Phantom

The first input argument that KomaMRI needs for simulating is the phantom.

This section goes over the concept of digital phantom and shows how it applies to the specific case of KomaMRI. We'll go into detail about the Phantom structure and its supported operations.

Digital Phantom

A digital phantom is basically a computer model of a physical object (like the human body or a body part) which is used in simulations to mimic the characteristics and behaviour that would be obtained from real MRI. Instead of using a physical object for testing, the digital phantom allows for virtual experiments.

This computer model should essentially contain information about the position and/or displacements of the tissues, as well as their MRI-related (T1, T2, PD, off-resonance...) values.

KomaMRI Phantom Overview

In Koma, a phantom is made up of a set of spins (which in many cases are also known as ''isochromats''). Each spin is independent of the others in terms of properties, position and state. This is a key feature of KomaMRI, as it is explained in the Simulation section.

A Phantom stores one value per spin for each physical property:

Field	Meaning
name	Phantom name.
x, y, z	Initial spin positions in metres.
ρ	Proton density.
T1, T2, T2s	Relaxation times in seconds.
Δw	Off-resonance in rad/s.
Dλ1, Dλ2, Dθ	Diffusion-related fields.
motion	Spin displacement model.

These vectors represent object properties, with each element holding a value associated with a single magnetization (i.e. a single spin). Specifically, x, y and z are the initial spatial coordinates of each spin. ρ stands for the proton density, and T1, T2 and T2s (standing for T2*) are the well-known relaxation times. Δw accounts for off-resonance effects. Dλ1, Dλ2 and Dθ are diffusion-related fields which are not in use at the moment. Last, the motion field stands for spin displacements, which are added to x, y and z when simulating in order to obtain the spin positions at each time step. For more information about motion, refer to Motion section.

To get an even better understanding on how this structure works, let's look at an example of a brain phantom:

obj = brain_phantom2D()

Phantom{Float64}
  name: String "brain2D_axial"
  x: Array{Float64}((6506,)) [-0.084, -0.084, -0.084, -0.084, -0.084, -0.084, -0.084, -0.084, -0.084, -0.084  …  0.084, 0.084, 0.084, 0.084, 0.086, 0.086, 0.086, 0.086, 0.086, 0.086]
  y: Array{Float64}((6506,)) [-0.03, -0.028, -0.026, -0.024, -0.022, -0.02, -0.018, -0.016, -0.014, -0.012  …  0.006, 0.008, 0.01, 0.012, -0.008, -0.006, -0.004, -0.002, 0.0, 0.002]
  z: Array{Float64}((6506,)) [-0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0  …  0.0, 0.0, 0.0, 0.0, -0.0, -0.0, -0.0, -0.0, 0.0, 0.0]
  ρ: Array{Float64}((6506,)) [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0  …  1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
  T1: Array{Float64}((6506,)) [0.569, 0.569, 0.569, 0.569, 0.569, 0.569, 0.569, 0.569, 0.569, 0.569  …  0.569, 0.569, 0.569, 0.569, 0.569, 0.569, 0.569, 0.569, 0.569, 0.569]
  T2: Array{Float64}((6506,)) [0.329, 0.329, 0.329, 0.329, 0.329, 0.329, 0.329, 0.329, 0.329, 0.329  …  0.329, 0.329, 0.329, 0.329, 0.329, 0.329, 0.329, 0.329, 0.329, 0.329]
  T2s: Array{Float64}((6506,)) [0.058, 0.058, 0.058, 0.058, 0.058, 0.058, 0.058, 0.058, 0.058, 0.058  …  0.058, 0.058, 0.058, 0.058, 0.058, 0.058, 0.058, 0.058, 0.058, 0.058]
  Δw: Array{Float64}((6506,)) [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
  Dλ1: Array{Float64}((6506,)) [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
  Dλ2: Array{Float64}((6506,)) [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
  Dθ: Array{Float64}((6506,)) [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
  motion: NoMotion NoMotion()

You can visualize the Phantom struct using the plot_phantom_map function, which is part of the KomaMRIPlots subdependency. This function plots the magnitude of a property for each magnetization at a specific spatial position. You can observe properties such as proton density and relaxation times, so feel free to replace the :T1 symbol with another property of the phantom in the example below:

p1 = plot_phantom_map(obj, :T1; height=450)

You can access and filter information for the all the field names of a Phantom using the dot notation:

obj.name

"brain2D_axial"

obj.x

6506-element Vector{Float64}:
 -0.084
 -0.084
 -0.084
 -0.084
 -0.084
 -0.084
 -0.084
 -0.084
 -0.084
 -0.084
  ⋮
  0.084
  0.084
  0.084
  0.086
  0.086
  0.086
  0.086
  0.086
  0.086

obj.motion

NoMotion()

Phantom Operations

In addition, KomaMRI supports some phantom operations:

Phantom Subset

It is possible to access a subset of spins in a Phantom by slicing or indexing. The result will also be a Phantom struct, allowing you to perform the same operations as you would with a full Phantom:

obj[1:2000]

Combination of Phantoms

In the same way, we can add two or more phantoms, resulting in another Phantom struct:

obj2 = pelvis_phantom2D()
obj_sum = obj + obj2

Scalar multiplication of a Phantom

Finally, multiplying a phantom by a scalar multiplies its proton density (ρ) by that amount:

obj_mul = 3*obj;

obj.ρ

6506-element Vector{Float64}:
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 ⋮
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0

obj_mul.ρ

6506-element Vector{Float64}:
 3.0
 3.0
 3.0
 3.0
 3.0
 3.0
 3.0
 3.0
 3.0
 3.0
 ⋮
 3.0
 3.0
 3.0
 3.0
 3.0
 3.0
 3.0
 3.0
 3.0

Phantom Storage and Sharing

Phantoms can be stored and shared thanks to our new Phantom File Format.

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