What voxel models are supported by QIT?

QIT has special features for working with model-based imaging data. Most imaging data represents colors or grayscale intensities at each pixel, but scientific imaging data can also represent physical measurements. Magnetic resonance (MR) imaging can also be used to depict a spatial distribution of such physical measurements. There are many types of physical processes that can be characterized using MR, for example relaxation rates, diffusivities, compartment proportions, etc. QIT is designed to support many of the commonly encountered models, particularly those obtained from diffusion MR imaging. In this section, we will discuss the way models are supported by QIT and how you can use them.

What is a Model?

A Model object represents a collection of parameters of some physical model, typically stored in an image voxel. We use this type of object-oriented approach because most useful models are multivariate and have some constraints on what model parameters are valid. QIT is designed to make it possible to treat these special imaging datasets like any other data, but it allows allows more advanced visualization techniques, like creating 3D renderings of model imaging data using glyphs.

There are several characteristics shared by all models:

• A Model can be encoded (or parameterized) by a Vect
• A Model has any number of named Vect valued features
• A Model has a way to compute the distance between it any other model of the same type

This representation is flexible and can be used for storing model data in Volume datasets, or any other datatype that uses Vect object. This simplifies things greatly, as all of their existing file formats and Module objects are available for use with model data. It also allows model data to be treated in special ways, for example, in specially designed image processing algorithms or in glyph-based visualization.

However, even though a Model can be converted to a Vect, it is important to remember that they often cannot be treated like vectors algebraically. For example, you may be tempted to add together, scale, or compute the magnitude of Vects derived from a Model; however, if the model parameters store a vector representing a 3D direction as a point on a sphere, then adding those values may leave you with model parameters that don’t make any sense, i.e. no longer lie on a sphere.

What types of Model are available?

Below is a detailed list of the models supported by QIT. A general description of each model is provided and any peculiarities are noted as well.

This list is a work in progress and will eventually be expanded to provide more detail regarding the parameters, features, and motivation behind each model.

Tensor

The Tensor model is the basis for diffusion tensor imaging (DTI). DTI depicts the decay of the diffusion signal using a 3x3 positive definite matrix, which provides a way to depict an ellipsoid-shaped pattern of diffusion. The shape of the tensor can be used to characterize the tissue being modeled, and this is usually done by extracting a variety of features. The primary orientation of the tensor is typically visualized to depict the dominant orientation of axonal fibers within the vowel. Fractional anisotropic is a feature that conveys the degree to which the tensor is anisotropic, or cigar-shaped. Mean diffusivity describes the overal shape of the tensor (regardless of its anisotropic). The tensor diffusivity can also be depicted in specific directions, for example, axial diffusivity describes the diffusivity in the direction of the primary orientation, and radial diffusivity describes the diffusivity in the plane orthogonal to the primary orientation.

Fibers

The Fibers model is used for representing the multi-compartment ball and sticks model. This model was developed to address shortcomings of the tensor model, namely that it cannot accurately depict voxels with multiple distinct components. For example, a voxel may contain some gray matter or cerebrospinal fluid in addition to white matter fibers, or it may combine white matter fibers from distinct fascicles that cross. Multi-compartment models address this issue by depicting the diffusion signal with a linear combination of tissue compartments. The ball and sticks model s a simple but powerful special case of this approach, in which the signal is decomposed into compartments for isotopic diffusion and some arbitrary number of fibers populations. The diffusivities of the compartments are assumed to be identical and each fiber compartment is formulated as an infinitely thin cylinder. This enables the model to distinguish between crossing fibers, as well as more complex mixtures with gray matter and CSF. Each compartment is assigned a volume fraction, which indicates the proportion of the signal that it explains. Two common features to extract are the total fiber volume fraction (the sum of the individual fiber compartment volume fractions), the isotopic volume fraction, and the diffusivity.

Spharm

The Spharm model represents a fiber orientation distribution (FOD) using a spherical harmonic basis. Spherical harmonics decompose a function on the sphere into a set of basis coefficients, analogous to a Fourier transform on a sphere. QIT supports even-order harmonics (orders 0, 2, 4, 6, 8, 10, 12, 14, and 16), with the number of coefficients increasing with the maximum order (e.g. 1, 6, 15, 28, 45 coefficients for orders 0 through 8). This representation provides a compact and rotationally convenient encoding of complex directional diffusion patterns, particularly in regions with crossing fibers where the tensor model is insufficient. FODs estimated by constrained spherical deconvolution can be stored and manipulated using this model, and they can be sampled in any direction to obtain the orientation distribution function value. Features include the baseline coefficient (related to total signal), as well as summary statistics of the coefficients. The Spharm model is commonly used with glyph visualizations and fiber tractography algorithms that support orientation distribution functions.

Noddi

The Noddi model is a biophysical model of brain tissue microstructure based on Neurite Orientation Dispersion and Density Imaging (NODDI). It decomposes the diffusion signal into three compartments: an intracellular compartment representing neurites (axons and dendrites), an extracellular compartment representing the space around neurites, and an isotropic compartment representing free water such as cerebrospinal fluid. The model is parameterized by a baseline signal, an intracellular volume fraction (FICVF, representing neurite density), an isotropic volume fraction (FISO), a concentration parameter (kappa) for the Watson distribution describing fiber orientation dispersion, and a 3D fiber direction. Several derived features can be extracted: the orientation dispersion index (ODI), which indicates the degree of fiber fanning or crossing; the extracellular volume fraction (ECVF); and tortuosity-related diffusivity measures. NODDI provides more biologically interpretable tissue parameters than standard DTI, making it valuable for characterizing white matter pathology, development, and aging.

Kurtosis

The Kurtosis model is the basis for diffusion kurtosis imaging (DKI), which extends the diffusion tensor model to capture non-Gaussian diffusion behavior. While DTI models signal decay with a second-order tensor (6 unique elements), DKI adds a fourth-order kurtosis tensor (15 unique elements), for a total of 22 model parameters plus a baseline signal. The kurtosis tensor characterizes the degree to which diffusion deviates from a Gaussian distribution, which is informative about tissue microstructural complexity. Key features include mean kurtosis (MK), axial kurtosis (AK), and radial kurtosis (RK), in addition to the standard DTI features (FA, MD, AD, RD). DKI requires multi-shell diffusion data (at least two non-zero b-values) and is particularly sensitive to microstructural changes in pathological conditions such as stroke, traumatic brain injury, and neurodegeneration. The implementation in QIT includes support for computing the diffusion and kurtosis orientation distribution functions.

ExpDecay

The ExpDecay model represents a simple exponential decay process of the form y = alpha * exp(-beta * x). The model has two parameters: alpha, representing the baseline signal amplitude, and beta, representing the decay rate. In the context of diffusion MRI, alpha corresponds to the unweighted signal intensity (S0) and beta corresponds to the apparent diffusion coefficient (ADC). This model provides a straightforward way to characterize signal attenuation without directional information and is commonly used for basic ADC mapping in clinical diffusion-weighted imaging, or as an initial fit before applying more complex models.