Превышение зависимости от предыдущих ожиданий при пересылке множественных склерозов.

Introduction

Multiple sclerosis (MS) is a chronic inflammatory disease of the central nervous system and remains one of the leading causes of non-traumatic disability among young adults. 1 Disability in MS is not limited to physical symptoms. Cognitive impairment is prevalent in MS and can lead to a reduced quality of life, social functioning, and employment. 2 , 3 Previous studies have shown that cognitive impairment can begin early in the disease course, even before the onset of other clinical signs and symptoms. 4 Moreover, cognitive decline and disease progression can occur even in the absence of other neurological signs, 5 underscoring the importance of cognitive assessment in patients with MS.

Despite the clinical importance of cognitive impairment in MS, its assessment and definition remain challenging. Systematic neuropsychological studies have demonstrated deficits across multiple domains, with impairments in information processing speed, memory, and executive functions consistently reported. 3 , 6 Among these, slowed information processing speed has long been considered a core feature of cognitive dysfunction in MS. The Symbol Digit Modalities Test (SDMT) has been widely used to assess this domain and has performed well as a screening tool. However, recent large longitudinal studies have questioned its sensitivity as a marker of cognitive decline and disease progression. 7 , 8 , 9 , 10 Moreover, MS is characterized by substantial heterogeneity in both clinical presentation and cognitive phenotypes. 11 , 12 , 13 Consequently, relying on a test targeting one specific domain may miss cognitive impairments in many patients. These limitations highlight the need to develop innovative approaches for cognitive evaluation in MS.

Notably, sensory processing deficits, memory dysfunction, and motor impairments are well-documented clinical features of MS. However, these components have not been systematically integrated into a unified framework to explain cognitive dysfunction. In this study, we adopt a Bayesian sensory-motor framework to address this gap. 14 Within this framework, the brain is viewed as an inference system that operates under uncertainty. Although the external world is rich in information, our ability to acquire sensory input is limited, and sensory measurements are inherently noisy. To overcome these constraints, the brain generates prior expectations and integrates them with incoming sensory evidence to optimize perception and action. Over the past two decades, this framework has proven valuable for studying brain function, supported by well-established behavioral paradigms and computational models (for review, see works by Ma and Jazayeri and by Körding and Wolpert 14 , 15 ).

In this study, we used a time reproduction paradigm within this Bayesian framework to investigate cognitive impairment in patients with MS. This task is particularly well suited to test sensory-motor hypotheses because it requires encoding a temporal interval from noisy sensory input, maintaining it in working memory and making inferences about it, and reproducing it through a motor response. 16 Previous studies have shown that this task engages multiple brain regions, reflecting the integration of distributed perceptual, cognitive, and motor systems. 17 , 18 At the computational level, well-established models allow task performance to be decomposed into distinct stages, enabling investigation of the mechanisms underlying different response patterns. 16 , 19

Results

Participants completed a tablet-based time reproduction task in which they measured and reproduced time intervals between two visual flashes ( Figure 1 ). Five interval durations (0.4–1.9 s) were presented pseudorandomly, and feedback was provided after each trial. For each participant, we performed a linear regression between presented and reproduced times, where the intercept captured overall over- or underestimation and the slope reflected sensitivity to duration changes and systematic bias. We then used a modified Bayesian observer model that divides time reproduction into three stages: sensory measurement, time estimation, and motor response. Each stage is described by one parameter: measurement noise (w m ), gain factor (α), and motor noise (wᵣ), respectively. The gain factor (α) captures systematic over- or underestimation in the estimation stage by applying a multiplicative scaling to the estimated interval (α > 1 indicates overestimation of time intervals, whereas α < 1 indicates underestimation). Figure 1 Time reproduction task paradigm Each trial began with a fixation point and two peripheral targets (fixation). After a random delay, the first wheel-like stimulus (stimulus I) was briefly presented, followed by a sample interval (t s ) and then a second stimulus (stimulus II). Participants were instructed to measure the duration between the two flashes and reproduce it (t r ) by tapping on the right side of the screen (reproduction). At the end of each trial, feedback was provided showing the response error (t r - t s ) in milliseconds (feedback).

We collected data from 92 patients with relapsing-remitting MS and 149 control participants. After exclusion, we enrolled 79 and 140 participants for the MS and control groups, respectively (see STAR Methods for details). The MS and control groups did not differ significantly in age (MS: 36.33 ± 7.64 years; control: 34.74 ± 8.12 years; p = 0.065), gender (MS: 73.42% female; control: 71.43% female; p = 0.99), or education (MS: 19.00% graduate degree; control: 22.14% graduate degree; p = 1.00). Patients showed significantly slower performance on the Nine-Hole Peg Test (9HPT; 24.72 ± 5.55 vs. 20.32 ± 2.93 s, p < 0.001) and reported higher anxiety levels (Beck Anxiety Inventory [BAI]; 12.76 ± 9.93 vs. 9.21 ± 7.72, p = 0.006). Other variables did not differ significantly between groups ( Table 1 ). Table 1 Demographic and clinical characteristics Variable MS ( N = 79) Healthy ( N = 140) p value Statistics Age 36.33 ± 7.64 34.74 ± 8.12 0.065 4726 Graduate degree 15 (19.00) 31 (22.14) 1 0 Gender, female 58 (73.42) 100 (71.43) 0.99 0 9HPT 24.72 ± 5.55 20.32 ± 2.93 < 0.001 2628 HADS 11.01 ± 7.67 10.84 ± 6.40 0.86 5680 MFIS-physical 12.57 ± 9.58 10.08 ± 7.40 0.07 4716 MFIS-cognitive 11.01 ± 9.06 9.31 ± 8.46 0.13 4841 MFIS-psychosocial 2.54 ± 2.54 3.08 ± 5.67 0.83 5615 Beck 13.54 ± 10.35 11.63 ± 9.50 0.16 4932 BAI 12.76 ± 9.93 9.21 ± 7.72 0.006 4347 FSS 36.13 ± 15.68 34.67 ± 11.92 0.16 4962 EDSS 1.06 ± 1.10 – – – Disease duration 9.33 ± 5.78 – – – Continuous variables are mean ± SD; categorical variables are n (%). The statistics column reports the Mann-Whitney U statistic for continuous variables and the chi-square (χ 2 ) statistic for categorical variables. 9HPT, Nine-Hole Peg Test; HADS, Hospital Anxiety and Depression Scale; MFIS, Modified Fatigue Impact Scale; BAI, Beck Anxiety Inventory; FSS, Fatigue Severity Scale; EDSS, Expanded Disability Status Scale. Bold values indicate p < 0.05.

Increased temporal bias in MS

We plotted the participants’ average reproduced time against the presented time interval for the control ( Figure 2 A) and the MS ( Figure 2 B) groups. We then applied linear regression between the presented time and the reproduced time, separately for the control and the MS participants. In this task, the intercept of the regression reflects overall shifts in time reproduction: higher intercepts indicate a general tendency to overestimate, while lower intercepts suggest underestimation. The slope represents sensitivity to changes in duration; a slope of 1 reflects optimal timing, whereas deviations from 1 indicate systematic bias in reproducing shorter or longer intervals. The slope of the fitted line was smaller in the MS group (mean ± standard deviation: 0.50 ± 0.26) than in the control group (0.58 ± 0.22, t(142.8) = 2.36, p = 0.027, Cohen’s d = 0.33; Figure 2 C), which means participants in the MS group were less sensitive to time than those in control groups (or more biased toward the mean). The intercept of the fitted lines was not different between the two groups (MS = 0.51 ± 0.27, control = 0.44 ± 0.23, U = 4,716, p = 0.07; Figure 2 D). Figure 2 Time reproduction in MS and control groups (A and B) Average reproduced time plotted against presented intervals for control (A, green; n = 140) and MS (B, orange; n = 79) groups. Solid circles indicate the mean reproduced time for each interval; error bars show the standard deviation (SD). Solid lines are the best-fit linear regressions (slope and intercept shown in each legend); gray circles and error bars show the mean ± SD of model simulations. The dashed diagonal is the identity line ( x = y ). Both groups overestimated shorter intervals and underestimated longer intervals, with a scalar increase in variability with interval duration; the Bayesian observer model captured both features. (C and D) Individual regression slopes (C) and intercepts (D) for control (green, n = 140) and MS (orange, n = 79) participants. Boxes show the median and interquartile range (IQR). Slopes were significantly lower in MS (independent-samples t test with Welch’s correction: t(142.8) = 2.36, p = 0.027, Cohen’s d = 0.33), indicating reduced sensitivity to interval duration; intercepts did not differ between groups (Mann-Whitney U test: U = 4,716, p = 0.07). ∗ p < 0.05.

Increased w m as a source of temporal bias in MS

To identify the source of decreased sensitivity (or increased bias toward the mean) in patients with MS, we applied a Bayesian observer model. This model allowed us to separately quantify variability at the time measurement stage (w m ), estimation stage (α), and motor reproduction stage (w r ). The model provided a good fit to the data for both the control (R 2 = 0.99) and MS (R 2 = 0.99) groups. We then compared the fitted parameters of the model between the two groups. The w m was significantly larger in the MS group (0.38 ± 0.15) than in the control group (0.32 ± 0.11; U = 4,328, p = 0.008, Cohen’s d = 0.44; Figure 3 A). In contrast, w r did not differ between the groups (control: 0.24 ± 0.09; MS: 0.24 ± 0.10; U = 5,713, p = 0.68; Figure 3 B). Similarly, α showed no significant difference between groups (control: 0.98 ± 0.20; MS: 0.96 ± 0.26; U = 5,414, p = 0.80; Figure 3 C). Figure 3 Bayesian observer model parameters in MS and control groups Model parameters fitted per participant: measurement noise (w m , A), motor noise (wᵣ, B), and gain factor (α, C) for control (green, n = 140) and MS (orange, n = 79) groups. Boxes show the median and IQR; points are individual participants. w m was significantly larger in MS (Mann-Whitney U test: U = 4,328, p = 0.008, Cohen’s d = 0.44), whereas wᵣ (U = 5,713, p = 0.68) and α (U = 5,414, p = 0.80) did not differ between groups. ∗ p < 0.05.

Impact of demographic and clinical factors on time reproduction

We used univariate linear regression to assess the effects of demographic and clinical factors on two key outcomes that were worse for MS patients than for the control group, the slope of reproduction time and w m , within each group. Regression results are presented in Table 2 . None of the demographic or clinical variables were significantly associated with time reproduction slope or w m in the MS group, though these null findings should be interpreted cautiously, given the exploratory nature of the analyses and the number of predictors tested. In healthy participants, age was significantly associated with reproduction slope (β = −0.007, t(138) = −3.004, p- adj = 0.035) and w m (β = 0.004, t(138) = 3.801, p- adj = 0.002). w m was also significantly associated with education (β = −0.066, t(126) = −3.011, p- adj = 0.012) and gender (β = −0.063, t(138) = −3.053, p- adj = 0.012). Table 2 Effects of demographic and clinical variables on time reproduction parameters Dependent MS Healthy independent variables independent variables Slope age (β = −0.008, t(77) = −2.163, p -adj = 0.159) age (β = −0.007, t(138) = −3.004, p -adj = 0.035) – education (β = 0.009, t(61) = 0.116, p -adj = 0.948) education (β = 0.091, t(126) = 1.998, p -adj = 0.239) – gender (β = 0.078, t(77) = 1.174, p -adj = 0.647) gender (β = 0.059, t(138) = 1.422, p- adj = 0.346) – 9HPT (β = −0.011, t(77) = −2.092, p -adj = 0.159) 9HPT (β = 0.007, t(138) = 1.05, p -adj = 0.43) – HADS (β = 0.002, t(77) = 0.434, p -adj = 0.888) HADS (β = −0.003, t(138) = −0.98, p -adj = 0.43) – MFIS-physical (β = 0.002, t(77) = 0.507, p -adj = 0.888) MFIS-physical (β = −0.005, t(136) = −1.842, p -adj = 0.239) – MFIS-cognitive (β = 0.0, t(77) = −0.065, p -adj = 0.948) MFIS-cognitive (β = −0.002, t(136) = −0.861, p -adj = 0.43) – MFIS-psychosocial (β = 0.002, t(77) = 0.182, p -adj = 0.948) MFIS-psychosocial (β = 0.002, t(136) = 0.502, p -adj = 0.616) – Beck (β = 0.003, t(77) = 0.994, p -adj = 0.647) Beck (β = −0.002, t(137) = −0.99, p -adj = 0.43) – BAI (β = −0.003, t(77) = −1.089, p -adj = 0.647) BAI (β = −0.002, t(138) = −0.862, p -adj = 0.43) – FSS (β = −0.001, t(77) = −0.528, p -adj = 0.888) FSS (β = −0.003, t(138) = −1.725, p -adj = 0.239) – EDSS (β = −0.061, t(76) = −2.321, p -adj = 0.159) – w m age (β = 0.005, t(77) = 2.333, p -adj = 0.134) age (β = 0.004, t(138) = 3.801, p -adj = 0.002) – education (β = −0.065, t(61) = −1.533, p -adj = 0.261) education (β = −0.066, t(126) = −3.011, p -adj = 0.012) – gender (β = −0.064, t(77) = −1.712, p -adj = 0.261) gender (β = −0.063, t(138) = −3.053, p -adj = 0.012) – 9HPT (β = 0.006, t(77) = 2.097, p- adj = 0.157) 9HPT (β = −0.005, t(138) = −1.425, p -adj = 0.287) – HADS (β = 0.0, t(77) = −0.076, p -adj = 0.985) HADS (β = 0.001, t(138) = 0.6, p -adj = 0.784) – MFIS-physical (β = 0.0, t(77) = −0.071, p -adj = 0.985) MFIS-physical (β = 0.002, t(136) = 1.588, p -adj = 0.252) – MFIS-cognitive (β = 0.0, t(77) = −0.117, p -adj = 0.985) MFIS-cognitive (β = 0.0, t(136) = 0.145, p -adj = 0.885) – MFIS-psychosocial (β = 0.0, t(77) = −0.019, p -adj = 0.985) MFIS-psychosocial (β = −0.001, t(136) = −0.467, p -adj = 0.784) – Beck (β = −0.001, t(77) = −0.615, p -adj = 0.811) Beck (β = 0.0, t(137) = 0.334, p -adj = 0.813) – BAI (β = 0.002, t(77) = 0.967, p -adj = 0.577) BAI (β = 0.001, t(138) = 0.555, p -adj = 0.784) – FSS (β = 0.002, t(77) = 1.604, p -adj = 0.261) FSS (β = 0.001, t(138) = 1.863, p -adj = 0.178) – EDSS (β = 0.038, t(76) = 2.584, p -adj = 0.134) – Regression results are reported as β (regression coefficient), t (test statistic, with degrees of freedom in parentheses), and p -adj (FDR-adjusted p value). 9HPT, Nine-Hole Peg Test; HADS, Hospital Anxiety and Depression Scale; MFIS, Modified Fatigue Impact Scale; BAI, Beck Anxiety Inventory; FSS, Fatigue Severity Scale; EDSS, Expanded Disability Status Scale. Bold values indicate p -adj < 0.05.

We then applied multivariate linear regression in the control group to assess the effects of age, gender, education, and hand motor performance (9HPT) on slope and w m . After adjustment for covariates, age remained the only significant predictor of both outcomes ( Table 3 ). Table 3 Effects of age on time reproduction parameters after controlling for gender, education, and hand motor performance Dependent Healthy multivariate regression model Slope age (β = −0.006, t(123) = −2.214, p -adj = 0.029) + – education (β = 0.051, t(123) = 1.024, p -adj = 0.308) + – gender (β = 0.021, t(123) = 0.457, p -adj = 0.649) + – 9HPT (β = 0.006, t(123) = 0.847, p -adj = 0.399) w m age (β = 0.003, t(123) = 2.719, p -adj = 0.007) + – education (β = −0.034, t(123) = −1.466, p -adj = 0.145) + – gender (β = −0.042, t(123) = −1.941, p -adj = 0.055) + – 9HPT (β = −0.004, t(123) = −1.212, p -adj = 0.145) Regression results are reported as β (regression coefficient), t (test statistic, with degrees of freedom in parentheses), and p -adj (FDR-adjusted p value). 9HPT, Nine-Hole Peg Test. Bold values indicate p -adj < 0.05.

To further investigate the effects of aging on time reproduction in MS versus control groups, we divided participants within each group into younger and older subgroups based on the median age of all participants (35 years; Figure 4 ). A two-way ANOVA showed significant main effects of age (F(1,215) = 6.50, p = 0.011) and group (F(1,215) = 4.18, p = 0.042) on slope, with no significant interaction between age and group (F(1,215) = 0.51, p = 0.47). Post hoc pairwise comparisons showed that the younger MS subgroup did not differ from the older control subgroup (t(68.4) = 0.08, p- adj = 0.935; Figure 4 A), whereas the older MS subgroup showed significantly lower slopes than the younger control subgroup, with a larger effect size as expected (t(73.4) = 3.03, p- adj = 0.020, Cohen’s d = 0.61; Figure 4 A). Similarly, a two-way ANOVA indicated significant main effects of age (F(1,215) = 14.73, p < 0.001) and group (F(1,215) = 6.97, p = 0.009) on w m , with no significant interaction (F(1,215) = 0.06, p = 0.81). Post hoc comparisons followed the same pattern: the younger MS subgroup did not differ from the older control subgroup (U = 1,074, p- adj = 0.89; Figure 4 B), while the older MS subgroup showed significantly higher w m values than the younger control subgroup (U = 1,029, p -adj = 0.001, Cohen’s d = 0.83; Figure 4 B). Figure 4 Effects of age on time reproduction in MS and control groups (A) Reproduction slope. A two-way ANOVA (age × group) showed significant main effects of age (F(1,215) = 6.50, p = 0.011) and group (F(1,215) = 4.18, p = 0.042), with no interaction (F(1,215) = 0.51, p = 0.47). FDR-corrected post hoc comparisons showed slope was significantly higher in young controls than in old controls (t(125.7) = 2.63, p -adj = 0.029, Cohen’s d = 0.45) and old MS (t(73.4) = 3.03, p -adj = 0.020, Cohen’s d = 0.61); young MS and old controls did not differ (t(68.4) = 0.08, p -adj = 0.935). (B) Measurement noise (w m ). A two-way ANOVA showed significant main effects of age (F(1,215) = 14.73, p < 0.001) and group (F(1,215) = 6.97, p = 0.009), with no interaction (F(1,215) = 0.06, p = 0.81). FDR-corrected post hoc comparisons showed w m was significantly lower in young controls than in old controls (U = 1,765, p -adj = 0.014, Cohen’s d = −0.514) and old MS (U = 1,029, p -adj = 0.001, Cohen’s d = 0.83); young MS and old controls did not differ (U = 1,074, p -adj = 0.89). ∗ p -adj < 0.05. Participants in each group were split into younger and older subgroups by the median age of all participants (35 years): young control ( n = 74), old control ( n = 66), young MS ( n = 32), and old MS ( n = 47). Scale bars show group mean ± SEM.

Furthermore, multivariate regression including group, age, and their interaction revealed that age was a significant predictor of both slope (β = −0.007, t(215) = −2.825, p = 0.005) and w m (β = 0.004, t(215) = 3.372, p = 0.001), with older age associated with a decreased slope and increased sensory noise. After controlling for age in this analysis, no significant group difference was observed for either slope (β = −0.019, t(215) = −0.125, p = 0.901) or w m (β = 0.025, t(215) = 0.309, p = 0.757), and no significant group × age interaction was found for either measure (slope: β = −0.001, t(215) = −0.315, p = 0.753; w m : β = 0.001, t(215) = 0.300, p = 0.765). Notably, the absence of a significant group effect in this regression analysis appears inconsistent with the significant differences observed in the age matched group comparisons and two-way ANOVA.

Discussion

We used the time reproduction paradigm within a Bayesian framework of perception to investigate cognitive impairment in patients with MS. Both the MS and the control groups showed a systematic bias in reproducing time, overestimating short intervals and underestimating long intervals. This pattern, known as the central tendency bias, has been reported in time reproduction tasks and other perceptual domains. 14 , 20 , 21 MS patients showed increased bias compared with controls. Using a modified Bayesian observer model, we demonstrated that this increased bias in the MS group was driven by greater w m during the sensory measurement stage.

Pathophysiological reliance on prior expectations

Based on Bayesian framework, 14 , 22 sensory processing involves combining information from the external world with prior expectations generated by the brain. Our results demonstrated an increased central tendency bias in patients with MS, indicating greater reliance on prior information than on sensory-motor information. This over-reliance may reflect the brain’s strategy under noisy conditions, where performance is optimized by assigning more weight to prior expectations relative to sensory-motor evidence. To place our findings in the larger context, it is helpful to consider evidence from other neurological and psychiatric conditions.

Previous studies using the time reproduction task in Parkinson’s disease have shown increased central tendency bias in patients. 23 , 24 , 25 , 26 This increased bias has been reported during medication-off periods and improved after dopamine replacement therapy 23 and deep brain stimulation of the subthalamic nucleus. 27 An over-reliance on prior expectations has also been reported both in subclinical hallucination-prone individuals 28 , 29 , 30 , 31 and in patients with schizophrenia experiencing hallucinations. 32 Previous studies in Parkinson’s and psychotic disorders have proposed different non-mutually exclusive mechanisms to explain this over-reliance on prior expectations, which may also account for our findings in MS: (1) when sensory information is weak or noisy, 33 , 34 the brain compensates by relying more heavily on prior expectations. (2) Circuit-level changes may lead to an overweighting of prior information in perceptual inference, independent of sensory noise. 31 (3) When motor responses are noisy or unreliable, the brain may rely more on prior expectations to stabilize motor output. (4) Deficits in short-term or working memory may further increase dependence on prior expectations. 24 , 25 , 35 , 36

In this study, we found that patients with MS showed increased w m at the sensory stage, while motor noise remained comparable to that of healthy controls. Although the underlying neural mechanisms were not directly examined, several pathophysiological processes characteristic of MS may contribute to elevated sensory noise.

First, white matter lesions and demyelination along sensory pathways, including thalamocortical circuits, may disrupt the precise temporal transmission of sensory signals, resulting in noisier sensory input. Second, gray matter atrophy in cortical regions involved in sensory processing and working memory may further degrade the fidelity of sensory encoding. Third, neuroinflammation and diffuse axonal damage may compromise information processing speed, a well-documented cognitive deficit in MS, which could manifest as increased variability in sensory measurements.

Given the distributed nature of MS pathophysiology, it is likely that multiple mechanisms contribute simultaneously, spanning early sensory perception through working memory maintenance. Future studies are needed to identify the specific neural correlates of increased sensory noise in MS.

Although working memory was not directly investigated in the present study, we propose that working memory dysfunction may contribute to the over-reliance on prior expectations observed in MS. The co-occurrence of working memory dysfunction and over-reliance on prior expectations has been previously reported in Parkinson’s disease 37 and psychotic disorders, 38 suggesting a potentially shared mechanism across conditions. Notably, our group has previously demonstrated working memory dysfunction in MS, 39 , 40 and the present study extends these findings by revealing over-reliance on prior expectations in the same population. Together, these observations may reflect shared pathophysiological mechanisms underlying cognitive impairments across MS, neurodegenerative, and psychotic disorders, and highlight a potential interaction between working memory dysfunction and over-reliance on prior expectations.

Importantly, a causal link between working memory dysfunction and over-reliance on prior expectations has been demonstrated experimentally. Akrami et al. 36 used optogenetic inactivation of the posterior parietal cortex (PPC) in mice to perturb working memory and showed that this manipulation led to increased bias and over-reliance on prior expectations, providing direct causal evidence for this interaction. Together, a potential explanation for the over-reliance on prior expectations in MS involves pathophysiological mechanisms that increase noise in sensory information, circuit-level changes that overweight prior information, and coexisting working memory dysfunction. Future studies are needed to directly investigate the neural mechanisms underlying these interactions, including the specific contributions of white matter integrity, thalamocortical connectivity, and working memory precision to sensory noise and prior weighting in MS.

Age and cognitive patterns in MS

The connection between our results in MS and findings from other neurodegenerative disorders highlights a potential interaction between the over-reliance on prior expectations and neurodegenerative processes. Age is one of the key factors that influence neurodegeneration and disease progression in MS, 41 , 42 and it provides an important context for interpreting our results. Our findings, along with previous studies (for review, see Turgeon et al. 43 ), showed that in healthy people, central tendency bias increases with age as reliance on prior expectations becomes stronger than sensory-motor evidence. Interestingly, we found that this age-related effect on bias was absent in patients with MS. Further analysis showed that both younger and older patients performed equally biased, and their performance was similar to that of older healthy participants. Moreover, this effect is not limited to the time reproduction task. In previous studies, our team found that working memory precision decreases with age in both healthy individuals and patients with MS. We also showed that the source of working memory error in patients with MS is similar to that observed in older healthy adults. 39 , 44 These findings suggest that MS may disrupt the normal age-related increase in reliance on prior expectations, such that both younger and older patients show levels of bias comparable to those seen in older healthy individuals. Whether this pattern reflects a true acceleration of cognitive aging cannot be determined from our cross-sectional data. Recent studies have reported accelerated biological aging in patients with MS compared with healthy individuals, 45 , 46 and the pattern observed in our study may represent one cognitive manifestation of this broader phenomenon; however, longitudinal studies are needed to directly test this interpretation.

It is important to note that the multivariate regression analysis, which included age as a continuous covariate, did not yield a significant group effect; however, this finding should be interpreted in the context of our case-control study design, in which the MS and healthy control groups were carefully matched for age. This inconsistency with the group comparisons and two-way ANOVA likely reflects the sensitivity of continuous regression to residual age variance. Notably, age was a significant predictor of both slope and w m in the regression model, highlighting its importance as a biological confound, particularly in healthy aging populations where age-related changes in sensory processing and cognitive speed may overlap with MS-related deficits. Given the careful age-matching procedure employed in our design, we consider the group comparisons and two-way ANOVA to be the primary analyses, with the multivariate regression serving as a sensitivity analysis that underscores the contribution of age to performance.

Limitations of the study

Our study has several limitations that should be acknowledged. First, the cross-sectional design prevents causal inference regarding the trajectory of cognitive changes in MS, and longitudinal studies are needed to confirm whether the pattern of disrupted age-related bias represents a true progression of cognitive decline. Second, we did not collect neuroimaging data, which limits our ability to associate the computational model parameters, particularly the increased w m , with underlying brain structural or functional changes. Third, clinical data (including annual relapse rate and detailed treatment history) were not extensively recorded, limiting our ability to fully assess the confounding effects of disease-related factors on cognitive performance. Fourth, our sample included a limited number of participants across different age ranges, which reduces the statistical power of age-stratified comparisons. Fifth, due to the exploratory nature of the regression analyses and the relatively large number of predictors tested, findings should be interpreted with caution. Although false discovery rate (FDR) correction was applied, the risk of false negatives cannot be excluded, particularly for variables showing non-significant associations. Despite these limitations, our study provides an initial step toward understanding the complex interaction between aging, MS, and cognitive decline, and offers a Bayesian sensory-motor framework that can be built upon in future work with larger, longitudinal, and neuroimaging-enriched cohorts.

Resource availability

Lead contact

Requests for further information and resources should be directed to and will be fulfilled by the lead contact, Mehdi Sanayei ( mehdi.sanayei@gmail.com ).

Materials availability

This study did not generate new unique reagents.

Data and code availability

• Behavioral data reported in this paper has been deposited at Zenodo: https://zenodo.org/records/21632046 and is publicly available as of the date of publication. • All original code has been deposited at Zenodo: https://zenodo.org/records/21632046 and is publicly available as of the date of publication. • Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Acknowledgments

The authors wish to thank the study participants for their contribution to this work.

Author contributions

Conceptualization, A.P., I.A., and M.S.; methodology, A.P., A.G., S.S., I.A., and M.S.; investigation, A.P., H.R., A.A., M.D., A.G., S.S.; writing – original draft, A.P. and M.S.; writing – review and editing, A.P., H.R., S.S., I.A., and M.S.; resources, I.A. and M.S.; supervision, I.A. and M.S.

Declaration of interests

The authors declare no competing interests.

Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work, the authors used ChatGPT in order to assist with grammar refinement and English language editing. After using this tool or service, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.

STAR★Methods

Key resources table

REAGENT or RESOURCE SOURCE IDENTIFIER Software and algorithms Python (v3.12.7) Python https://www.python.org SciPy (Nelder–Mead optimization) Python https://scipy.org statsmodels (OLS regression) Python https://www.statsmodels.org Xcode (v13)/Swift Apple https://developer.apple.com/xcode Bayesian observer model fitting code This paper Zenodo: https://zenodo.org/records/21632046 Other Apple iPad (10-inch) Apple N/A

Experimental model and study participant details

We enrolled 92 patients with relapsing-remitting multiple sclerosis (MS), recruited through a full-census approach from the multiple sclerosis clinic at Kashani Hospital, Isfahan, Iran. Healthy control participants were included as a comparator group to provide a normative baseline for sensory-motor and Bayesian inference processes, enabling identification of MS-specific alterations beyond general population variability. The control group comprised 149 healthy individuals with no first-degree relatives diagnosed with MS.

Inclusion criteria consisted of a confirmed diagnosis of MS, 47 age between 18 and 55 years, an Expanded Disability Status Scale (EDSS) score between 0 and 6, and normal or corrected-to-normal visual acuity.

Exclusion criteria included a clinical relapse or corticosteroid use within three months prior to enrollment; major neurological disorders other than MS (e.g., stroke, epilepsy, brain tumors, or CNS infections); history of brain surgery; psychiatric illnesses (e.g., major depressive disorder, bipolar disorder, or schizophrenia); substance or alcohol abuse; acute febrile illness at the time of testing; chronic systemic conditions such as diabetes, renal or hepatic failure, chronic obstructive pulmonary disease (COPD), hypothyroidism, or hyperthyroidism; and abnormal performance on the Nine-Hole Peg Test (9-HPT >45 s).

The MS group had a mean EDSS score of 1.06 ± 1.10 and a mean disease duration of 9.33 ± 5.78 years. All patients were receiving disease-modifying therapy (DMT), specifically B-cell depleting therapies (ocrelizumab or rituximab).

All participants were Iranian. The study was conducted in accordance with the Declaration of Helsinki and its subsequent revisions. Ethical approval was obtained from the Ethics Committee of Isfahan University of Medical Sciences (Ethics Code: IR.ARI.MUI.REC.1403.132).

Method details

Time reproduction task

The time reproduction task was developed as and iPadOS app using Swift programming language and in Xcode (version 13) and was used on a 10-inch Apple iPad. Details of the task and its ipadOS application design have been described previously. 48 , 49

The task paradigm is illustrated in Figure 1 . Each trial began with the presentation of a central fixation point (diameter: 0.2°, at 50 cm distance) and two peripheral targets (left target: 0.5° diameters, right target: 2° diameter, 10° eccentricity). The peripheral targets were not relevant to the time reproduction task and were included to maintain consistency with other timing paradigms not reported here. Importantly, their presence does not affect the logic or performance of the time reproduction task. After a random delay (0.5 s plus a random time from 0 to 0.2 s), two similar wheel-like stimuli (2.5° diameter) were flashed (for 33.3 ms each) sequentially around the fixation point. The subject measured the time between two flashes, sample interval or t s , and produced a matching interval, t r , by tapping on the right side of screen. Across trials, t s was sampled from one of 5 discrete values pseudorandomly (0.4, 0.5, 0.7, 1.1, 1.9 s, uniform distributions). At the end of each trial, we showed the response error (t r - t s ) as feedback for 1 s to the subject. The inter-trial interval was 2 s, and each block contained 40 trials. Each subject participated in a short training and 6 blocks.

Data collection and questionnaires

First, all participants received detailed instructions and provided written informed consent. They then participated in an interview to collect demographic and clinical information, followed by 9-HPT and EDSS administered by a neurologist. Subsequently, they completed a series of standardized self-report questionnaires in Persian, including Beck Depression Inventory-II (BDI-II), 50 Beck Anxiety Inventory (BAI), 51 Hospital Anxiety and Depression Scale (HADS), 52 Modified Fatigue Impact Scale (MFIS), 53 and Fatigue Severity Scale (FSS). 54

Quantification and statistical analysis

For each participant, we applied the 1.5 interquartile range (IQR) method to exclude outlier trials. We then performed a linear regression between the presented time and the reproduced time for each participant. In this task, the intercept of the regression reflects overall shifts in time reproduction: higher intercepts indicate a general tendency to overestimate, whereas lower intercepts suggest underestimation. The slope represents sensitivity to changes in duration (or bias toward the mean): a slope of 1 reflects optimal timing, while deviations from 1 indicate systematic bias in reproducing shorter and longer intervals.

A slope of zero or negative values indicates unreliable time reproduction for that participant. Based on this reliability criterion, we excluded 9 participants (out of 149, 6.67%, 2 males) from the control group, and 13 (out of 92, 16.46%, 1 male) from the MS group. The number of excluded participants was significantly higher in the MS group than in the control group (Chi-square, χ 2 = 4.48, p < 0.05). The average percentage of excluded trials per subject, based on 1.5 IQR method, was 4.86 ± 2.23% in the control group and 5.74 ± 3.00% in the MS group which was not significantly different between the two groups (Mann-Whitney test, p = 0.06).

Sensitivity analyses including all participants yielded consistent results with the main results, with the MS group showing significantly lower slopes (MS: 0.41 ± 0.34 vs. Control: 0.54 ± 0.26, p = 0.003) and higher w m (MS: 0.41 ± 0.16 vs. Control: 0.34 ± 0.14, p = 0.001), confirming that our findings are not dependent on the exclusion criteria applied.

Statistical analyses were performed using Python 3.12.7, with statistical significance defined as p < 0.05. To compare the MS and control groups, we first assessed the normality of data distributions using the Shapiro-Wilk test. If the data were not normally distributed, we applied the Mann-Whitney U test; otherwise, we used the independent-samples t test. For regression analyses, we used the OLS function from the statsmodels library in Python. Because multiple regression analyses were performed across several predictors and outcomes, p -values were adjusted to control for the increased risk of false-positive findings. Multiple comparisons were corrected using the FDR method. For each analysis, we report the statistical test, test statistic, effect size, and p value. For parametric tests, degrees of freedom are also reported.

The bayesian observer model

To investigate the sources of temporal error, we applied a modified version of the Bayesian observer model, 16 , 48 , 55 which partitions time reproduction into three stages: sensory measurement, time estimation, and motor reproduction. In the measurement stage, the observer takes noisy measurements (t m ) of the sample intervals (t s ). Measurement noise (w m ) is the model parameter corresponding to this stage.

Equation 1. Measurement stage: p ( t m ∣ t s ) = 1 2 π ( w m t s ) 2 exp ( − ( t s − t m ) 2 ( w m t s ) 2 ) In the estimation stage, the Bayesian model combines the likelihood function with the prior and uses the mean of the resulting posterior distribution to generate an estimate (t e ). In our model, Bayes least squares (BLS) was used as the mapping rule. The gain factor (α) captures systematic over- or underestimation in the estimation stage by applying a multiplicative scaling to the estimated interval (α > 1 indicates overestimation of time intervals, whereas α < 1 indicates underestimation). 55 Including α is particularly important in studies involving patient populations, as it allows the model to account for consistent over- or underestimation observed in some participants.

Equation 2. Estimation stage: t e = f B L S ( t m ) = ∫ t s min t s max α · t s p ( t m ∣ t s ) d t s ∫ t s min t s max p ( t m ∣ t s ) d t s In the motor response stage, the observer uses t e to reproduce noisy response, t r . Motor noise (w r ) is the model parameter corresponding to this stage.

Equation 3. Motor response stage: p ( t r ∣ t e ) = 1 2 π ( w r t e ) 2 exp ( − ( t r − t e ) 2 ( w r t e ) 2 ) In our dataset, each trial comprised a sample time interval (t s ) and the corresponding reproduced time (tᵣ). The model was fit on a per-subject basis using trial-by-trial pairs of t s and t r . To implement the Bayesian observer model and capture the direct relationship between t s and tᵣ, we applied the following formulation.

Equation 4. Full model: p ( t r ∣ t s , w m , w r , α ) = ∫ p ( t r ∣ f B L S ( t m ) , w r ) p ( t m ∣ t s , w m ) d t m

To evaluate whether including α improved model fit, we compared the three-parameter model (w m , w r , α) against a two-parameter model (w m , w r ) using the Bayesian Information Criterion (BIC). The three-parameter model provided better fit in both groups (controls: −6.55 ± 160.46 vs. 27.81 ± 177.31; U = 8315, p = 0.028, d = −0.287; MS: 7.81 ± 190.89 vs. 92.83 ± 178.14; t(155.3) = −3.11, p = 0.002, d = −0.494), with stronger improvement in the MS group. In MS participants, the three-parameter model was strongly preferred in 75% of cases (ΔBIC >10) and comparable in the remaining 25% (|ΔBIC| ≤ 10); the two-parameter model was never preferred (ΔBIC < −10; Figure S2 ). Conceptually, α corresponds to a clock-speed-like multiplicative scaling of subjective duration, analogous to the subjective-to-objective duration ratio used to index internal clock speed in previous work. 56 , 57

We used maximum likelihood estimation to fit the model and determine the optimal parameters (w m , wᵣ, α) for each participant. Model fitting was performed in Python using the SciPy library with the Nelder-Mead downhill simplex optimization method. To ensure robustness, the fitting procedure was repeated with multiple different initial parameter values. Representative model fits for two example participants (one from each group) are shown in Figure S1 .

The initial parameter values used were 0.3, 0.3, and 0.8 for w m , w r , and α respectively. To ensure robustness of the solution, we systematically tested multiple initial values across the plausible parameter space (w m and w r in the range [0, 1], and α in the range [0, 2]), with parameter bounds set to [0.001, 10] for all parameters during optimization. All fits converged to the same optimal solution regardless of initial values, confirming that the reported parameters represent a global rather than local minimum.

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Supplemental information can be found online at https://doi.org/10.1016/j.isci.2026.117323 .