In the last post we took a loot at the NODDI model that provides neurite density and orientation dispersion estimates by disentangling two key contributing factors to FA. This enables the analysis of each factor individually.
The following image helps summarize the model components:
As mentioned above and in the previous post, NODDI model consists of 3 major sub-models for fitting the data in:
- Intra-Cellular Region
- Extra-Cellular Region
- Cerebrospinal Fluid (CSF Area)
A major shortcoming of the NODDI model was that it could fit only one fiber at a time for neurite orientation patterns observed in brain tissue that include:
- Highly coherently oriented white matter structures, such as the corpus
- White matter structures composed of bending and fanning axons, such as the centrum semiovale.
- The cerebral cortex and subcortical gray matter structures characterized by sprawling dendritic processes in all directions.
However, with the NODDIx model, we can fit 2 fibers that are in the form of crossings and visualize them using Microstructure Imaging. An example of the same would be as follows:
The code has been written in such a way that we can make use of the dame functions in the code to generate a signal per voxel and make sure that the model is fitting properly.
To do so, we fix the input parameters that we are giving to generate the signal and try to estimate them using the NODDIx model. Note, we will have 2 fiber crossings and we can explicitly test for different angles between the fibers with pre-defined volume fractions.
For simplicity and easy understanding of the estimates, we set the parameters as follows:
The volume fractions have been set to equal: Intracellular Volume Fraction 1: 0.2 Intracellular Volume Fraction 2: 0.2 Extracellular Volume Fraction 1: 0.2 Extracellular Volume Fraction 2: 0.2 CSF Volume Fraction: 0.2
Lets now fix the Orientation Dispersions (OD) and the Thetas and Phis:
OD1: 0.2 Theta1: 0.72 Phi1: 1.57 OD2: 0.24 Theta2: 0.72 Phi2: 1.57 For both the fibers, the angle between the Theta and the Phi has been set to 41 degrees approximately.
These are the 11 parameters that the model is estimating… Lets see how the estimates look on the simulation data!
[Note: We expect the estimates to be almost the same as the input values…]
The estimated volume fractions are: Intracellular Volume Fraction 1: 0.19739277 Intracellular Volume Fraction 2: 0.1947075 Extracellular Volume Fraction 1: 0.20260892 Extracellular Volume Fraction 2: 0.2052905 CSF Volume Fraction: 0.20000128
The volume fractions seem to be estimated almost perfectly! Lets take a look at the ODs, Thetas and Phis;
OD1: 0.20045016 Theta1: 0.72000357 Phi1: 1.56999562 OD2: 0.24062461 Theta2: 0.71999553 Phi2: 1.5700052 Yep, they look almost the same! So basically, the NODDIx Model is up and running! [Note: Code for the above simulation and fit can be found here]
The speed of the fit needs to be taken care of though!
In the next post, I will try to speedup the code and have a rigorous code profiling!