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Model Mathematics

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Component: environment

Component: ATbl

\frac{d}{d time} (ATbl) = Qb (CTbf - CTblf) + Qp (CTpf - CTbl) + Ql (CTlf - CTbl) + Qt (1.0 - ts) (CTtv - CTblf) + k2T

Component: ADbl

\frac{d}{d time} (ADbl) = Qbt (CDbf - CDblf) + Qp (CDpf - CDblf) + Ql (CDlf - CDbl)

Component: CT_A

\frac{d}{d time} (CT_A) = kTA_on CTblf CAf - (kTA_off CT_A)

Component: CD_A

\frac{d}{d time} (CD_A) = kDA_on CDblf CAf - (kDA_off CD_A)

Component: CTblf

CTblf = CTbl - CT_A

Component: CDblf

CDblf = CDbl - CD_A

Component: CAf

CAf = CA - (CT_A + CD_A)

Component: ATl

\frac{d}{d time} (ATl) = Ql (CTbl - CTlf) - (\frac{Vmax1 CTlf}{km5alpha + CTlf} + k1T \frac{ATl}{PTl})

Component: ADl

\frac{d}{d time} (ADl) = Ql (CDbl - CDlf) - (\frac{Vmax1 CTlf}{km5alpha + CTlf} + k1D \frac{ADl}{PDl})

Component: CTlf

CTlf = \frac{CTl}{PTl}

Component: CDlf

CDlf = \frac{CDl}{PDl}

Component: ATif

\frac{d}{d time} (ATif) = Qt (1.0 - ts) (CTblf - (\frac{CTif}{PTif})) + mu (\frac{CTst}{PTst} - CTif) + k1T CLH

Component: ATst

\frac{d}{d time} (ATst) = mu (CTif - (\frac{CTst}{PTst}))

Component: CTtv

CTtv = \frac{CTif}{PTif}

Component: ATp

\frac{d}{d time} (ATp) = Qp (CTbl - CTpf) - (\frac{Vmax0 CTpf}{km5alpha + CTpf})

Component: ADp

\frac{d}{d time} (ADp) = Qp (CDbl - CDpf) - (\frac{Vmax0 CTpf}{km5alpha + CTpf})

Component: CT_R

\frac{d}{d time} (CT_R) = kTR_on CTpf CRf - (kTR_off CT_R)

Component: CD_R

\frac{d}{d time} (CD_R) = kDR_on CDpf CRf - (kDR_off CD_R)

Component: CDT

\frac{d}{d time} (CDT) = kDT_on CD_R CT_R - (kDT_off CDT)

Component: CDD

\frac{d}{d time} (CDD) = kDD_on {CD_R}^{2.0} - (kDD_off CDD)

Component: CTT

\frac{d}{d time} (CTT) = kTT_on {CT_R}^{2.0} - (kTT_off CTT)

Component: CDD5a

\frac{d}{d time} (CDD5a) = kDNA_onDD5a CDD CDNA5af - (kDNA_offDD5a CDD5a)

Component: CDDcd

\frac{d}{d time} (CDDcd) = kDNA_onDDcd CDD CDNAcdf - (kDNA_offDDcd CDDcd)

Component: CDDsec

\frac{d}{d time} (CDDsec) = kDNA_onDDsec CDD CDNAsecf - (kDNA_offDDsec CDDsec)

Component: CDDcp

\frac{d}{d time} (CDDcp) = kDNA_onDDcp CDD CDNAcpf - (kDNA_offDDcp CDDcp)

Component: CDT5a

\frac{d}{d time} (CDT5a) = kDNA_onDT5a CDT CDNA5af - (kDNA_offDT5a CDT5a)

Component: CDTcd

\frac{d}{d time} (CDTcd) = kDNA_onDTcd CDT CDNAcdf - (kDNA_offDTcd CDTcd)

Component: CDTsec

\frac{d}{d time} (CDTsec) = kDNA_onDTsec CDT CDNAsecf - (kDNA_offDTsec CDTsec)

Component: CDTcp

\frac{d}{d time} (CDTcp) = kDNA_onDTcp CDT CDNAcpf - (kDNA_offDTcp CDTcp)

Component: CTT5a

\frac{d}{d time} (CTT5a) = kDNA_onTT5a CTT CDNA5af - (kDNA_offTT5a CTT5a)

Component: CTTcd

\frac{d}{d time} (CTTcd) = kDNA_onTTcd CTT CDNAcdf - (kDNA_offTTcd CTTcd)

Component: CTTsec

\frac{d}{d time} (CTTsec) = kDNA_onTTsec CTT CDNAsecf - (kDNA_offTTsec CTTsec)

Component: CTTcp

\frac{d}{d time} (CTTcp) = kDNA_onTTcp CTT CDNAcpf - (kDNA_offTTcp CTTcp)

Component: CTpf

CTpf = \frac{CTp - (CT_R + 2.0 CTT + CDT + T)}{1.0 + NTp} T = CTTsec + CDTsec + CTT5a + CDT5a + CTTcd + CDTcd + CTTcp + CDTcp

Component: CDpf

CDpf = \frac{CDp - (CD_R + 2.0 CDD + CDT + D)}{1.0 + NDp} D = CDDsec + CDTsec + CDD5a + CDT5a + CDDcd + CDTcd + CDDcp + CDTcp

Component: CRf

CRf = CR - (CT_R + CD_R + 2.0 (CTT + CDD + CDT) + 2.0 (CDNAcdf + CDNAsecf + CDNAcpf + CDNA5af))

Component: CDNAcdf

CDNAcdf = CDNAcd - (CTTcd + CDDcd + CDTcd)

Component: CDNAsecf

CDNAsecf = CDNAsec - (CTTsec + CDDsec + CDTsec)

Component: CDNA5af

CDNA5af = CDNA5a - (CTT5a + CDD5a + CDT5a)

Component: CDNAcpf

CDNAcpf = CDNAcp - (CTTcp + CDDcp + CDTcp)

Component: DNAocp

DNAocp = \frac{CTTcp + CDDcp + CDTcp}{CDNAcp}

Component: DNAosec

DNAosec = \frac{CTTsec + CDDsec + CDTsec}{CDNAsec}

Component: DNAocd

DNAocd = \frac{CTTcd + CDDcd + CDTcd}{CDNAcd}

Component: DNAo5a

DNAo5a = \frac{CTT5a + CDD5a + CDT5a}{CDNA5a}

Component: ATb

\frac{d}{d time} (ATb) = Qb (CTblf - (\frac{CTb}{PTb}))

Component: ADb

\frac{d}{d time} (ADb) = Qbt (CDblf - (\frac{CDb}{PDb}))

Component: ALH

A = (- kLH1) (alpha_T CTblf + alpha_D CDblf) + kLH2 B = kLH3 \frac{d}{d time} (ALH) = \{\begin{matrix} A - (kLH4 ALH) if A > B \\ B - (kLH4 ALH) otherwise \end{matrix}

Component: AR

\frac{d}{d time} (AR) = k1R - (keR CRf)

Component: CR

CR = \frac{AR}{Vp}

Component: Qp

Qp = kQp Vpc Vpc = VPC1 + VPC2

Component: Vmax

Vmax = k5a DNAo5a

Component: VPC1

\frac{d}{d time} (VPC1) = \frac{VPC1}{VPC1b} kcpl DNAocp - (kcd1 (1.0 - DNAocd) VPC1)

Component: VPL1

\frac{d}{d time} (VPL1) = \frac{VPC1}{VPC1b} ksec DNAosec - (kflo VPL1)

Component: Vp

Vp = VPC1 + VPC2 + VPL1 + VPL2

Component: model_parameters

Qb = Qc - (Qp + Qt + Ql) Qbt = Qc - (Qp + Ql) CTbf = \frac{CTb}{PTb} CDbf = \frac{CDb}{PDb}

Source: Derived from workspace Potter, Zager, Barton, 2006 at changeset 941e8c510816.

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Mathematical model for the androgenic regulation of the prostate in intact and castrated adult male rats.