Mathematical modelling characterises fatigability as a distinct phenomenon in patients with multiple sclerosis

Background: Cognitive fatigue may manifest as subjective sensation or objective changes in performance, referred as fatigue and fatigability, respectively. There are difficulties in measuring fatigability and it is debated whether it may represent an aspect of cognitive impairment rather than a distinct phenomenon. Objective: To apply analythical models to experimental data of processing speed obtained with the Symbol Digit Modalities Test (SDMT) to test whether cognitive impaired patients (CI) behaviour differently from cognitive preserved (CP) ones. Methods: Patients with MS and healthy subjects (HS) underwent an extended version of the SDMT. The number of correct answers (NCA) was recorded every 30s for a total time of 180s. The total score at 90s was used to divide patients into 2 groups: cognitive impaired (CI) or cognitive preserved (CP) according to a test score below or above the 10th percentile of normative data. The Modified Fatigue Impact Scale (MFIS) and the Beck Depression Inventory (BDI) were also administered to measure subjective fatigue and depression. We applied mathematical modelling to investigate whether the behavioural of the SDMT performance over time is a log linear relationship or need a more complex function. Results: We enrolled 173 patients (age 47.3+/-8.6 year old, 116 women, disease duration 12.4+/-8.4 years), distinguished in 119 CI (49.0+/-8.1 years old) and 34 CP (43.5+/-8.6 years old), and 34 HS (43.0+/-14.2, 19 women). CI were older compared with CP and HS (respectively p< 1E-4, p< 0.03), no difference were found between HS and CP. The addition of a parameter b to the loglinear model was necessary to describe the deflection of the performance at the end of task CP and to a lesser extent in HS (CPs p< 5e-4 and p< 0.01 respectively). This parameter b, that could express fatigability, is relevant in CP (5.4+/-2.0) while being close to 0 and affected by variance in HS (2.8+/-2.3). In CI the loglinear model was enough to explain the performance over time without the addition of parameter b. In patients, the b parameter did not correlated with MFIS and BDI scores. Conclusions: We suggest that cognitive fatigability is a distinct phenomenon that can be properly quantified in the single patient by the calculation of the b parameter. Cognitive fatigability that is only detectable in the CP group, should be taken into account in the administration of cognitive batteries