Detecting microstructural white matter abnormalities of frontal pathways in children with ADHD using advanced diffusion models

Abstract

Studies using diffusion tensor imaging (DTI) have documented alterations in the attention and executive system in children and adolescents with attention-deficit/hyperactivity disorder (ADHD). While abnormalities in the frontal lobe have also been reported, the associated white matter fiber bundles have not been investigated comprehensively due to the complexity in tracing them through fiber crossings. Furthermore, most studies have used a non-specific DTI model to understand white matter abnormalities. We present results from a first study that uses a multi-shell diffusion MRI (dMRI) data set coupled with an advanced multi-fiber tractography algorithm to probe microstructural measures related to axonal/cellular density and volume of fronto-striato-thalamic pathways in children with ADHD (N = 30) and healthy controls (N = 28). Head motion was firstly examined as a priority in order to assure that no group difference existed. We investigated 45 different white matter fiber bundles in the brain. After correcting for multiple comparisons, we found lower axonal/cellular packing density and volume in ADHD children in 8 of the 45 fiber bundles, primarily in the right hemisphere as follows: 1) Superior longitudinal fasciculus-II (SLF-II) (right), 2) Thalamus to precentral gyrus (right), 3) Thalamus to superior-frontal gyrus (right), 4) Caudate to medial orbitofrontal gyrus (right), 5) Caudate to precentral gyrus (right), 6) Thalamus to paracentral gyrus (left), 7) Caudate to caudal middlefrontal gyrus (left), and 8) Cingulum (bilateral). Our results demonstrate reduced axonal/cellular density and volume in certain frontal lobe white matter fiber tracts, which sub-serve the attention function and executive control systems. Further, our work shows specific microstructural abnormalities in the striato-thalamo-cortical connections, which have not been previously reported in children with ADHD.

Appendix

Let $A = \left \{ x_{j} \right \}_{j = 1}^{n_{1}}$denote all ADHD samples and $C = \left \{ {x_{j} } \right \}_{j = n_{1} + 1}^{n_{1} + n_{2} }$ be the health controls. Then, the mean for each group can be computed as follows:

$$ m_{A} = \frac{1}{n_{1} }\sum\limits_{j = 1}^{n_{1} } {x_{j} } ,\text{ } \text{ } m_{C} = \frac{1}{n_{2} }\sum\limits_{j = n_{1} + 1}^{n_{1} + n_{2} } {x_{j} } $$

(3)

The covariance matrix for each group can be computed as follows:

$$ \begin{array}{@{}rcl@{}} S_{A} &=& \sum\limits_{j = 1}^{n_{1} } {\left( {x_{j} - m_{A} } \right) \cdot \left( {x_{j} - m_{A} } \right)^{T}} ,\\ \text{ }S_{C} &=& \sum\limits_{j = n_{1} + 1}^{n_{1} + n_{2} } {\left( {x_{j} - m_{C} } \right) \cdot \left( {x_{j} - m_{C} } \right)^{T}} \end{array} $$

(4)

Then, the within-class covariance matrix Θ_W is given by:

$$ {\Theta}_{W} = \frac{n_{1} }{n_{1} + n_{2} } \cdot S_{A} + \frac{n_{2} }{n_{1} + n_{2} } \cdot S_{C} $$

(5)

Let m be the overall mean of all samples, then we have:

$$ m = \frac{1}{n_{1} + n_{2} }\sum\limits_{j = 1}^{n_{1} + n_{2} } {x_{j} } $$

(6)

The between-class variance matrix Θ_B can then be written as:

$$ \begin{array}{@{}rcl@{}} {\Theta}_{B} &=& \frac{n_{1} }{n_{1} + n_{2} } \cdot \left( {m_{A} - m} \right) \cdot \left( {m_{A} - m} \right)^{T} \\ &&+ \frac{n_{2} }{n_{1} + n_{2} } \cdot \left( {m_{C} - m} \right) \cdot \left( {m_{C} - m} \right)^{T} \end{array} $$

(7)

Then, the matrix ${\Theta } = {\Theta }_{W}^{- 1} \cdot {\Theta }_{B}$, and the projection onto Y is computed as: Y = X ⋅Θ.