From 922e610c4d767fe5d434e3b345892bf29f96d905 Mon Sep 17 00:00:00 2001 From: aarsh <144159115+Aarshpatel12@users.noreply.github.com> Date: Sat, 24 Jan 2026 17:25:43 +0530 Subject: [PATCH] Fix: Add missing anchors to Section M (Fixes #42) --- docs/perfusionModels.md | 56 ++++++++++++++++++++--------------------- 1 file changed, 28 insertions(+), 28 deletions(-) diff --git a/docs/perfusionModels.md b/docs/perfusionModels.md index 638de5eb..762fe9e2 100644 --- a/docs/perfusionModels.md +++ b/docs/perfusionModels.md @@ -74,15 +74,15 @@ Non-zero exchange for the restricted ones | Code | OSIPI name | Alternative names | Notation |Description | Reference | | -- | -- | -- | -- | -- | -- | -| M.SM6.001 | DSC Multi-echo (GE) model | -- | -- | This forward model is given by the following equation:
$S=S_{DCE,FXL}(R_1)e^{-TE\cdot R_2^*}$
where $S_{DCE,FXL}$($R_1$) is a forward model selected from [Magnitude models: DCE- R1 in fast water exchange limit](perfusionModels.md#Magnitude models: DCE - R1 in the fast water exchange limit),
[TE (Q.MS1.005)](quantities.md#TE){:target="_blank"},
[R2* (Q.EL1.007)](quantities.md#R2Star){:target="_blank"},
[S (Q.MS1.001)](quantities.md#S){:target="_blank"} | -- | -| M.SM6.002 | DSC Multi-echo (SE) model | -- | -- | This forward model is given by the following equation:
$S=S_{DCE,FXL}(R_1)e^{-TE\cdot R_2}$
where $S_{DCE,FXL}$($R_1$) is a forward model selected from [Magnitude models: DCE- R1 in fast water exchange limit](perfusionModels.md#Magnitude models: DCE - R1 in the fast water exchange limit),
[TE (Q.MS1.005)](quantities.md#TE){:target="_blank"},
[R2 (Q.EL1.004)](quantities.md#R2){:target="_blank"},
[S (Q.MS1.001)](quantities.md#S){:target="_blank"} | -- | +| M.SM6.001 | DSC Multi-echo (GE) model | -- | -- | This forward model is given by the following equation:
$S=S_{DCE,FXL}(R_1)e^{-TE\cdot R_2^*}$
where $S_{DCE,FXL}$($R_1$) is a forward model selected from [Magnitude models: DCE- R1 in fast water exchange limit](perfusionModels.md#Magnitude models: DCE - R1 in the fast water exchange limit),
[TE (Q.MS1.005)](quantities.md#TE){:target="_blank"},
[R2* (Q.EL1.007)](quantities.md#R2Star){:target="_blank"},
[S (Q.MS1.001)](quantities.md#S){:target="_blank"} | -- | +| M.SM6.002 | DSC Multi-echo (SE) model | -- | -- | This forward model is given by the following equation:
$S=S_{DCE,FXL}(R_1)e^{-TE\cdot R_2}$
where $S_{DCE,FXL}$($R_1$) is a forward model selected from [Magnitude models: DCE- R1 in fast water exchange limit](perfusionModels.md#Magnitude models: DCE - R1 in the fast water exchange limit),
[TE (Q.MS1.005)](quantities.md#TE){:target="_blank"},
[R2 (Q.EL1.004)](quantities.md#R2){:target="_blank"},
[S (Q.MS1.001)](quantities.md#S){:target="_blank"} | -- | | M.SM6.999 | Model not listed | -- | -- | This is a custom free-text item, which can be used if a model of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage. | -- | ### Phase models: DSC | Code | OSIPI name| Alternative names|Notation|Description|Reference| | -- | -- | -- | -- | -- | -- | -| M.SM7.001 | Linear susceptibility signal model | -- | -- | This forward model is given by the following equation:
$S=k\cdot \chi$,
with
[k (Q.GE1.009)](quantities.md#const){:target="_blank"},
[$\chi$ (Q.EL1.011)](quantities.md#Chi){:target="_blank"},
[S (Q.MS1.001)](quantities.md#S){:target="_blank"}. | -- | +| M.SM7.001 | Linear susceptibility signal model | -- | -- | This forward model is given by the following equation:
$S=k\cdot \chi$,
with
[k (Q.GE1.009)](quantities.md#const){:target="_blank"},
[$\chi$ (Q.EL1.011)](quantities.md#Chi){:target="_blank"},
[S (Q.MS1.001)](quantities.md#S){:target="_blank"}. | -- | | M.SM7.999 | Model not listed | -- | -- | This is a custom free-text item, which can be used if a model of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage. | -- | @@ -93,12 +93,12 @@ This section covers models that describe how electromagnetic properties (EP), su | Code | OSIPI name| Alternative names|Notation|Description|Reference| | -- | -- | -- | -- | -- | -- | -| M.EL1.001 | Transverse relaxation rate (GE), linear with relaxivity model | Effective relaxation rate (GE), linear with relaxivity model | -- | This forward model is given by the following equation:
$R_2^*=R_{20}^*+r_2^*\cdot C$
with
[R20* (Q.EL1.008)](quantities.md#R2Star0){:target="_blank"},
[r2* (Q.EL1.017)](quantities.md#r2star){:target="_blank"},
[C (Q.IC1.001)](quantities.md#C){:target="_blank"},
[R2* (Q.EL1.007)](quantities.md#R2Star){:target="_blank"} | (Rosen et al. 1990) | -| M.EL1.002 | Transverse relaxation rate (SE), linear with relaxivity model | Natural relaxation rate (GE), linear with relaxivity model | -- | This forward model is given by the following equation:
$R_2=R_{20}+r_2\cdot C$
with
[R20 (Q.EL1.005)](quantities.md#R20){:target="_blank"},
[r2 (Q.EL1.016)](quantities.md#r2){:target="_blank"},
[C (Q.IC1.001)](quantities.md#C){:target="_blank"},
[R2 (Q.EL1.004)](quantities.md#R2){:target="_blank"} | (Rosen et al. 1990) | -| M.EL1.003 | Longitudinal relaxation rate, linear with relaxivity model | -- | -- | This forward model is given by the following equation:
$R_1=R_{10}+r_1\cdot C$
with
[R10 (Q.EL1.002)](quantities.md#R10){:target="_blank"},
[r1 (Q.EL1.015)](quantities.md#r1){:target="_blank"},
[C (Q.IC1.001)](quantities.md#C){:target="_blank"},
[R1 (Q.EL1.001)](quantities.md#R1){:target="_blank"} | (Rosen et al. 1990) | -| M.EL1.004 | Transverse relaxation rate (GE) with gradient leakage correction model | -- | -- | This forward model is given by the following equation:
$R_2^*=R_{20}^*+r_{2v}^*\left\| C_p-C_e \right\| +r_{2e}^*C_e,$
with
[$R_{20}^*$ (Q.EL1.008)](quantities.md#R2Star0){:target="_blank"},
[$C_p$ (Q.IC1.001.p)](quantities.md#C){:target="_blank"},
[$C_e$ (Q.IC1.001.e)](quantities.md#C){:target="_blank"},
[$r_{2e}^*$ (Q.EL1.017.e)](quantities.md#r2star){:target="_blank"},
[$r_{2v}^*$ (Q.EL1.017.v)](quantities.md#r2star){:target="_blank"},
[$R_2^*$(Q.EL1.007)](quantities.md#R2Star){:target="_blank"} | Sourbron et al 2012 | -| M.EL1.005 | Transverse relaxation rate (GE), quadratic model | -- | -- | This forward model is given by the following equation:
$R_2^*=R_{20}^*+k_1\cdot C_p+k_2C_p^2$
with
[$R_{20}^*$ (Q.EL1.008)](quantities.md#R2Star0){:target="_blank"},
[$C_p$ (Q.IC1.001.p)](quantities.md#C){:target="_blank"},
[[$k_1$,$k_2$] (Q.EL1.020)](quantities.md#k1k2){:target="_blank"},
[$R_2^*$ (Q.EL1.007)](quantities.md#R2Star){:target="_blank"} | Van Osch 2003 (also see Calamante 2013) | -| M.EL1.006 | Linear susceptibility concentration model | -- | -- | This forward model is given by the following equation:
$\chi=\chi_0+\delta\chi\cdot C$
with
[$\chi_0$ (Q.EL1.012)](quantities.md#Chi0){:target="_blank"},
[$\delta\chi$ (Q.EL1.013)](quantities.md#DeltaChi){:target="_blank"},
[$C$ (Q.IC1.001)](quantities.md#C){:target="_blank"},
[$\chi$ (Q.EL1.011)](quantities.md#Chi){:target="_blank"} | (Conturo et al. 1992) | +| M.EL1.001 | Transverse relaxation rate (GE), linear with relaxivity model | Effective relaxation rate (GE), linear with relaxivity model | -- | This forward model is given by the following equation:
$R_2^*=R_{20}^*+r_2^*\cdot C$
with
[R20* (Q.EL1.008)](quantities.md#R2Star0){:target="_blank"},
[r2* (Q.EL1.017)](quantities.md#r2star){:target="_blank"},
[C (Q.IC1.001)](quantities.md#C){:target="_blank"},
[R2* (Q.EL1.007)](quantities.md#R2Star){:target="_blank"} | (Rosen et al. 1990) | +| M.EL1.002 | Transverse relaxation rate (SE), linear with relaxivity model | Natural relaxation rate (GE), linear with relaxivity model | -- | This forward model is given by the following equation:
$R_2=R_{20}+r_2\cdot C$
with
[R20 (Q.EL1.005)](quantities.md#R20){:target="_blank"},
[r2 (Q.EL1.016)](quantities.md#r2){:target="_blank"},
[C (Q.IC1.001)](quantities.md#C){:target="_blank"},
[R2 (Q.EL1.004)](quantities.md#R2){:target="_blank"} | (Rosen et al. 1990) | +| M.EL1.003 | Longitudinal relaxation rate, linear with relaxivity model | -- | -- | This forward model is given by the following equation:
$R_1=R_{10}+r_1\cdot C$
with
[R10 (Q.EL1.002)](quantities.md#R10){:target="_blank"},
[r1 (Q.EL1.015)](quantities.md#r1){:target="_blank"},
[C (Q.IC1.001)](quantities.md#C){:target="_blank"},
[R1 (Q.EL1.001)](quantities.md#R1){:target="_blank"} | (Rosen et al. 1990) | +| M.EL1.004 | Transverse relaxation rate (GE) with gradient leakage correction model | -- | -- | This forward model is given by the following equation:
$R_2^*=R_{20}^*+r_{2v}^*\left\| C_p-C_e \right\| +r_{2e}^*C_e,$
with
[$R_{20}^*$ (Q.EL1.008)](quantities.md#R2Star0){:target="_blank"},
[$C_p$ (Q.IC1.001.p)](quantities.md#C){:target="_blank"},
[$C_e$ (Q.IC1.001.e)](quantities.md#C){:target="_blank"},
[$r_{2e}^*$ (Q.EL1.017.e)](quantities.md#r2star){:target="_blank"},
[$r_{2v}^*$ (Q.EL1.017.v)](quantities.md#r2star){:target="_blank"},
[$R_2^*$(Q.EL1.007)](quantities.md#R2Star){:target="_blank"} | Sourbron et al 2012 | +| M.EL1.005 | Transverse relaxation rate (GE), quadratic model | -- | -- | This forward model is given by the following equation:
$R_2^*=R_{20}^*+k_1\cdot C_p+k_2C_p^2$
with
[$R_{20}^*$ (Q.EL1.008)](quantities.md#R2Star0){:target="_blank"},
[$C_p$ (Q.IC1.001.p)](quantities.md#C){:target="_blank"},
[[$k_1$,$k_2$] (Q.EL1.020)](quantities.md#k1k2){:target="_blank"},
[$R_2^*$ (Q.EL1.007)](quantities.md#R2Star){:target="_blank"} | Van Osch 2003 (also see Calamante 2013) | +| M.EL1.006 | Linear susceptibility concentration model | -- | -- | This forward model is given by the following equation:
$\chi=\chi_0+\delta\chi\cdot C$
with
[$\chi_0$ (Q.EL1.012)](quantities.md#Chi0){:target="_blank"},
[$\delta\chi$ (Q.EL1.013)](quantities.md#DeltaChi){:target="_blank"},
[$C$ (Q.IC1.001)](quantities.md#C){:target="_blank"},
[$\chi$ (Q.EL1.011)](quantities.md#Chi){:target="_blank"} | (Conturo et al. 1992) | | M.EL1.999 | Model not listed | -- | -- | This is a custom free-text item, which can be used if a model of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage. | -- | @@ -159,8 +159,8 @@ but at the same time cannot be derived as a composition of kinetic models, elect | Code | OSIPI name| Alternative names|Notation|Description|Reference| | -- | -- | -- | -- | -- | -- | -| M.LC1.001 | Boxerman-Schmainda-Weisskoff (BSW) leakage correction model | -- | BSW leakage correction model | This forward model is given by the following equation:
$R_2^*(t)=R_{20}^*+K_1\overline{\Delta R_{2,ref}^*(t)}-K_2\int_0^t \overline{\Delta R_{2,ref}^*(t')dt'},$
with
[[$\overline{\Delta R_{2,ref}^*}$(Q.EL1.010)](quantities.md#R2ref){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}]
[$R_{20}^*$ (Q.EL1.008)](quantities.md#R2Star0){:target="_blank"},
[$K_1$ (Q.LC1.001)](quantities.md#K1){:target="_blank"},
[$K_2$ (Q.LC1.002)](quantities.md#K2){:target="_blank"},
[[$R_2^*$ (Q.EL1.007)](quantities.md#R2Star){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}] | -- | -| M.LC1.002 |Bidirectional leakage correction model | -- | -- | This forward model is given by the following equation:
$R_2^*(t)=R_{20}^*+K_1\overline{\Delta R_{2,ref}^*(t)}$
    $-K_2\int_0^t \overline{\Delta R_{2,ref}^*(t')}\cdot e^{-k_{e->p}(t-t')}dt',$
with
[[$\overline{\Delta R_{2,ref}^*}$(Q.EL1.010)](quantities.md#R2ref){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}]
[$R_{20}^*$ (Q.EL1.008)](quantities.md#R2Star0){:target="_blank"},
[$K_1$ (Q.LC1.001)](quantities.md#K1){:target="_blank"},
[$K_2$ (Q.LC1.002)](quantities.md#K2){:target="_blank"},
[$k_{e->p}$ (Q.PH1.009.e->p)](quantities.md#k){:target="_blank"}
[[$R_2^*$ (Q.EL1.007)](quantities.md#R2Star){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}] | -- | +| M.LC1.001 | Boxerman-Schmainda-Weisskoff (BSW) leakage correction model | -- | BSW leakage correction model | This forward model is given by the following equation:
$R_2^*(t)=R_{20}^*+K_1\overline{\Delta R_{2,ref}^*(t)}-K_2\int_0^t \overline{\Delta R_{2,ref}^*(t')dt'},$
with
[[$\overline{\Delta R_{2,ref}^*}$(Q.EL1.010)](quantities.md#R2ref){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}]
[$R_{20}^*$ (Q.EL1.008)](quantities.md#R2Star0){:target="_blank"},
[$K_1$ (Q.LC1.001)](quantities.md#K1){:target="_blank"},
[$K_2$ (Q.LC1.002)](quantities.md#K2){:target="_blank"},
[[$R_2^*$ (Q.EL1.007)](quantities.md#R2Star){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}] | -- | +| M.LC1.002 | Bidirectional leakage correction model | -- | -- | This forward model is given by the following equation:
$R_2^*(t)=R_{20}^*+K_1\overline{\Delta R_{2,ref}^*(t)}$
    $-K_2\int_0^t \overline{\Delta R_{2,ref}^*(t')}\cdot e^{-k_{e->p}(t-t')}dt',$
with
[[$\overline{\Delta R_{2,ref}^*}$(Q.EL1.010)](quantities.md#R2ref){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}]
[$R_{20}^*$ (Q.EL1.008)](quantities.md#R2Star0){:target="_blank"},
[$K_1$ (Q.LC1.001)](quantities.md#K1){:target="_blank"},
[$K_2$ (Q.LC1.002)](quantities.md#K2){:target="_blank"},
[$k_{e->p}$ (Q.PH1.009.e->p)](quantities.md#k){:target="_blank"}
[[$R_2^*$ (Q.EL1.007)](quantities.md#R2Star){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}] | -- | | M.LC1.999 | Model not listed | -- | -- | This is a custom free-text item, which can be used if a model of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage. | -- | @@ -172,29 +172,29 @@ This group is divided into the derivation of scalar quantities and the derivatio | Code | OSIPI name| Alternative names|Notation|Description|Reference| | -- | -- | -- | -- | -- | -- | -| M.ID1.001 | Central volume theorem | -- | CVT |This forward model is given by the following equation:
$v_p=MTT\cdot F_p$
with
[MTT (Q.PH1.006)](quantities.md#MTT){:target="_blank"},
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"},
[$v_p$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"} | -- | -| M.ID1.002 | Total volume of distribution | -- | -- | This forward model is given by the following equation:
$v=v_p+v_e+v_i$
with
[$v_p$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"},
[$v_e$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"},
[$v_i$ (Q.PH1.001.i)](quantities.md#v){:target="_blank"},
[$v$ (Q.PH1.001)](quantities.md#v){:target="_blank"} | -- | -| M.ID1.003 | Blood vs plasma volume fraction | -- | -- | This forward model is given by the following equation:
$v_b=\frac{v_p}{(1-Hct)}$
with
[$v_p$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"},
[$Hct$ (Q.PH1.012)](quantities.md#Hct){:target="_blank"},
[$v_b$ (Q.PH1.001.b)](quantities.md#v){:target="_blank"}. | -- | -| M.ID1.004 | Blood vs plasma flow | -- | -- | This forward model is given by the following equation:
$F_b=\frac{F_p}{(1-Hct)}$
with
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"},
[$Hct$ (Q.PH1.012)](quantities.md#Hct){:target="_blank"},
[$F_b$ (Q.PH1.003)](quantities.md#Fb){:target="_blank"}| -- | -| M.ID1.005 | Blood vs plasma AIF | -- | -- | This forward model is given by the following equation:
$C_{a,b}(t)=C_{a,p}(t)\cdot(1-Hct_a)$,
with
[[$C_{a,p}$ (Q.IC1.001.a,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_{a,b}$ (Q.IC1.001.a,b)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$Hct_a$ (Q.PH1.012.a)](quantities.md#Hct){:target="_blank"} | -- | -| M.ID1.006 | Small vessel hematocrit correction | -- | -- | This forward model is given by the following equation:
$Hct_f=\frac{1-Hct_a}{1-Hct_t}$
with
[$Hct_a$ (Q.PH1.012.a)](quantities.md#Hct){:target="_blank"},
[$Hct_t$ (Q.PH1.012.t)](quantities.md#Hct){:target="_blank"},
[$Hct_f$ (Q.PH1.013)](quantities.md#Hctf){:target="_blank"}| -- | -| M.ID1.007 | Compartment extraction fraction | -- | -- | This forward model is given by the following equation:
$E=\frac{PS}{F_p+PS}$
with
[$PS$ (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"},
[$E$ (Q.PH1.005)](quantities.md#E){:target="_blank"}| -- | -| M.ID1.008 | Plug flow extraction fraction | -- | -- | This forward model is given by the following equation:
$E=1-e^{-\frac{PS}{F_p}}$
with
[$PS$ (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"},
[$E$ (Q.PH1.005)](quantities.md#E){:target="_blank"} | -- | -| M.ID1.009 | Plasma MTT identity | -- | -- | This forward model is given by the following equation:
$MTT_p=\frac{v_p}{F_p+PS}$
with
[$v_p$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"},
[$PS$ (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"},
[$MTT_p$ (Q.PH1.006.p)](quantities.md#MTT){:target="_blank"} | -- | -| M.ID1.010 | Interstitial MTT identity | -- | -- | This forward model is given by the following equation:
$MTT_e=\frac{v_e}{PS}$
with
[$v_e$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"},
[$PS$ (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$MTT_e$ (Q.PH1.006.e)](quantities.md#MTT){:target="_blank"} | -- | -| M.ID1.011 | $K^{trans}$ identity | -- | -- | This forward model is given by the following equation:
$K^{trans}=E\cdot F_p$,
with
[E (Q.PH1.005)](quantities.md#E){:target="_blank"},
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"},
[$K^{trans}$ (Q.PH1.008)](quantities.md#Ktrans){:target="_blank"} | -- | -| M.ID1.012 | $k_{ep}$ identity | -- | -- | This forward model is given by the following equation:
$k_{ep}=\frac{K^{trans}}{v_e}$,
[$K^{trans}$ (Q.PH1.008)](quantities.md#Ktrans){:target="_blank"},
[$v_e$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"},
[$k_{e->p}$ (Q.PH1.009.e->p)](quantities.md#k){:target="_blank"} | -- | +| M.ID1.001 | Central volume theorem | -- | CVT |This forward model is given by the following equation:
$v_p=MTT\cdot F_p$
with
[MTT (Q.PH1.006)](quantities.md#MTT){:target="_blank"},
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"},
[$v_p$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"} | -- | +| M.ID1.002 | Total volume of distribution | -- | -- | This forward model is given by the following equation:
$v=v_p+v_e+v_i$
with
[$v_p$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"},
[$v_e$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"},
[$v_i$ (Q.PH1.001.i)](quantities.md#v){:target="_blank"},
[$v$ (Q.PH1.001)](quantities.md#v){:target="_blank"} | -- | +| M.ID1.003 | Blood vs plasma volume fraction | -- | -- | This forward model is given by the following equation:
$v_b=\frac{v_p}{(1-Hct)}$
with
[$v_p$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"},
[$Hct$ (Q.PH1.012)](quantities.md#Hct){:target="_blank"},
[$v_b$ (Q.PH1.001.b)](quantities.md#v){:target="_blank"}. | -- | +| M.ID1.004 | Blood vs plasma flow | -- | -- | This forward model is given by the following equation:
$F_b=\frac{F_p}{(1-Hct)}$
with
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"},
[$Hct$ (Q.PH1.012)](quantities.md#Hct){:target="_blank"},
[$F_b$ (Q.PH1.003)](quantities.md#Fb){:target="_blank"}| -- | +| M.ID1.005 | Blood vs plasma AIF | -- | -- | This forward model is given by the following equation:
$C_{a,b}(t)=C_{a,p}(t)\cdot(1-Hct_a)$,
with
[[$C_{a,p}$ (Q.IC1.001.a,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_{a,b}$ (Q.IC1.001.a,b)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$Hct_a$ (Q.PH1.012.a)](quantities.md#Hct){:target="_blank"} | -- | +| M.ID1.006 | Small vessel hematocrit correction | -- | -- | This forward model is given by the following equation:
$Hct_f=\frac{1-Hct_a}{1-Hct_t}$
with
[$Hct_a$ (Q.PH1.012.a)](quantities.md#Hct){:target="_blank"},
[$Hct_t$ (Q.PH1.012.t)](quantities.md#Hct){:target="_blank"},
[$Hct_f$ (Q.PH1.013)](quantities.md#Hctf){:target="_blank"}| -- | +| M.ID1.007 | Compartment extraction fraction | -- | -- | This forward model is given by the following equation:
$E=\frac{PS}{F_p+PS}$
with
[$PS$ (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"},
[$E$ (Q.PH1.005)](quantities.md#E){:target="_blank"}| -- | +| M.ID1.008 | Plug flow extraction fraction | -- | -- | This forward model is given by the following equation:
$E=1-e^{-\frac{PS}{F_p}}$
with
[$PS$ (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"},
[$E$ (Q.PH1.005)](quantities.md#E){:target="_blank"} | -- | +| M.ID1.009 | Plasma MTT identity | -- | -- | This forward model is given by the following equation:
$MTT_p=\frac{v_p}{F_p+PS}$
with
[$v_p$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"},
[$PS$ (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"},
[$MTT_p$ (Q.PH1.006.p)](quantities.md#MTT){:target="_blank"} | -- | +| M.ID1.010 | Interstitial MTT identity | -- | -- | This forward model is given by the following equation:
$MTT_e=\frac{v_e}{PS}$
with
[$v_e$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"},
[$PS$ (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$MTT_e$ (Q.PH1.006.e)](quantities.md#MTT){:target="_blank"} | -- | +| M.ID1.011 | $K^{trans}$ identity | -- | -- | This forward model is given by the following equation:
$K^{trans}=E\cdot F_p$,
with
[E (Q.PH1.005)](quantities.md#E){:target="_blank"},
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"},
[$K^{trans}$ (Q.PH1.008)](quantities.md#Ktrans){:target="_blank"} | -- | +| M.ID1.012 | $k_{ep}$ identity | -- | -- | This forward model is given by the following equation:
$k_{ep}=\frac{K^{trans}}{v_e}$,
[$K^{trans}$ (Q.PH1.008)](quantities.md#Ktrans){:target="_blank"},
[$v_e$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"},
[$k_{e->p}$ (Q.PH1.009.e->p)](quantities.md#k){:target="_blank"} | -- | | M.ID1.999 | Model not listed | -- | -- | This is a custom free-text item, which can be used if a model of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage. | -- | ### Scalars derived from dynamic curves | Code | OSIPI name| Alternative names|Notation|Description|Reference| | -- | -- | -- | -- | -- | -- | -| M.ID2.001 | Bolus delay identity | -- | -- | This forward model is given by the following equation:
$MTT_a=\int_{0}^{\infty}h_a(t)dt$
with
[ [$h_a$ (Q.IC1.004)](quantities.md#ha){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$MTT_a$ (Q.PH1.006.a)](quantities.md#MTT){:target="_blank"} | -- | -| M.ID2.002 | Tissue mean transit time identity | -- | -- | This forward model is given by the following equation:
$MTT_t=\int_{0}^{\infty}R(t)dt$
with
[ [$R$ (Q.IC1.002)](quantities.md#R){:target="_blank"},
[$t$ (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$MTT_t$ (Q.PH1.006.t)](quantities.md#MTT){:target="_blank"} | -- | -| M.ID2.003 | Blood plasma flow from maximum | -- | -- | This forward model is given by the following equation:
$F_p=max(I(t))$
with
[ [$I$ (Q.IC1.005)](quantities.md#IRF){:target="_blank"}, [$t$ (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"} | -- | -| M.ID2.004 | Blood plasma flow from first time frame | -- | -- | This forward model is given by the following equation:
$F_p=I(0)$
with
[ [$I$ (Q.IC1.005)](quantities.md#IRF){:target="_blank"}, [$t$ (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"} | -- | -| M.ID2.005 | Capillary transit time heterogeneity identity | -- | -- | This forward model is given by the following equation:
$CTTH=\int_{0}^{\infty}\sqrt{(t-MTT)^2}h(t)dt$
with
[[$h$ (Q.IC1.003)](quantities.md#h){:target="_blank"}, [$t$ (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$MTT$ (Q.PH1.006)](quantities.md#MTT){:target="_blank"},
[$CTTH$ (Q.PH1.014)](quantities.md#CTTH){:target="_blank"} | -- | +| M.ID2.001 | Bolus delay identity | -- | -- | This forward model is given by the following equation:
$MTT_a=\int_{0}^{\infty}h_a(t)dt$
with
[ [$h_a$ (Q.IC1.004)](quantities.md#ha){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$MTT_a$ (Q.PH1.006.a)](quantities.md#MTT){:target="_blank"} | -- | +| M.ID2.002 | Tissue mean transit time identity | -- | -- | This forward model is given by the following equation:
$MTT_t=\int_{0}^{\infty}R(t)dt$
with
[ [$R$ (Q.IC1.002)](quantities.md#R){:target="_blank"},
[$t$ (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$MTT_t$ (Q.PH1.006.t)](quantities.md#MTT){:target="_blank"} | -- | +| M.ID2.003 | Blood plasma flow from maximum | -- | -- | This forward model is given by the following equation:
$F_p=max(I(t))$
with
[ [$I$ (Q.IC1.005)](quantities.md#IRF){:target="_blank"}, [$t$ (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"} | -- | +| M.ID2.004 | Blood plasma flow from first time frame | -- | -- | This forward model is given by the following equation:
$F_p=I(0)$
with
[ [$I$ (Q.IC1.005)](quantities.md#IRF){:target="_blank"}, [$t$ (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"} | -- | +| M.ID2.005 | Capillary transit time heterogeneity identity | -- | -- | This forward model is given by the following equation:
$CTTH=\int_{0}^{\infty}\sqrt{(t-MTT)^2}h(t)dt$
with
[[$h$ (Q.IC1.003)](quantities.md#h){:target="_blank"}, [$t$ (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$MTT$ (Q.PH1.006)](quantities.md#MTT){:target="_blank"},
[$CTTH$ (Q.PH1.014)](quantities.md#CTTH){:target="_blank"} | -- | | M.ID2.999 | Model not listed | -- | -- | This is a custom free-text item, which can be used if a model of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage. | -- |