diff --git a/Social Card.png b/Social Card.png new file mode 100644 index 00000000..3934d88e Binary files /dev/null and b/Social Card.png differ diff --git a/docs/contributionTutorial.md b/docs/contributionTutorial.md index 68fab801..c0ce53a3 100644 --- a/docs/contributionTutorial.md +++ b/docs/contributionTutorial.md @@ -294,9 +294,10 @@ with an optional configuration inside `{}`(1) at the end. For example,
`![te 1. Multiple configurations should all be included within a single `{}` with spaces between, e.g. `{ width="100" align=right }`. -![test](osipiImgs/OSIPI_logo_only_square.png){ width="100" } -![test](osipiImgs/OSIPI_logo_only_square.png){ width="100" align=right } +![test](osipiImgs/OSIPI_logo_only_square.png){ width="150" align=right } + +![test](osipiImgs/OSIPI_logo_only_square.png){ width="150" } We can also align the image to the right using `{ align=right }`. diff --git a/docs/generalPurposeProcesses.md b/docs/generalPurposeProcesses.md index e67dca24..1dcd4f26 100644 --- a/docs/generalPurposeProcesses.md +++ b/docs/generalPurposeProcesses.md @@ -1,5 +1,5 @@ -# Sections G: General purpose processes +# Section G: General purpose processes ## Forward model inversion diff --git a/docs/perfusionModels.md b/docs/perfusionModels.md index c2844cec..638de5eb 100644 --- a/docs/perfusionModels.md +++ b/docs/perfusionModels.md @@ -1,5 +1,5 @@ -# Section M: Perfusion Models +# Section M: Perfusion Models ## General forward model @@ -112,18 +112,18 @@ We provide the differential equations and impulse response functions using the c | Code | OSIPI name| Alternative names|Notation|Description|Reference| | -- | -- | -- | -- | -- | -- | -| M.IC1.001 | Linear and stationary system model | -- | LSS model | This forward model is given by the following equations:
$C(t)=I(t)\ast C_{a,p}(t)$
with
[[I (Q.IC1.005)](quantities.md#IRF){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_{a,p}$ (Q.IC1.001.a,p)](quantities.md#C){:target="_blank"}, [$t$ (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_t$ (Q.IC1.001.t)](quantities.md#C){:target="_blank"}, [$t$ (Q.GE1.004)](quantities.md#time){:target="_blank"}] | (Rempp et al. 1994) | -| M.IC1.002 | One-compartment, no indicator exchange model | -- | 1CNEX model | The one compartment no indicator exchange model describes an intravascular model with no vascular to EES indicator exchange. This forward model is given by the following differential equation:
$v_{p}\frac{dC_{t}(t)}{dt} = F_{p}C_{a,p} - F_{p}C_{c,p}(t)$
The impulse response function is given by:
$I(t) = F_{p}e^{{-\frac{F_{p}}{v_{p}}t}}$
with
[[$C_{a,p}$ (Q.IC1.001.a,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_{c,p}$ (Q.IC1.001.c,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_t$ (Q.IC1.001.t)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[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"},
[$v_{p}$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"} | (Tofts et al. 1999) | -| M.IC1.003 | One-compartment, fast indicator exchange model | -- | 1CFEX model | The one compartment fast exchange model describes infinitely fast bi-directional exchange of indicator between vascular to extravascular extracellular spaces. The capillary and EES effectively act as a single compartment. This forward model is given by the following differential equation:
$\frac{dC_{t}(t)}{dt} = F_{p}C_{a,p} - \frac{F_{p}}{v_{p} + v_{e}}C_{t}(t)$
The impulse response function is given by:
$I(t) = F_{p}e^{{-\frac{F_{p}}{v_{p} + v_{e}}t}}$
with
[[$C_{a,p}$ (Q.IC1.001.a,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_t$ (Q.IC1.001.t)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[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"},
[$v_{p}$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"},
[$v_{e}$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"} | (Sourbron et al. 2013) | +| M.IC1.001 | Linear and stationary system model | -- | LSSM | This forward model is given by the following equations:
$C(t)=I(t)\ast C_{a,p}(t)$
with
[[I (Q.IC1.005)](quantities.md#IRF){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_{a,p}$ (Q.IC1.001.a,p)](quantities.md#C){:target="_blank"}, [$t$ (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_t$ (Q.IC1.001.t)](quantities.md#C){:target="_blank"}, [$t$ (Q.GE1.004)](quantities.md#time){:target="_blank"}] | (Rempp et al. 1994) | +| M.IC1.002 | One-compartment, no indicator exchange model | -- | 1CNEXM | The one compartment no indicator exchange model describes an intravascular model with no vascular to EES indicator exchange. This forward model is given by the following differential equation:
$v_{p}\frac{dC_{t}(t)}{dt} = F_{p}C_{a,p} - F_{p}C_{c,p}(t)$
The impulse response function is given by:
$I(t) = F_{p}e^{{-\frac{F_{p}}{v_{p}}t}}$
with
[[$C_{a,p}$ (Q.IC1.001.a,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_{c,p}$ (Q.IC1.001.c,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_t$ (Q.IC1.001.t)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[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"},
[$v_{p}$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"} | (Tofts et al. 1999) | +| M.IC1.003 | One-compartment, fast indicator exchange model | -- | 1CFEXM | The one compartment fast exchange model describes infinitely fast bi-directional exchange of indicator between vascular to extravascular extracellular spaces. The capillary and EES effectively act as a single compartment. This forward model is given by the following differential equation:
$\frac{dC_{t}(t)}{dt} = F_{p}C_{a,p} - \frac{F_{p}}{v_{p} + v_{e}}C_{t}(t)$
The impulse response function is given by:
$I(t) = F_{p}e^{{-\frac{F_{p}}{v_{p} + v_{e}}t}}$
with
[[$C_{a,p}$ (Q.IC1.001.a,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_t$ (Q.IC1.001.t)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[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"},
[$v_{p}$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"},
[$v_{e}$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"} | (Sourbron et al. 2013) | | M.IC1.004 | Tofts Model | Kety model, Generalized Kinetic Model | TM | The Tofts model describes bi-directional exchange of indicator between vascular to extravascular extracellular spaces. The capillary compartment is assumed to have negligible volume. The EES is modeled as well-mixed compartment. The forward model is given by the following differential equation:
$\frac{dC_{t}(t)}{dt} = K^{trans}C_{a,p} - \frac{K^{trans}}{v_{e}}C_{t}(t)$
The impulse response function is given by:
$I(t) = K^{trans}e^{{-\frac{K^{trans}}{v_{e}}t}}$
with
[[$C_{a,p}$ (Q.IC1.001.a,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_t$ (Q.IC1.001.t)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[I (Q.IC1.005)](quantities.md#IRF){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$K^{trans}$ (Q.PH1.008)](quantities.md#Ktrans){:target="_blank"},
[$v_{e}$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"} | (Tofts and Kermode 1991) | | M.IC1.005 | Extended Tofts Model | Modified Tofts Model, Extended Generalized Kinetic Model, Modified Kety model | ETM | The extended Tofts model describes bi-directional exchange of indicator between vascular to extravascular extracellular spaces. The capillary and EES are modeled as well-mixed compartments. It is equivalent to the 2CXM in the highly perfused limit. Dispersion of indicator within the capillary bed is assumed negligible:
$C_{c,p} = C_{a,p}$
The forward model is given by the following differential equation:
$v_{e}\frac{dC_{e}(t)}{dt} = PSC_{c,p} - PSC_{e}(t)$
The impulse response function is given by:
$I(t) = v_{p}\delta(t) + K^{trans}e^{{-\frac{K^{trans}}{v_{e}}t}}$
with
[[$C_{c,p}$ (Q.IC1.001.c,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_e$ (Q.IC1.001.e)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[I (Q.IC1.005)](quantities.md#IRF){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$\delta$ (M.DM1.009)](quantities.md#delta){:target="_blank"},
[PS (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$v_{e}$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"},
[$K^{trans}$ (Q.PH1.008)](quantities.md#Ktrans){:target="_blank"} | (Tofts 1997) | | M.IC1.006 | Patlak Model | -- | PM | The Patlak model allows uni-directional exchange of indicator from vascular to extravascular extracellular spaces. Indicator exchange from the EES to the intravascular space is considered negligible during the timeframe of the imaging experiment. The capillary and EES are modeled as well-mixed compartments. It is equivalent to the two compartment uptake model in the highly perfused limit. Dispersion of indicator within the capillary bed is assumed negligible:
$C_{c,p} = C_{a,p}$
The forward model is given by the following differential equation:
$v_{e}\frac{dC_{e}(t)}{dt} = PSC_{c,p}$
The impulse response function is given by:
$I(t) = v_{p}\delta(t) + PS$
with
[[$C_{c,p}$ (Q.IC1.001.c,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_e$ (Q.IC1.001.e)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[I (Q.IC1.005)](quantities.md#IRF){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$\delta$ (Q.PH1.009)](quantities.md#delta){:target="_blank"},
[PS (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$v_{p}$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"} | (Patlak et al. 1983) | | M.IC1.007 | Two compartment uptake model | -- | 2CUM | The 2CU model allows uni-directional exchange of indicator from vascular to extravascular extracellular spaces. Indicator exchange from the EES to the intravascular space is considered negligible during the timeframe of the imaging experiment. The capillary and EES are modeled as well-mixed compartments. The forward model is given by the following differential equations:
$v_{p}\frac{dC_{c,p}(t)}{dt} = F_{p}C_{a,p} - F_{p}C_{c,p} - PSC_{a,p}$

$v_{e}\frac{dC_{e}(t)}{dt} = PSC_{a,p}$
The impulse response function is given by:
$I(t) = F_{p}e^{-({\frac{F_{p} + PS}{v_{p}}})t} + E(1 - e^{-({\frac{F_{p} + PS}{v_{p}}})t})$
with
[[$C_{a,p}$ (Q.IC1.001.a,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_{c,p}$ (Q.IC1.001.c,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_{e}$ (Q.IC1.001.e)](quantities.md#C), [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[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"},
[PS (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[E (Q.PH1.005)](quantities.md#E){:target="_blank"},
[$v_{e}$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"},
[$v_{p}$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"} | (Pradel et al. 2003), (Sourbron 2009) | | M.IC1.008 | Plug flow uptake model | -- | PFUM | The plug flow uptake model allows uni-directional exchange of indicator from vascular to extravascular extracellular spaces. Indicator exchange from the EES to the intravascular space is considered negligible during the timeframe of the imaging experiment. The capillary space is modeled as a plug flow system and the EES as a well-mixed compartment. The forward model is given by the following differential equations:
$v_{p}\frac{\partial C_{c,p}(x_{ax}, t)}{\partial t} = -F_{p}L_{ax}\frac{\partial C_{a,p}(x_{ax}, t)}{\partial x_{ax}} - PSC_{a,p}(x_{ax}, t)$

$v_{e}\frac{dC_{e}(t)}{dt} = PS \int_{0}^{L_{ax}} C_{c,p} (x_{ax},t) dx$
The impulse response function is ... TO ADD IRF
with
[[$C_{c,p}$ (Q.IC1.001.c,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_{e}$ (Q.IC1.001.e)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[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"},
[PS (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$v_{e}$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"},
[$v_{p}$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"},
[$L_{ax}$ (Q.GE1.007)](quantities.md#Lax){:target="_blank"},
[$x_{ax}$ (Q.GE1.008)](quantities.md#xax){:target="_blank"} | (St. Lawrence and Frank 2000) | | M.IC1.009 | Two compartment exchange model | -- | 2CXM | The 2CX model allows bi-directional exchange of indicator between vascular and extravascular extracellular compartments. Indicator is assumed to be well mixed within each compartment. The forward model is given by the following differential equations:
$v_{p}\frac{dC_{c,p}}{dt} = F_{p}C_{a,p}(t) - F_{p}C_{c,p}(t) - PSC_{c,p}(t) + PSC_{e}(t)$

$v_{e}\frac{dC_{e}}{dt} = PSC_{c,p}(t) - PSC_{e}(t)$
The impulse response function is given by
$I(t) = F_{p}e^{-K_{+}t} + E_{-}(e^{-K_{+}t} - e^{-K_{-}t})$

$K_{\pm} = \frac{1}{2}\Biggl(\frac{F_{p} + PS}{v_{p}} + \frac{PS}{v_{p}} \pm \sqrt{(\frac{F_{p} + PS}{v_{p}} + \frac{PS}{v_{e}})^{2} - 4\frac{F_{p}PS}{v_{p}v_{e}}}\Biggl)$

$E_{-} = \frac{K_{+} + \frac{F_{p}}{v_{p}}}{K_{+} + K_{-}}$
with
[[$C_{a,p}$ (Q.IC1.001.a,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_{c,p}$ (Q.IC1.001.c,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_{e}$ (Q.IC1.001.e)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[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"},
[PS (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$v_{e}$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"},
[$v_{p}$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"} | (Brix et al. 2004), (Sourbron et al. 2009), (Donaldson et al. 2010) | -| M.IC1.010 | Distributed parameter model | -- | DPM | This is a placeholder for the distributed parameter model | (Sangren and Sheppard 1953) (Sourbron 2011) | -| M.IC1.011 | Tissue homogeneity model | Johnson-Wilson model | THM | This is a placeholder for the tissue homogeneity model | (Johnson and Wilson 1966) (Lawrence and Lee 1998) (Kershaw 2010) (Koh et al. 2003)| -| M.IC1.012 | Adiabatic Approximation to the Tissue homogeneity model | | AATHM | This is a placeholder for the adiabatic approximation to the tissue homogeneity model | (Lawrence and Lee 1998) Kershaw et al. 2010) (Sourbron et al. 2012) | +| M.IC1.010 | Distributed parameter model | -- | DPM | The DP model allows bi-directional exchange of indicator between vascular and extravascular extracellular compartments. The capillary space is modeled as a plug flow system. The EES is modeled as a series of infinitesimal compartments which only exchange indicator with nearby locations in the capillary bed.This forward model is given by the following differential equations:
$v_{p}\frac{∂C_{c,p}}{∂t}(x_{ax},t) = F_{p}L_{ax}\frac{∂C_{cp}}{∂x_{ax}}(x_{ax},t) - PSC_{c,p}(x_{ax},t) + PSC_{e}(x_{ax},t)$

$v_{e}\frac{∂C_{e}}{∂t}(x_{ax},t) = PSC_{c,p}(x_{ax},t) - PSC_{e}(x_{ax},t)$
The impulse response function is given by
$I(t) = F_{p}(1-u(t{-}\frac{v_{p}}{F_{p}})) e^\frac{-PS}{F_{p}} (1-\int_{0}^{t{-} \frac{v_{p}}{F_{p}}} x(τ)dτ)$
where
$x(τ) = u(t) e^\frac{-t\cdot PS}{v_{e}} \sqrt{\frac{PS^2}{t\cdot v_{e} \cdot F_{p}}} I_{1}\Bigl(2\sqrt{\frac{PS^2 \cdot t}{v_{e}\cdot F_{p}}}\Bigl)$

Where $I_{1}$ is the first order bessel function of the first kind with
[[$C_{c,p}$ ((Q.IC1.001.c,p))](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],[[$C_{e}$ (Q.IC1.001.e)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[I (Q.IC1.005)](quantities.md#IRF){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[u (M.DM1.001)](quantities.md#u){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"},
[PS (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$v_{e}$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"},
[$v_{p}$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"},
[$L_{ax}$ (Q.GE1.007)](quantities.md#Lax){:target="_blank"},
[$x_{ax}$ (Q.GE1.008)](quantities.md#xax){:target="_blank"} | (Sangren and Sheppard 1953) (Sourbron 2011) | +| M.IC1.011 | Tissue homogeneity model | Johnson-Wilson model | THM |The TH model allows bi-directional exchange of indicator between vascular and extravascular extracellular compartments. The capillary space is modeled as a plug flow system and the EES as a well mixed compartment. This forward model is given by the following differential equations:
$v_{p}\frac{∂C_{e}}{∂t}(x_{ax},t) = -F_{p}L_{ax}\frac{∂C_{c,p}}{∂x_{ax}}(x_{ax},t) - PSC_{c,p}(x_{ax},t) + PSC_{e}$

$v_{e}\frac{∂C_{e}}{∂t} = \frac{PS}{L_{ax}} \int_{0}^{L_{ax}} C_{c,p}(x_{ax},t)dx - PSC_{e}(t)$
The impulse response function is given by:

$I(t) = u(t) - u(t-\frac{v_{p}}{F_{p}})(1-E)\left\{ 1 + \int_{0}^{t - \frac{v_{p}}{F_{p}}} \sqrt{\frac{F_{p}}{v_{e} τ}} ln(1-E)I_{1}(2ln(1-E)\sqrt{\frac{F_{p}}{v_{e}τ}} dτ)\right\}$

Where $I_{1}$ is the first order bessel function of the first kind with
[[$C_{c,p}$ ((Q.IC1.001.c,p))](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],[[$C_{e}$ (Q.IC1.001.e)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[I (Q.IC1.005)](quantities.md#IRF){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[u (M.DM1.001)](quantities.md#u){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"},
[PS (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$v_{e}$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"},
[$v_{p}$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"},
[$L_{ax}$ (Q.GE1.007)](quantities.md#Lax){:target="_blank"},
[$x_{ax}$ (Q.GE1.008)](quantities.md#xax){:target="_blank"} | (Johnson and Wilson 1966) (Lawrence and Lee 1998) (Kershaw 2010) (Koh et al. 2003)| +| M.IC1.012 | Adiabatic Approximation to the Tissue homogeneity model | | AATHM | The AATH model allows bi-directional exchange of indicator between vascular and extravascular extracellular compartments. The capillary space is modeled as a plug flow system and the EES as a well mixed compartment. The adiabatic approximation assumes that the indicator concentration in the EES changes much more slowly than the change in concentration in the plasma.

This forward model is given by the following differential equations:
$v_{p}\frac{∂C_{e}}{∂t}(x_{ax},t) = -F_{p}L_{ax}\frac{∂C_{c,p}}{∂x_{ax}}(x_{ax},t)$

$v_{e} \frac{dC_{e}}{dt}(t) = EF_{p}C_{p}(L_{ax},t) - EF_{p}C_{e}(t)$

The impulse response function is given by:

$I(t) = EF_{p}e^\frac{EF_{p}}{v_e}(t-{v_{p}}{F_{p}}) , for \quad t >\!\frac{v_{p}}{F_{p}}$
with
[[$C_{c,p}$ ((Q.IC1.001.c,p))](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],[[$C_{e}$ (Q.IC1.001.e)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[I (Q.IC1.005)](quantities.md#IRF){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[u (M.DM1.001)](quantities.md#u){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[$F_p$ (Q.PH1.002)](quantities.md#Fp){:target="_blank"},
[PS (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$v_{e}$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"},
[$v_{p}$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"},
[$L_{ax}$ (Q.GE1.007)](quantities.md#Lax){:target="_blank"},
[$x_{ax}$ (Q.GE1.008)](quantities.md#xax){:target="_blank"} | ((Lawrence and Lee 1998)Kershaw et al. 2010) (Sourbron et al. 2012) | | M.IC1.013 | Two compartment filtration model | -- | 2CFM | The 2CFM models unidirectional flow (filtration) from a vascular compartment into an extravascular compartment. A fraction of the filtrate (1-f) is reabsorbed. This model is appropriate for the kidney cortex or whole kidney. The forward model is given by the following differential equations:
$v_{p}\frac{dC_{c,p}}{dt} = F_{p}C_{a,p}(t) - F_{p}C_{c,p}(t) - PSC_{c,p}(t)$

$v_{e}\frac{dC_{e}}{dt} = PSC_{c,p}(t) - (1 - f)PSC_{e}(t)$
. The impulse response function is given by:
$I(t) = v_{p}C_{c,p} + PSe^{-t\frac{(1-f)PS}{v_{e}}} \circledast C_{c,p}$

where $C_{c,p} = \frac{F_{p}}{v_{p}}e^{-t\frac{F_{p}}{v_{p}}}$
with
[[$C_{a,p}$ (Q.IC1.001.a,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_{c,p}$ (Q.IC1.001.c,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[$C_{e}$ (Q.IC1.001.e)](quantities.md#C), [t (Q.GE1.004)](quantities.md#time){:target="_blank"}],
[[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"},
[PS (Q.PH1.004)](quantities.md#PS){:target="_blank"},
[$v_{e}$ (Q.PH1.001.e)](quantities.md#v){:target="_blank"},
[$v_{p}$ (Q.PH1.001.p)](quantities.md#v){:target="_blank"},
[$f$ (Q.PH1.018)](quantities.md#f){:target="_blank"} | [Sourbron et al. 2008](https://doi.org/10.1097/RLI.0b013e31815597c5){:target="_blank"} | | M.IC1.999 | 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. | -- | diff --git a/docs/perfusionProcesses.md b/docs/perfusionProcesses.md index f69f8be9..2c82a4f1 100644 --- a/docs/perfusionProcesses.md +++ b/docs/perfusionProcesses.md @@ -1,5 +1,5 @@ -# Sections P: Perfusion Processes +# Section P: Perfusion Processes ## Native R1 estimation diff --git a/docs/quantities.md b/docs/quantities.md index 25d5b66d..bbcac967 100644 --- a/docs/quantities.md +++ b/docs/quantities.md @@ -1,5 +1,5 @@ -# Sections Q: Quantities +# Section Q: Quantities ## MR signal quantities The items in this group are related to the MR signal and quantities of the MR sequence used to acquire the signal. diff --git a/mkdocs.yml b/mkdocs.yml index 90cf21da..b4339935 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -89,6 +89,16 @@ markdown_extensions: - md_in_html - abbr + + +extra: + og: + type: website + title: Contrast-agent based perfusion MRI lexicon (CAPLEX) + description: CAPLEX + image: Social Card.png + url: https://osipi.github.io/OSIPI_CAPLEX/ + extra_javascript: - javascripts/extra.js - javascripts/mathjax.js