midi

A Shiny app for designing diffusion MRI protocols

A. Stamm

Department of Mathematics Jean Leray, UMR CNRS 6629, Nantes University, Ecole Centrale de Nantes, France

2024-06-14

Context

Brain microstructure

https://giphy.com/gifs/2bYewTk7K2No1NvcuK

What is of interest ?

Neural transmission

https://opentextbc.ca/biology/chapter/16-1-neurons-and-glial-cells/

Parameters of interest

Axonal density: \(0.5-0.8\);
Axon diameter: \(0.5-10\,\mu m\);
Glial cell density: \(0.1-0.5\);
Glial cell diameter: \(20-30\,\mu m\).

What can we see to the naked eye ?

Principle of diffusion MRI

The Human body is made of \(70\%\) of water.
Water molecules are in constant motion due to thermal agitation.
Water trapped in biological tissues is hindered by the presence of cell membranes, axons, dendrites, etc.

https://radiologykey.com/concepts-of-diffusion-in-mri/

Principle of diffusion MRI (2/2)

Apply magnetic field gradients \(\mathbf{q}\) in different directions;
Measure the signal attenuation \(S(\mathbf{q})\) induced by restricted diffusion;

Measured signal carries information on the microstructure.

\[ S(\mathbf{q}) = \int_{\mathbb{R}^3} \rho(\mathbf{r}) e^{-i \mathbf{q} \cdot \mathbf{r}} \, d\mathbf{r} \]

Voxel size VS microstructure

Palombo et al. (2020)

\[ S(\mathbf{q}) = \sum_{i=1}^N f_i S_i(\mathbf{q}) \quad \text{with} \quad S_i(\mathbf{q}) = \int_{\mathbb{R}^3} \rho_i(\mathbf{r}) e^{-i \mathbf{q} \cdot \mathbf{r}} \, d\mathbf{r} \]

Compartment modeling

Fick, Wassermann, and Deriche (2019)

Data acquisition and modeling

Imaging parameters

\[ \mathbf{q} = \frac{\gamma \delta G}{2 \pi} \mathbf{n} \]

\(\gamma\): gyromagnetic ratio;
\(\delta\): gradient duration;
\(G\): gradient amplitude;
\(\mathbf{n}\): gradient direction.

Sensitivity to microstructure

Freely diffusing water:

\[ S(\mathbf{q}) = S_0 \exp \left( - b D \right) \]

with \(b = \gamma^2 \delta^2 G^2 \left( \Delta - \frac{\delta}{3} \right)\).

midi – a tool powered by R and Shiny

Overview

Objective

Shiny for user-friendly interface to simulate MR signals from microstructure models;
Design best experimental protocols for accurate estimation of a given set of microstructural parameters of interest.

How does it work ?

choose a set of experimental conditions;
choose a multi-compartment model to describe microstructure;
pick a microstructural parameter of interest;
fix the other model parameters (with sensible defaults provided by the app);
plot the MR signal wrt the microstructural parameter of interest.

The midi package

An R6-based package

#' Base compartment class
#'
#' @description The base class for compartment models.
#'
#' @keywords internal
BaseCompartment <- R6::R6Class(
  "BaseCompartment",
  public = list(
    #' @description Computes the signal attenuation predicted by the model.
    #'
    #' @param small_delta A numeric value specifying the duration of the
    #'   gradient pulse in milliseconds.
    #' @param big_delta A numeric value specifying the duration between the
    #'   gradient pulses in milliseconds.
    #' @param G A numeric value specifying the strength of the gradient in
    #'   mT.\eqn{\mu}m\eqn{^{-1}}.
    #' @param direction A numeric vector specifying the direction of the
    #'   gradient. Defaults to `c(0, 0, 1)`.
    #' @param echo_time A numeric value specifying the echo time in
    #'   milliseconds.
    #' @param n_max An integer value specifying the maximum order of the Bessel
    #'   function. Defaults to `20L`.
    #' @param m_max An integer value specifying the maximum number of extrema
    #'   for the Bessel function. Defaults to `50L`.
    #'
    #' @return A numeric value storing the predicted signal attenuation.
    #'
    #' @examples
    #' freeComp <- FreeCompartment$new()
    #' freeComp$get_signal(small_delta = 30, big_delta = 30, G = 0.040)
    #'
    #' sphereComp <- SphereCompartment$new()
    #' sphereComp$get_signal(small_delta = 30, big_delta = 30, G = 0.040)
    #'
    #' sodermanComp <- SodermanCompartment$new()
    #' sodermanComp$get_signal(small_delta = 30, big_delta = 30, G = 0.040)
    #'
    #' staniszComp <- StaniszCompartment$new()
    #' staniszComp$get_signal(small_delta = 30, big_delta = 30, G = 0.040)
    #'
    #' neumanComp <- NeumanCompartment$new()
    #' neumanComp$get_signal(
    #'   small_delta = 30, big_delta = 30, G = 0.040,
    #'   echo_time = 40
    #' )
    #'
    #' callaghanComp <- CallaghanCompartment$new()
    #' callaghanComp$get_signal(small_delta = 30, big_delta = 30, G = 0.040)
    #'
    #' vanGelderenComp <- VanGelderenCompartment$new()
    #' vanGelderenComp$get_signal(small_delta = 30, big_delta = 30, G = 0.040)
    get_signal = function(small_delta, big_delta, G,
                          direction = c(0, 0, 1),
                          echo_time = NULL,
                          n_max = 20L,
                          m_max = 50L) {
      private$compute_signal(
        small_delta = small_delta,
        big_delta = big_delta,
        G = G,
        direction = direction,
        echo_time = echo_time,
        n_max = n_max,
        m_max = m_max
      )
    },

    #' @description Returns the names of the compartment parameters
    #'
    #' @return A character vector storing the names of the compartment
    #'   parameters.
    #'
    #' @examples
    #' freeComp <- FreeCompartment$new()
    #' freeComp$get_parameter_names()
    get_parameter_names = function() {
      names(private$parameters())
    },

    #' @description Returns the values of the compartment parameters
    #'
    #' @return A numeric vector storing the values of the compartment
    #'   parameters.
    #'
    #' @examples
    #' freeComp <- FreeCompartment$new()
    #' freeComp$get_parameters()
    get_parameters = function() {
      private$parameters()
    }
  )
)

Should faciliate implementation of new compartment models.

Class hierarchy

The midi Shiny application

V1 powered by Quarto dashboard

I learned a lot about Quarto dashboards
The design is not very appealing
The engine behind the scene is bslib

A better app design

\[ \scriptsize{ \color{cornflowerblue}{S}(\color{salmon}{\mathbf{q}}; \Theta, \mathbf{f}) = \color{lightgreen}{f_\mathrm{free}} \cdot S_\mathrm{free}(\color{salmon}{\mathbf{q}}) + \color{lightgreen}{f_\mathrm{sphere}} \cdot \color{gold}{S_\mathrm{sphere}}(\color{salmon}{\mathbf{q}}; \color{lightgreen}{\Theta_\mathrm{sphere}}) \\ + \color{gold}{f_\mathrm{cylbundle}} \cdot \color{gold}{S_\mathrm{cylbundle}}(\color{salmon}{\mathbf{q}}; \color{lightgreen}{\Theta_\mathrm{cylbundle})}, \quad f_\mathrm{free} + f_\mathrm{sphere} + f_\mathrm{cylbundle} = 1 } \]

Courtesy of Manon Simonot

V2 powered by shiny and bslib

rhinoisation (1/2)

library(rhino)
rhino::init()

rhinoisation (2/2)

library(rhino)
rhino::init()

app directory

main.R: app source code;
js: javascript code;
logic: R objects other than UI/Server;
static: images or other static files;
styles: scss code;
view: modules.

Root files

app.R: contains only rhino::app() to launch the application;
dependencies.R: lists all dependencies;
renv/renv.lock: handles dependency versions;
config.yml/rhino.yml: configuration files;
tests: folder containing files for testing.

References

Fick, Rutger HJ, Demian Wassermann, and Rachid Deriche. 2019. “The Dmipy Toolbox: Diffusion MRI Multi-Compartment Modeling and Microstructure Recovery Made Easy.” Frontiers in Neuroinformatics 13: 64.

Palombo, Marco, Andrada Ianus, Michele Guerreri, Daniel Nunes, Daniel C Alexander, Noam Shemesh, and Hui Zhang. 2020. “SANDI: A Compartment-Based Model for Non-Invasive Apparent Soma and Neurite Imaging by Diffusion MRI.” Neuroimage 215: 116835.

Ren, Mengwei, Heejong Kim, Neel Dey, and Guido Gerig. 2021. “Q-Space Conditioned Translation Networks for Directional Synthesis of Diffusion Weighted Images from Multi-Modal Structural MRI.” In Medical Image Computing and Computer Assisted Intervention–MICCAI 2021: 24th International Conference, Strasbourg, France, September 27–October 1, 2021, Proceedings, Part VII 24, 530–40. Springer.