This study was approved by the Institutional Review Board of the Ethics Committee of the University of Siena, and a written consent was obtained by all the subjects. 52 patients with MS (32 females and 20 males; mean age 42.6±12.1 years) and 27 age-matched healthy volunteers (13 females and 14 males; mean age 37.8±11.2 years) were enrolled. Patients and healthy subjects underwent neurological assessment and CDS examination.
The patients were divided into the four different subgroups of MS, and the fifth reference group of controls. Group 1 included clinically isolated syndrome (CIS) (n:2), Group 2 included relapsing remitting MS (RRMS) (n: 31), Group 3 included secondary progressive MS (SPMS) (n:17), Group 4 included primary progressive MS (PPMS) (n:2), and Group 5 included controls (n:27). The degree of patients' disability was assessed using the Expanded Disability Status Scale (EDSS), 
the arm/hand dexterity was tested by nine hole peg test (NHPT) and leg function by timed 8meter walk test (T8) 
prior to the CDS studies.
CDS was performed by two skilled neuroradiologists (LM, and EM) with experience in ultrasound field by using a colour-coded ultrasound system (SEQUOIA, Siemens, Erlangen, Deutschland) and a 7 to 9 MHz linear probe.
The first consecutive 30 subjects (28 MS patients, and 2 controls) were examined separately by the two neuroradiologists, each blinded to the results obtained by the other one. The operators were not blinded for clinical status as healthy subjects or MS patient, but were blinded for MS subgroups. The results were then compared to evaluate the inter-observer concordance.
IJVs and VVs were studied in B-mode. To define the stenosis the vessel calibre was reduced more than 50%. The cross-sectional area (CSA) of IJVs and VVs were measured in horizontal plane, avoiding any vessel compression. The CSA of right and left IJVs were measured at their middle tract, and under valve plane in both clinostatism and seated position. The CSA of right and left VVs were measured under the valve plane in both clinostatism and seated position. Exact angle correction of Doppler frequencies was achieved by adjusting the angle between the Doppler bean and the longitudinal axes of the vessel.
CVF of IJVs and VVs was calculated from the time average velocity (TAV) and the CSA of the vessel (CVF
CSAxTAV). TAV was measured over a minimum of the three cardiac cycles at the end of the expiratory phase. 
CVF of each vein was calculated in both clinostatism and seated position. The sum of all the venous flows was then calculated in clinostatism (CVFC) and in seated position (CVFS). The difference between the CVFC and CVFS (Δ value
CVFC-CVFS) has been named ΔCVF, and included in the analysis. CBF was calculated in the same way, based on the TAV and CSA of internal carotid and vertebral arteries, only in clinostatism. 
A statistical analysis was performed between the groups (healthy subjects and MS patients) evaluating the Δ value (positive or negative) and characteristics of CVF at 0° and 90°, Δ CSA of IJVs at 0°and 90°, CBF, and clinical conditions including EDSS, disease duration, age, gender, NHPT, and T8.
Statistical analysis was performed by Fisher's exact test, non parametric Mann-Whitney U test, ANOVA Kruskal-Wallis test, and non linear correlation (correntropy coefficient).
The data showed a non Gaussian and a non symmetric behaviour, when collected by groups they even resulted in small sets of observations. The statistical analysis was performed by means of non parametric tests, namely Fisher's exact test for assessing the significance of differences in contingency tables, Mann-Whitney test and ANOVA Kruskal-Wallis test for comparing the medians of two or more groups, respectively. The level of interaction between the ΔCVF and the other variables was determined by the correntropy coefficient, which is a measure of correlation suitable for nonlinear, non Gaussian data, ranging in the interval [−1, +1], sensitive to higher order moments of the signals. More specifically, the correntropy function can be seen as a generalized correlation function in the space (feature space) spanned by the nonlinear mapping (kernel mapping) of the original data.
Unlike the Pearson's coefficient, the correntropy coefficient will produce a non zero value for two uncorrelated but not independent variables and in the context of generalized synchronization, the correntropy coefficient is able to characterize both higher order relationship and nonlinearity between interacting systems. The geometrical elucidation of the correntropy coefficient essentially is that it computes the cosine of the angle between two nonlinear transformed vectors in the higher dimensional feature space. Thus, only if the two compared series are independent, their vectors in the higher dimensional feature space will be orthogonal, and so the cosine of their angle is equal to zero. For this reason, we can recognize the correntropy coefficient as a measure of dependence (conveyed either by a linear relationship or by a nonlinear one).