Model Mathematics

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Component: lpc

hrf = \frac{60}{HR} beattime = t - (⌊ \frac{t}{hrf} ⌋ hrf) Tsv = TsvK \sqrt{\frac{1 1}{HR}} 7.745966692414832 Tsa = TsaK \sqrt{\frac{1}{HR}} 7.745966692414832 trelv = beattime - PRint trela = beattime yla = \{\begin{matrix} \frac{1 - (\cos (\frac{π trela}{Tsa}))}{2} if trela \geq 0 \land trela ≦ Tsa \\ \frac{1 + \cos (\frac{2 π (trela - Tsa)}{Tsa})}{2} if trela < 1.5 Tsa \land trela \geq Tsa \\ 0 otherwise \end{matrix} yra = yla ylv = \{\begin{matrix} \frac{1 - (\cos (\frac{π trelv}{Tsv}))}{2} if trelv \geq 0 \land trelv ≦ Tsv \\ \frac{1 + \cos (\frac{2 π (trelv - Tsv)}{Tsv})}{2} if trelv < 1.5 Tsv \land trelv \geq Tsv \\ 0 otherwise \end{matrix} yrv = ylv Era = (Emaxra - Eminra) yra + Eminra Erv = (Emaxrv - Eminrv) yrv + Eminrv Ela = (Emaxla - Eminla) yla + Eminla Elv = (Emaxlv - Eminlv) ylv + Eminlv \frac{d}{d t} (Faod) = \frac{Paodc - (Faod Raod) - Psap}{Laod} \frac{d}{d t} (Faop) = \frac{Paopc - (Faop Raop 16.66666666666667) - Paodc}{Laop} 0.059999999999999984 Fcorao = \frac{Pcoraoc - Pcoreac}{Rcorao} Fcorcap = \frac{Pcorcapc - Pcorsvc}{Rcorcap} Fcorea = \frac{Pcoreac - Pcorlac}{Rcorea} Fcorev = \frac{Pcorevc - Prac}{Rcorev} Fcorla = \frac{Pcorlac - Pcorsac}{Rcorla} Fcorlv = \frac{Pcorlvc - Pcorevc}{Rcorlv} Fcorsa = \frac{Pcorsac - Pcorcapc}{Rcorsa} Fcorsv = \frac{Pcorsvc - Pcorlvc}{Rcorsv} Fcrb = \frac{Paodc - Pvcc}{Rcrb} Fla = \{\begin{matrix} \frac{Plac - Plvc}{Rla} if Plac > Plvc \\ 0 otherwise \end{matrix} Flv = \{\begin{matrix} \frac{Plvc - Paopc}{Rav} if Plvc > Paopc \\ 0 otherwise \end{matrix} Fpa = \frac{Ppac - Ppcc}{Rpa} \frac{d}{d t} (Fpad) = \frac{Ppadc - Ppac - (Fpad Rpad)}{Lpad} \frac{d}{d t} (Fpap) = \frac{Ppapc - Ppadc - (Fpap Rpap 16.66666666666667)}{Lpa} 0.059999999999999984 Fpc = \frac{Ppcc - Ppvc}{Rpc} Fps = \frac{Ppac - Ppvc}{Rps} Fpv = \frac{Ppvc - Plac}{Rpv} Fra = \{\begin{matrix} \frac{Prac - Prvc}{Rra} if Prac > Prvc \\ 0 otherwise \end{matrix} Frv = \{\begin{matrix} \frac{Prvc - Ppapc}{Rpuv} if Prvc > Ppapc \\ 0 otherwise \end{matrix} Fsa = \frac{Psa - Psc}{Rsa} Fsap = \frac{Psap - Psa}{Rsap} Fsc = \frac{Psc - Psv}{Rsc} Fsv = \frac{Psv - Pvcc}{Rsv} Fvc = \frac{Pvcc - Prac}{Rvc} \frac{d}{d t} (MAP) = \frac{Psa - MAP}{COtau} P_QRSwave = \{\begin{matrix} 5 if t > beattime \land t < beattime + 0.02 \\ 10 if t > beattime + PRint \land t < beattime + PRint + 0.02 \\ 0 otherwise \end{matrix} Paod = Paodc - Pbs Paodc = \frac{((Rtaod Rcrb Faop - (Rtaod Rcrb Faod 0.059999999999999984)) + \frac{Vaod Rcrb}{Caod} 0.060000000000000005 - (\frac{Rcrb Px2}{ⅇ^{\frac{Vaod}{Vx8}} - 1} 0.059999999999999984)) + Pvcc Rtaod 0.059999999999999984}{Rcrb + Rtaod} 16.66666666666667 Paop = Paopc - Pplc \frac{d}{d t} (Paopc) = (Flv - (\frac{d}{d t} (Vaop)) - (Faop 16.66666666666667) - Fcorao) (\frac{1}{Ccorao} + \frac{\frac{Px2}{1} ⅇ^{\frac{Vcorao}{Vx1}}}{{(ⅇ^{\frac{Vcorao}{Vx1}} - 1)}^{2}}) Pcorao = Paop Pcoraoc = Paopc Pcorcap = \frac{Vcorcap}{Ccorcap} - (\frac{Px1 1}{ⅇ^{\frac{Vcorcap}{Vx1}} - 1}) Pcorcapc = Pcorcap + Pcorisfc Pcorea = \frac{Vcorea}{Ccorea} - (\frac{Px1 1}{ⅇ^{\frac{Vcorea}{Vx1}} - 1}) Pcoreac = Pcorea + Ppcdc Pcorev = \frac{Vcorev}{Ccorev} - (\frac{Px2 1}{ⅇ^{\frac{Vcorev}{Vx8}} - 1}) Pcorevc = Pcorev + Ppcdc Pcorisfc = | \frac{Plvc - Ppcdc}{2} | Pcorla = \frac{Vcorla}{Ccorla} - (\frac{Px1 1}{ⅇ^{\frac{Vcorla}{Vx1}} - 1}) Pcorlac = Pcorla + Pcorisfc Pcorlv = \frac{Vcorlv}{Ccorlv} - (\frac{Px1 1}{ⅇ^{\frac{Vcorlv}{Vx1}} - 1}) Pcorlvc = Pcorlv + Ppcdc Pcorsa = \frac{Vcorsa}{Ccorsa} - (\frac{Px1 1}{ⅇ^{\frac{Vcorsa}{Vx1}} - 1}) Pcorsac = Pcorsa + Pcorisfc Pcorsv = \frac{Vcorsv}{Ccorsv} - (\frac{Px1 1}{ⅇ^{\frac{Vcorsv}{Vx1}} - 1}) Pcorsvc = Pcorsv + Ppcdc Pla = (Vla - Vlar) Ela - (\frac{Px2 1}{ⅇ^{\frac{Vla}{Vx8}} - 1}) Plac = Pla + Ppcdc Plv = (Vlv - Vlvr) Elv - (\frac{Px2 1}{ⅇ^{\frac{Vlv}{Vx8}} - 1}) Plvc = Plv + Ppcdc Ppa = \frac{Vpa}{Cpa} - (\frac{Px2 1}{ⅇ^{\frac{Vpa}{Vx8}} - 1}) Ppac = Ppa + Pplc Ppad = Ppadc - Pplc Ppadc = \frac{d}{d t} (Vpad) Rtpad + Pplc + \frac{Vpad}{Ctpad} - (\frac{Px2 1}{ⅇ^{\frac{Vpad}{Vx8}} - 1}) Ppap = Ppapc - Pplc Ppapc1 = \frac{((\frac{Rpuv Vpap}{Ctpap} - (\frac{Rpuv Px2 1}{ⅇ^{\frac{Vpap}{Vx8}} - 1})) + Prvc Rtpap - (Rpuv Rtpap Fpap 16.666666666666668)) + Pplc Rpuv}{Rtpap + Rpuv} Ppapc2 = \frac{Vpap}{Ctpap} + Pplc - (Rtpap Fpap 16.666666666666668) - (\frac{Px2 1}{ⅇ^{\frac{Vpap}{Vx8}} - 1}) Ppapc = \{\begin{matrix} Ppapc1 if Prvc > Ppapc1 \\ Ppapc2 otherwise \end{matrix} Ppc = \frac{Vpc}{Cpc} - (\frac{Px2 1}{ⅇ^{\frac{Vpc}{Vx8}} - 1}) Ppcc = Ppc + Pplc Ppcd = K_pcd ⅇ^{\frac{Vpcd - Vpcd_o}{phi_pcd}} - (\frac{Px2 1}{ⅇ^{\frac{Vpcd}{Vx75}} - 1}) Ppcdc = Ppcd + Pplc Ppl = Pplc - Pbs Ppv = \frac{Vpv}{Cpv} - (\frac{Px2 1}{ⅇ^{\frac{Vpv}{Vx8}} - 1}) Ppvc = Ppv + Pplc Pra = (Vra - Vrar) Era - (\frac{Px2 1}{ⅇ^{\frac{Vra}{Vx8}} - 1}) Prac = Pra + Ppcdc Prv = (Vrv - Vrvr) Erv - (\frac{Px2 1}{ⅇ^{\frac{Vrv}{Vx8}} - 1}) Prvc = Prv + Ppcdc Psa_a = Kc \log_{10} (\frac{Vsa - Vsa_o}{Do} + 1) Psa = F_vaso Psa_a + (1 - F_vaso) Psa_p Psa_p = Kp1 ⅇ^{tau_p (Vsa - Vsa_o)} + Kp2 {(Vsa - Vsa_o)}^{2} Psap = \frac{Vsap}{Csap} - (\frac{Px2 1}{ⅇ^{\frac{Vsap}{Vx8}} - 1}) Psc = \frac{Vsc}{Csc} - (\frac{Px2 1}{ⅇ^{\frac{Vsc}{Vx8}} - 1}) Psv = Kv \log_{10} (\frac{Vmax_sv}{Vsv} - 0.99) (- 1) PulArtVol = Vpap + Vpad + Vpa PulVenVol = Vpv Pvc = \{\begin{matrix} D2 + K2 ⅇ^{\frac{Vo}{Vmin_vc}} + \frac{K1 (Vvc - Vo)}{1} - (\frac{Px2}{ⅇ^{\frac{Vvc}{Vx8}} - 1}) if Vvc > Vo \\ D2 + K2 ⅇ^{\frac{Vvc}{Vmin_vc}} - (\frac{Px2}{ⅇ^{\frac{Vvc}{Vx8}} - 1}) otherwise \end{matrix} Pvcc = Pvc + Pplc Rsa = Rsao + Kr ⅇ^{4 F_vaso} + Kr {(\frac{Vsa_max}{Vsa})}^{2} Rvc = KR {(\frac{Vmax_vc}{Vvc})}^{2} + Ro SV = \frac{COutput}{HR} 60 SysArtVol = Vaop + Vaod + Vsa + Vsap SysVenVol = Vsv + Vvc VBcirc = Vtot - perifl \frac{d}{d t} (Vaod) = (Faop - (Faod 0.059999999999999984) - (Fcrb 0.059999999999999984)) 16.66666666666667 \frac{d}{d t} (Vaop) = \frac{(Paopc - (\frac{Vaop}{Caop})) + \frac{Px2 1}{ⅇ^{\frac{Vaop}{Vx8}} - 1}}{Rtaop} \frac{d}{d t} (Vcorao) = Flv - (\frac{d}{d t} (Vaop)) - (Faop 16.66666666666667) - Fcorao \frac{d}{d t} (Vcorcap) = Fcorsa - Fcorcap Vcorcirc = Vcorao + Vcorea + Vcorla + Vcorsa + Vcorcap + Vcorsv + Vcorlv + Vcorev \frac{d}{d t} (Vcorea) = Fcorao - Fcorea \frac{d}{d t} (Vcorev) = Fcorlv - Fcorev \frac{d}{d t} (Vcorla) = Fcorea - Fcorla \frac{d}{d t} (Vcorlv) = Fcorsv - Fcorlv \frac{d}{d t} (Vcorsa) = Fcorla - Fcorsa \frac{d}{d t} (Vcorsv) = Fcorcap - Fcorsv \frac{d}{d t} (Vla) = Fpv - Fla Vlar = (1 - yla) (Vlard - Vlars) + Vlars \frac{d}{d t} (Vlv) = Fla - Flv Vlvr = (1 - ylv) (Vlvrd - Vlvrs) + Vlvrs \frac{d}{d t} (Vpa) = Fpad - Fps - Fpa \frac{d}{d t} (Vpad) = (Fpap - (Fpad 0.059999999999999984)) 16.66666666666667 \frac{d}{d t} (Vpap) = Frv - (Fpap 16.66666666666667) \frac{d}{d t} (Vpc) = Fpa - Fpc Vpcd = Vrv + Vra + Vlv + Vla + perifl + Vmyo + Vcorcirc \frac{d}{d t} (Vpv) = Fpc + Fps - Fpv \frac{d}{d t} (Vra) = (Fvc - Fra) + Fcorev Vrar = (1 - yra) (Vrard - Vrars) + Vrars \frac{d}{d t} (Vrv) = Fra - Frv Vrvr = (1 - yrv) (Vrvrd - Vrvrs) + Vrvrs \frac{d}{d t} (Vsa) = Fsap - Fsa \frac{d}{d t} (Vsap) = Faod - Fsap \frac{d}{d t} (Vsc) = Fsa - Fsc \frac{d}{d t} (Vsv) = Fsc - Fsv Vtot = Vra + Vrv + Vpap + Vpad + Vpa + Vpc + Vpv + Vla + Vlv + Vaop + Vaod + Vsa + Vsap + Vsc + Vsv + Vvc + perifl + Vcorcirc \frac{d}{d t} (Vvc) = Fsv + Fcrb - Fvc