf LogA2 - logarithm of plasma angiotensin concentration [ pg/ml]) Calculation of plasma angiotensin concentration and logarithm of plasma angiotensin concentration (most of the action of angiotensin are logarithmic in nature: concentration changes at higher concentrations produce less of an Calculates conductance of afferent artery of Afferent artery [ml/min/torr] E F F E R E N T A R T E R Y loga2 INPUTS : loga2 - logarithm of angiotensin concentration EffC MDSig - Macula densa feedback signal [ x Normal] MDSig EffNorm - Normal conductance in afferent artery [ml/min/torr] 25.1 OUTPUT : EffC - Vascular conductance [ml/min/torr] Ef f Norm 25 Normal conductance Calculates conductance of efferent artery of Efferent artery [ml/min/torr] R E N I N MDSig INPUTS : MDSig - Macula densa feedback signal [ x Normal] PRA VECml - Ectracellular fluid volume OUTPUT : VECml PRA - Plasma renin activity [ Units/ml] 1 Converting Enzyme Calculation of plasma renin activity Activity 0 Angiotensin Infusion Rate VECml M A C U L A D E N S A MDNaFlow INPUTS : MDNaFlow - Macula densa sodium flow [mmol/min] MDSig loga2 - Logarithm of plasma angiotensin concentration [pg/ml] LogA2 MDNorm - Normal macula densa feedback signal [ x Normal] OUTPUT : MDSig - Macula densa feedback signal [ x Normal] MDNorm Macula densa feedback signal calculation based on macula densa sodium flow and angiotensin concentration 1 Normal macula densa feedback signal effect than changes of the same size at lower concentrations) A L D O S T E R O N E loga2 LogA2 INPUTS : loga2 - Logarithm of plasma angiotensin concentration [pg/ml] Aldo AldoInf - Aldosterone infusion rate [ng/min] VTW - Total body water content [ml] OUTPUT : Aldo - Plasma aldosterone concentration [ ng/dl] Calculation of plasma aldosterone concentration AldoInf 0 Aldosteron Infusion Rate VTWml -C- Totasl body water content [ml] Aldo MDNaFlow Aldo N A T R I U M - D I S T A L T U B U L E DisNaFlow INPUTS : MDNaFlow - Sodium inflow [mmol/min] Aldo - Plasma aldosterone level [pg/ml] DisFNaNorm - Normal value of sodium distal fractional reabsorbtion [relative number] DisNaReab DistNaFlow OUTPUTS : DisNaFlow - Sodium outflow [mmol/min] DisFNaNorm DisNaReab - Distal sodium reabsorbrtion [mmol/min] DisFNa - Distal fractional sodium reabsorbtion DisFNa Normal distal [relative number] fractional reabsorbtion for Na Calculation of distal tubule sodium reabsorbtion 2159 S I M P L E S O D I U M B A L A N C E Matlab/Simulink NaDiet ZNAE INPUTS : NaDIet - Dietary sodium intake [mmol/min] NaUrine - Sodium urine outflow [mmol/min] NaUrine VECml - Extracellular fluid volume [ml] PNa OUTPUT : ZNAE - ECF sodium content [mmol] VECml PNa - Plasma sodium concentration [mmol/ml] Extracellular sodium quantity is the integral over time dietary sodium intake minus urinary sodium loss NaDiet [mmol/min] Extracellular fluid volume[mmol/min] N A T R I U M - C O L L E C T I N G D U C T NaUrine INPUTS : DisNaFlow DisNaFlow - Sodium inflow [mmol/min] CDFNaNorm - Normal value of sodium distal fractional reabsorbtion [relative number] CDNaReab OUTPUTS : NaUrine - Sodium urine outflow [mmol/min] CDNaReab - Collecting duct sodium reabsorbrtion [mmol/min] CDFNaNorm CDFNa CDFNa - Collecting duct fractional sodium reabsorbtion [relative number] 0.93 Normal collecting duct fractional reabsorbtion for Na Calculation of collecing duct sodium reabsorbtion

33 Modelica pro simulace

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45 Děkuji za pozornost Modelica pro simulace