Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
, 24, 101990

Fractal Dimension of Cerebral White Matter: A Consistent Feature for Prediction of the Cognitive Performance in Patients With Small Vessel Disease and Mild Cognitive Impairment

Affiliations

Fractal Dimension of Cerebral White Matter: A Consistent Feature for Prediction of the Cognitive Performance in Patients With Small Vessel Disease and Mild Cognitive Impairment

Leonardo Pantoni et al. Neuroimage Clin.

Abstract

Patients with cerebral small vessel disease (SVD) frequently show decline in cognitive performance. However, neuroimaging in SVD patients discloses a wide range of brain lesions and alterations so that it is often difficult to understand which of these changes are the most relevant for cognitive decline. It has also become evident that visually-rated alterations do not fully explain the neuroimaging correlates of cognitive decline in SVD. Fractal dimension (FD), a unitless feature of structural complexity that can be computed from high-resolution T1-weighted images, has been recently applied to the neuroimaging evaluation of the human brain. Indeed, white matter (WM) and cortical gray matter (GM) exhibit an inherent structural complexity that can be measured through the FD. In our study, we included 64 patients (mean age ± standard deviation, 74.6 ± 6.9, education 7.9 ± 4.2 years, 53% males) with SVD and mild cognitive impairment (MCI), and a control group of 24 healthy subjects (mean age ± standard deviation, 72.3 ± 4.4 years, 50% males). With the aim of assessing whether the FD values of cerebral WM (WM FD) and cortical GM (GM FD) could be valuable structural predictors of cognitive performance in patients with SVD and MCI, we employed a machine learning strategy based on LASSO (least absolute shrinkage and selection operator) regression applied on a set of standard and advanced neuroimaging features in a nested cross-validation (CV) loop. This approach was aimed at 1) choosing the best predictive models, able to reliably predict the individual neuropsychological scores sensitive to attention and executive dysfunctions (prominent features of subcortical vascular cognitive impairment) and 2) identifying a features ranking according to their importance in the model through the assessment of the out-of-sample error. For each neuropsychological test, using 1000 repetitions of LASSO regression and 5000 random permutations, we found that the statistically significant models were those for the Montreal Cognitive Assessment scores (p-value = .039), Symbol Digit Modalities Test scores (p-value = .039), and Trail Making Test Part A scores (p-value = .025). Significant prediction of these scores was obtained using different sets of neuroimaging features in which the WM FD was the most frequently selected feature. In conclusion, we showed that a machine learning approach could be useful in SVD research field using standard and advanced neuroimaging features. Our study results raise the possibility that FD may represent a consistent feature in predicting cognitive decline in SVD that can complement standard imaging.

Keywords: Fractal dimension; LASSO regression; Machine learning; Mild cognitive impairment; Small vessel disease; White matter.

Conflict of interest statement

None.

Figures

Fig. 1
Fig. 1
Overview of the neuroimaging feature extraction procedure for LASSO (least absolute shrinkage and selection operator) regression. We fitted a separate regression model for each neuropsychological test. WM and GM volumes are normalized to the estimated intracranial volume (EPVS = enlarged perivascular spaces, FD = fractal dimension, FLAIR = Fluid-attenuated inversion recovery, GM = gray matter, Mfs = maximum fractal scale, mfs = minimum fractal scale, WM = white matter). Demographic variables (age, sex and level of education) have been inserted as additional predictors to model possible residual effects in the patient population.
Fig. 2
Fig. 2
Example of a WM and a cortical GM segmentation mask in one patient with SVD and MCI. A) A 3-D view of the GM/WM interface surface; B) A coronal slice of the WM volume mask; C) The log-log plot of N(r) counts vs. cube side r (mm) is shown for the cerebral WM volume mask. The regression line, which showed the highest R2adj (0.9999) and a sign changed slope (i.e., FD) equal to 2.4530, is also superimposed. The WM mfs was 21 = 2 mm and the WM Mfs was 25 = 32 mm; D) A 3-D view of the pial surface; E) A coronal slice of the GM volume mask; F) The log-log plot of N(r) counts vs. cube side r (mm) is shown for the cortical GM volume mask. The regression line, which showed the highest R2adj (0.9996) and a sign changed slope (i.e., FD) equal to 2.4429, is also superimposed. The GM mfs was 20 = 1 mm and the GM Mfs was 25 = 32 mm.
Fig. 3
Fig. 3
Ranking of LASSO-based neuroimaging feature selection. For each significant model, the frequency with which each feature was selected (coefficient different from zero) across all outer CV folds in 1000 repetitions of LASSO regression is shown. The features have been reordered based on the occurring average frequencies. Red bars indicate the frequency with which the corresponding coefficient was positive (direct association with the neuropsychological scores) – whereas blue bars, the frequency with which the corresponding coefficient was negative (inverse association with the neuropsychological scores).
Fig. 4
Fig. 4
The average frequency among MoCA, SDMT and TMT-A tests with which each neuroimaging feature was selected (coefficient different from zero) across all outer CV folds in 1000 repetitions of LASSO regression among MoCA, SDMT and TMT-A tests is shown.

Similar articles

See all similar articles

References

    1. Ad-Dab'bagh Y., Singh V., Robbins S., Lerch J., Lyttelton O., Fombonne E., Evans A. 11th Annual Organization for Human Brain Mapping Meeting. 2005. Native-space cortical thickness measurement and the absence of correlation to cerebral volume.
    1. Breiman L., Spector P. Submodel selection and evaluation in regression. The X-random case. Int. Stat. Rev. 1992;60:29.
    1. Bullmore E., Brammer M., Harvey L., Persaud R., Murray R. Fractal analysis of the boundary between white matter and cerebral cortex in magnetic resonance images: a controlled study of schizophrenic and mani-depressive patients. Psychol. Med. 1994;24:771–781. - PubMed
    1. Caffarra P., Vezzadini G., Dieci F., Zonato F., Venneri A. Rey-Osterrieth complex figure: normative values in an Italian population sample. Neurol. Sci. 2002;22:443–447. - PubMed
    1. Caffarra P., Vezzadini G., Dieci F., Zonato F., Venneri A. Una versione abbreviata del test di Stroop. Dati normativi nella popolazione italiana. Nuova Rivista di Neurologia. 2002;12:111–115.

LinkOut - more resources

Feedback