### Installing Development Tools via winget on Windows

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

This snippet provides commands to install essential development tools (Git, Miniconda, VSCode) on Windows using the winget package manager. It offers a quick setup alternative to manual installation for users looking for a streamlined process.

```Command Line
winget install -e --id Git.Git
winget install -e --id Anaconda.Miniconda3
winget install -e --id Microsoft.VisualStudioCode
```

--------------------------------

### Installing mkdocs-material using pip

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

This command installs the mkdocs-material package, a theme for MkDocs used to build the project documentation, into the currently active Conda environment using the pip package manager. It's important to stick to either pip or conda for installations within one environment.

```shell
pip install mkdocs-material
```

--------------------------------

### Installing mkdocs-material using conda-forge

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

This command provides an alternative method to install the mkdocs-material package using the conda package manager from the conda-forge channel. Users should choose either this method or the pip method but not mix them within the same environment.

```shell
conda install -c conda-forge mkdocs-material
```

--------------------------------

### Applying Custom Button CSS Class in HTML

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

Illustrates how to apply the custom CSS class `md-button--example` alongside the base `md-button` class in HTML using the `class` attribute.

```HTML
class="md-button md-button--example"
```

--------------------------------

### Creating a new Conda environment for CAPLEX

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

This command creates a new isolated Conda environment named 'CAPLEX' and installs the latest compatible version of Python within it. This is the first step in setting up the project's development environment.

```shell
conda activate CAPLEX
```

--------------------------------

### Embedding Button and Anchor in Markdown Table

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

Shows an example of embedding the hyperlink button and its required anchor element within a cell of a Markdown table row for correct functionality, allowing the button to copy the link to the anchor's ID.

```Markdown
| Q.MS1.001.[j] <button class="md-button md-button--hyperlink">COPY LINK</button> | <a id="S"></a> Signal | -- | *S<sub>j</sub>* | The MR signal (magnitude, phase or complex depending on context) in compartment *j*. | a.u. | -- |
```

--------------------------------

### Adding a New Quantity Entry (Markdown)

Source: https://github.com/osipi/osipi_caplex/blob/main/README.md

This snippet demonstrates how to add a new row to the markdown table in the lexicon file to define a new electromagnetic quantity. It shows the required columns and placeholders for information like code, name, notation, description, units, and reference.

```Markdown
| Q.EL1.020 | <a name="k1k2"></a> Transverse relaxivities of the quadratic model (GE) | -- | [*k<sub>1</sub>*,k<sub>2</sub>] | First and second order relaxivities for the quadratic model of the transverse relaxation rate (GE) | [1/s/mM,1/s/mM]| -- |
| Q.EL1.021 | <a name="new link"></a> New quantity                                    | **add alternative name here** | **add notation here** | **add description here** | **add units here** | **add reference here** |
| Q.EL1.999 | <a name="not listed EL1"></a> Quantity not listed | -- | -- | This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage. | [variable] | -- |
```

--------------------------------

### Removing a Conda environment

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

This command removes a specified Conda environment and all packages installed within it. Replace ENV_NAME with the name of the environment to be removed (e.g., 'CAPLEX'). It's recommended to deactivate the environment and close any applications using it before running this command.

```shell
conda remove -n ENV_NAME --all
```

--------------------------------

### Serve Local Website with MkDocs

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

Run the 'mkdocs serve' command to build and host a local version of the website, typically accessible at 127.0.0.1:8000. The site automatically rebuilds on file changes.

```Shell
mkdocs serve
```

--------------------------------

### Adding Images using Markdown

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

Demonstrates the basic Markdown syntax for embedding images, including optional configuration attributes like width, alignment, and lazy loading.

```Markdown
![Image name](Image url)
```

```Markdown
![test](osipiImgs/OSIPI_logo_only_square.png){ width="100" }
```

--------------------------------

### Creating Basic Markdown Link

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

Explains the basic syntax for creating hyperlinks in Markdown, linking text to a specified URL. The URL can be internal or external.

```Markdown
[shown text](url)
```

--------------------------------

### Change Directory using Shell

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

Use the 'cd' command to navigate the terminal into the directory containing the mkdocs.yml file. Tab completion can be used to simplify path typing.

```Shell
cd .\\
```

--------------------------------

### Defining Custom Button CSS Class

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

Shows the CSS syntax for defining a custom style extension based on the base `md-button` class in the `extra.css` file.

```CSS
.md-button.md-button--example {}
```

--------------------------------

### Adding Hyperlink Button using HTML

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

Provides the HTML structure for creating a button with specific CSS classes to enable hyperlink copying functionality.

```HTML
<button class="md-button md-button--hyperlink">COPY LINK</button>
```

--------------------------------

### Configure Git User Information (Git)

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

Configures the global Git user name and email address. This information is used to identify the author of commits. Replace 'YOUR NAME' and 'YOUR EMAIL' with your actual name and email.

```Git
git config --global user.name "YOUR NAME"
git config --global user.email "YOUR EMAIL"
```

--------------------------------

### P.SC2.999 - Method not listed - Description

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionProcesses.md

A placeholder entry for custom methods not explicitly listed in the lexicon. Users should provide a literature reference and request the method's formal addition.

```Text Description
This is a custom free-text item, which can be used if a method of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
```

--------------------------------

### Add HTML Anchor for Navigation

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

Insert an HTML anchor tag with a unique 'id' attribute to create a specific point within a document that can be linked to directly. This is primarily used for creating reference points.

```HTML
<a id="example"></a>
```

--------------------------------

### P.SC2.001 - S0 from native R1 estimation - Description

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionProcesses.md

Estimates the signal scaling factor (S0) by utilizing a native R1 estimation method that is designed to output S0. The specific R1 estimation method must be selected as an input.

```Text Description
In this method *S\u2080* is estimated as described in the native *R\u2081* -estimation methods which have *S\u2080* as output. \n **Input:** \n Select a [native R1 estimation method](#Native R1 estimation methods) with *S\u2080* as output \n **Output**: \n [*S\u2080* (Q.MS1.010)](quantities.md#S_0)
```

--------------------------------

### Plug flow extraction fraction - Mathematical Notation

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

This forward model is given by the following equation: E=1-e^{-\frac{PS}{F_p}}. It calculates the extraction fraction (E) in a plug flow model based on permeability-surface area product (PS) and plasma flow (F_p).

```Mathematical Notation
E=1-e^{-\frac{PS}{F_p}}
```

--------------------------------

### Ktrans identity - Mathematical Notation

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

This forward model is given by the following equation: K^{trans}=E\cdot F_p. It defines the volume transfer constant (K^{trans}) based on the extraction fraction (E) and plasma flow (F_p).

```Mathematical Notation
K^{trans}=E\cdot F_p
```

--------------------------------

### P.SC2.002 - S0 from baseline signal of dynamic data - Description

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionProcesses.md

Estimates the signal scaling factor (S0) by inverting a specified MR signal model using a given inversion method, applied to the baseline signal and baseline relaxation rate from dynamic data. Requires specific inputs including the inversion method, forward model, and baseline quantities.

```Text Description
In this method *S\u2080* is estimated by inverting a specified MR signal model according to a specified inversion method for the baseline signal and baseline relaxation rate. \n **Input:** \n Inversion method (select from [Inversion methods](generalPurposeProcesses.md#Inversion methods)) with [Forward model (M.GF1.001)](perfusionModels.md#Forward model) = select from [MR signal models](perfusionModels.md#MR signal models) with \n [*R\u2081* (Q.EL1.001)](quantities.md#R1) = [*R\u2081\u2080* (Q.EL1.002)](quantities.md#R10) \n or \n [*R\u2082* (Q.EL1.004)](quantities.md#R2) = [*R\u2082\u2080* (Q.EL1.005)](quantities.md#R20) \n or \n [*R\u2082\u207B* (Q.EL1.007)](quantities.md#R2Star) = [*R\u2082\u2080\u207B* (Q.E.008)](quantities.md#R2Star0), \n [S (Q.MS1.001)](quantities.md#S) = [*S\u2093\u2097*(Q.MS1.002)](quantities.md#S_BL) \n**Output**: \n [*S\u2080* (Q.MS1.010)](quantities.md#S_0)
```

--------------------------------

### Central volume theorem - Mathematical Notation

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

This forward model is given by the following equation: v_p=MTT\cdot F_p. It relates plasma volume (v_p) to mean transit time (MTT) and plasma flow (F_p).

```Mathematical Notation
v_p=MTT\cdot F_p
```

--------------------------------

### Blood vs plasma AIF - Mathematical Notation

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

This forward model is given by the following equation: C_{a,b}(t)=C_{a,p}(t)\cdot(1-Hct_a). It relates arterial blood concentration (C_{a,b}) over time (t) to arterial plasma concentration (C_{a,p}) over time (t) and arterial hematocrit (Hct_a).

```Mathematical Notation
C_{a,b}(t)=C_{a,p}(t)\cdot(1-Hct_a)
```

--------------------------------

### Blood vs plasma volume fraction - Mathematical Notation

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

This forward model is given by the following equation: v_b=\frac{v_p}{(1-Hct)}. It relates blood volume (v_b) to plasma volume (v_p) and hematocrit (Hct).

```Mathematical Notation
v_b=\frac{v_p}{(1-Hct)}
```

--------------------------------

### P.AE1.001 - Estimate arterial input function - Description

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionProcesses.md

Processes a dataset to return the arterial input function (AIF) using a specified estimation method. Allows optional specification of AIF correction methods (like partial volume correction) or details about measurement preparation (like dual bolus).

```Text Description
This process returns the AIF from a given data set, derived using a specified AIF estimation method. Furthermore, it can be optionally specified if an AIF correction method (.e.g. Partial volume correction) will be applied or if a measurement preparation (e.g. dual bolus) has been done for data acquisition. \n **Input:** \n AIF estimation method (select from [AIF estimation methods](#AIF estimation methods)), \n *optional*: \n AIF correction or measurement preparation (select from [AIF correction and measurement preparation](#AIF correction and measurement preparation)). \n **Output**: \n [[C\u2090\u2097 (Q.IC1.001.[a,p])](quantities.md#C), [t (Q.GE1.004)](quantities.md#time)] or \n [[C\u2090\u2091 (Q.IC1.001.[a,b])](quantities.md#C), [t (Q.GE1.004)](quantities.md#time)]
```

--------------------------------

### Total volume of distribution - Mathematical Notation

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

This forward model is given by the following equation: v=v_p+v_e+v_i. It defines the total volume of distribution (v) as the sum of plasma volume (v_p), extracellular volume (v_e), and intracellular volume (v_i).

```Mathematical Notation
v=v_p+v_e+v_i
```

--------------------------------

### Blood vs plasma flow - Mathematical Notation

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

This forward model is given by the following equation: F_b=\frac{F_p}{(1-Hct)}. It relates blood flow (F_b) to plasma flow (F_p) and hematocrit (Hct).

```Mathematical Notation
F_b=\frac{F_p}{(1-Hct)}
```

--------------------------------

### Compartment extraction fraction - Mathematical Notation

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

This forward model is given by the following equation: E=\frac{PS}{F_p+PS}. It calculates the extraction fraction (E) in a compartment model based on permeability-surface area product (PS) and plasma flow (F_p).

```Mathematical Notation
E=\frac{PS}{F_p+PS}
```

--------------------------------

### Plasma MTT identity - Mathematical Notation

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

This forward model is given by the following equation: MTT_p=\frac{v_p}{F_p+PS}. It defines the plasma mean transit time (MTT_p) based on plasma volume (v_p), plasma flow (F_p), and permeability-surface area product (PS).

```Mathematical Notation
MTT_p=\frac{v_p}{F_p+PS}
```

--------------------------------

### Model not listed IC2

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

Placeholder entry for AIF models not currently listed in the lexicon. Provides guidance on how to request a new model to be added.

```Markdown
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.
```

--------------------------------

### Patlak Model (PM) Equations

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

Mathematical equations for the Patlak Model (PM), which describes uni-directional exchange of indicator from vascular to extravascular extracellular spaces, assuming negligible reverse exchange. Includes the differential equation for the forward model and the impulse response function.

```LaTeX
$v_{e}\frac{dC_{e}(t)}{dt} = PSC_{c,p}$

$I(t) = v_{p}\delta(t) + PS$
```

--------------------------------

### Weinmann AIF model

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

Describes the Weinmann AIF model, a simple biexponential function scaled by the contrast agent dose. It includes the model equation, parameter definitions, and default values.

```Markdown
This forward model is given by the following equation: 
$C_{a,p}(t)=D(a_1e^{-m_1t}+a_2e^{-m_2t}),$
where $D$ is the dose of contrast agent and $a_1$, $a_2$, $m_1$ and $m_2$ are the amplitudes and time constants of the exponential terms, and [[$C_{a,p}$ (Q.IC1.001.a,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}]. 
If the model parameters are not specified, the values from the publication are assumed: [$D$, $a_1$, $m_1$, $a_2$, $m_2$] = [0.25 mmol/kg, 3.99 kg/l, 0.0024 $s^{-1}$, 4.78 kg/l, 0.0002 $s^{-1}$].
```

--------------------------------

### Deactivating the current Conda environment

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/contributionTutorial.md

This command deactivates the currently active Conda environment, returning the terminal session to the base environment or the previous environment in the stack. This is necessary before removing an environment.

```shell
conda deactivate
```

--------------------------------

### Extended Tofts Model (ETM) Equations

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

Mathematical equations for the Extended Tofts Model (ETM), which describes bi-directional exchange of indicator between vascular and extravascular extracellular spaces. Includes the differential equation for the forward model and the impulse response function.

```LaTeX
$v_{e}\frac{dC_{e}(t)}{dt} = PSC_{c,p} - PSC_{e}(t)$

$I(t) = v_{p}\delta(t) + K^{trans}e^{{-\frac{K^{trans}}{v_{e}}t}}$
```

--------------------------------

### Parker AIF model

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

Describes the Parker AIF model, a two-Gaussian and one-sigmoid-exponential function used to model the arterial input function in DCE-MRI. It includes the model equation, parameter definitions, and default values from the original publication.

```Markdown
This forward model is given by the following equation: 
$C_{a,b}(t)=\sum_{n=1}^{2}\frac{A_n}{\sigma_n\sqrt{2\pi}}e^{-\frac{(t-T_n)^2}{2\sigma_n^2}}+\frac{\alpha e^{-\beta t}}{1+e^{-s(t-\tau)}},$
where $A_n$, $T_n$ and $\sigma_n$ are the scaling constants, center and widths of the nth Gaussian; $\alpha$ and $\beta$ are the amplitude and decay constants of the exponential; and $s$ and $\tau$ are the width and center of the sigmoid, and [[$C_{a,b}$ (Q.IC1.001.a,b)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}]. If not specified otherwise, the values from the publication are assumed: [$A_1$, $A_2$, $T_1$, $T_2$, $\sigma_1$, $\sigma_2$, $\alpha$ , $\beta$ , s, $\tau$ ] = [48.54 mmol $\cdot$ s, 19.8 mmol $\cdot$ s, 10.2276 s, 21.9 s, 3.378 s, 7.92 s, 1.050 mmol, 0.0028 s-1, 0.6346 s-1, 28.98 s].
```

--------------------------------

### Georgiou AIF model

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

Describes the Georgiou AIF model, which uses exponential terms and a gamma distribution function to model the arterial input function, accounting for recirculation. It includes the model equations, parameter definitions, and default values.

```Markdown
The AIF between the start of the nth recirculation and (n+1)th recirculation is given by: 
$C_{a,p}(t)=(\sum_{i=1}^{3}A_ie^{-m_it})\cdot(\sum_{j=0}^{n}\gamma((j+1)\alpha+j,\beta,t-j\tau)),$
with $n\tau<t<(n+1)\tau$
and $\gamma(\alpha, \beta, \tau)=\frac{t^\alpha e^{-\frac{t}{\beta}}}{\beta^{\alpha+1}\Gamma(\alpha +1)}$ with $t\geq 0$,
where $A_1$, $A_2$, $A_3$ and $m_1$, $m_2$, $m_3$ are the amplitudes and time constants of the exponential terms, the coefficients and reflect the number of theoretical mixing chambers and the ratio of the volume of the mixing chambers to the volume flow rate, and is the recirculation time, [[$C_{a,p}$ (Q.IC1.001.a,p)](quantities.md#C){:target="_blank"}, [t (Q.GE1.004)](quantities.md#time){:target="_blank"}]. $\gamma = 0$ for $t<0$. 
If not specified otherwise, the values from the publication are assumed: [ $A_1$, $A_2$, $A_3$, $m_1$, $m_2$, $m_3$, $\alpha$, $\beta$ , $\tau$ ] = [0.37 mM, 0.33 mM, 10.06 mM, 0.002 $s^{-1}$, 0.02 $s^{-1}$, 0.267 $s^{-1}$, 5.26, 1.92 s, 7.74 s].
```

--------------------------------

### Single-shot inversion recovery SPGR with centric encoding model (Equation)

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

A single-shot inversion recovery SPGR model with centric encoding. It relates signal (S) to S0, R1, and preparation delay (PD), accounting for inversion and subsequent recovery.

```Equation
S = S_0\cdot(1-2e^{-PD\cdot R_1})
```

--------------------------------

### Interstitial MTT identity - Mathematical Notation

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

This forward model is given by the following equation: MTT_e=\frac{v_e}{PS}. It defines the interstitial mean transit time (MTT_e) based on extracellular volume (v_e) and permeability-surface area product (PS).

```Mathematical Notation
MTT_e=\frac{v_e}{PS}
```

--------------------------------

### Small vessel hematocrit correction - Mathematical Notation

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

This forward model is given by the following equation: Hct_f=\frac{1-Hct_a}{1-Hct_t}. It calculates a hematocrit correction factor (Hct_f) based on arterial hematocrit (Hct_a) and tissue hematocrit (Hct_t).

```Mathematical Notation
Hct_f=\frac{1-Hct_a}{1-Hct_t}
```

--------------------------------

### Single-shot saturation recovery SPGR with centric encoding model (Equation)

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

A single-shot saturation recovery SPGR model with centric encoding. It simplifies to a relationship between signal (S), initial signal (S0), R1, and preparation delay (PD), assuming full saturation.

```Equation
S = S_0\cdot(1-e^{-PD\cdot R_1})
```

--------------------------------

### Two Compartment Uptake Model (2CUM) Equations

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

Mathematical equations for the Two Compartment Uptake Model (2CUM), which describes uni-directional exchange of indicator from vascular to extravascular extracellular spaces. Includes two differential equations for the forward model and the impulse response function.

```LaTeX
$v_{p}\frac{dC_{c,p}(t)}{dt} = F_{p}C_{a,p} - F_{p}C_{c,p} - PSC_{a,p}$

$v_{e}\frac{dC_{e}(t)}{dt} = PSC_{a,p}$

$I(t) = F_{p}e^{-({\frac{F_{p} + PS}{v_{p}}})t} + E(1 - e^{-({\frac{F_{p} + PS}{v_{p}}})t})$
```

--------------------------------

### Inversion-recovery spoiled gradient recalled echo with linear encoding model (Equation)

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

An inversion-recovery turboFLASH (SPGR) model with linear k-space encoding. This detailed model describes the signal (S) based on S0, R1, PD, alpha, TR, and k-space indices (n, N), incorporating inversion, recovery, and encoding dynamics.

```Equation
S=S_0\cdot sin(\alpha)\cdot [\frac{(C+bA-\frac{1}{cos(\alpha)}D+1)}{1+BD}\cdot e^{-PD\cdot R_1}a^{n-1}\n\t\t+(1-e^{-PD\cdot R_1})a^{n-1}+b\frac{1-a^{n-1}}{1-a}]\nwith\na=cos(\alpha)e^{-TR\cdot R_1},\nb=1-e^{-TR\cdot R_1},\nC=a^{N-1}(1-e^{-PD\cdot R_1}),\nA=\frac{1-a^{N-1}}{1-a},\nD=cos(\alpha)e^{-PD\cdot R_1},\nB=a^{N-1}e^{-PD\cdot R_1}
```

--------------------------------

### Spoiled gradient recalled echo model (Equation)

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

The standard spoiled gradient recalled echo model relating signal (S) to initial signal (S0), R1, repetition time (TR), and flip angle (alpha). It accounts for T1 recovery and spoiling effects.

```Equation
S=S_0 \cdot \frac{sin(\alpha)[1-e^{TR\cdot R_1}]}{1-cos(\alpha)\cdot e^{-TR\cdot R_1}}
```

--------------------------------

### Saturation-recovery SPGR with linear encoding model (Equation)

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

A saturation-recovery turbo SPGR model with linear k-space encoding. This complex model relates signal (S) to S0, R1, PD, TR, flip angle (alpha, typically 90°), and the k-space index (n), incorporating recovery and encoding effects.

```Equation
S=S_0\cdot sin(\alpha)\cdot[(1-e^{-PD\cdot R_1})a^{n-1}+b\frac{(1-a^{n-1})}{(1-a)}]\nwith\na=cos(\alpha)\cdot e^{-TR\cdot R_1},\nb=1-e^{-TR\cdot R_1}
```

--------------------------------

### Linear model (Equation)

Source: https://github.com/osipi/osipi_caplex/blob/main/docs/perfusionModels.md

Describes a simple linear relationship between signal (S) and the longitudinal relaxation rate (R1), scaled by a constant (k). Used in specific scenarios where this approximation holds.

```Equation
S=k \cdot R_1
```

=== COMPLETE CONTENT === This response contains all available snippets from this library. No additional content exists. Do not make further requests.