Baseline Characteristics of Participants

We excluded 1,020 patients diagnosed with TIA, 451 with cerebellar infarcts, and 422 with brainstem infarcts. Additionally, 3,163 patients without neuroimaging data, 805 with incomplete cerebral imaging, 1,011 with incomplete cerebellar imaging, and 84 without 3-month EQ-5D-3L data were also excluded. Consequently, 8,210 individuals with SIS were eligible for this study (Additional file 1, Figure S2). Notably, 260 patients dropped out at 12 months after discharge; therefore, 7,950 patients were analyzed at the 12-month follow-up. Additionally, the distribution classified according to the HRQoL levels in the CNSR-III cohort suggests that, compared with the 3-month HRQoL, the population proportion with severity levels of ‘moderate problem’ and ‘severe problem’ in each dimension in the 12-month outcome has decreased (Table S1). The comprehensive HRQoL assessment at 12 months (CHI: [−0.29 ± 0.43], VAS: [83.02 ± 14.41]) was higher than that at 3 months (CHI: [−0.32 ± 0.45], VAS: [81.49 ± 16.00]) in the whole cohort (Table S2).

Among the 8,210 patients, the mean age was 62.39 ± 11.12 years, and 5,553 (67.64%) were male. Regarding HRQoL outcomes, at 3 months, UA was the most frequently reported domain with moderate to severe problems (28.53%), followed by MO (28.51%), PD (20.39%), and AD (18.29%). Table S3 presents the association between baseline characteristics and 3-month HRQoL among these patients. The results showed that patients having SIS with more severe neurological deficits, such as higher NIHSS and mRS scores at admission (all p < 0.0001), were associated with poorer outcomes across the five dimensions of HRQoL. Smaller cerebral infarct volume (all p < 0.0001) and eTIV (MO: p = 0.0014; SC: p = 0.0008; UA: p = 0.0015; PD: p = 0.0091; AD: p = 0.0001) were positively associated with better 3-month HRQoL outcomes.

Table S4 presents the 39 cerebellar regional volumes in relation to each of the 3-month HRQoL outcomes. The regional volumes, excluding most of lobules IX and X, vermis, and fastigial nuclei, were significantly smaller at baseline as EQ-5D-3L levels increased (Additional file 2, Table S4, all p < 0.0013). A similar pattern was observed for the five HRQoL dimensions at 12 months (Additional file 2, Table S5).

Association Between Cerebellar Regional Volumes and HRQoL

To further validate the association between cerebellar regional volumes and HRQoL at 3 months post-SIS, multivariable ordinal logistic regression analyses were performed. Notably, according to HRQoL definitions, the five dimensions used in this study were designed to capture three functional domains: physical (MO and SC), social (UA), and mental (AD) functions [25]. In particular, upon reviewing the questions within the scale, “MO” primarily reflects walking and gait, while “SC” focuses on activities like washing and dressing. This differentiation enabled a distinction between lower and upper-extremity limb motor functions.

Association Between Cerebellar Regional Volumes and Physical Function

After Bonferroni correction, adjusting for multiple confounders, smaller cerebellar whole volumes and regional volumes of bilateral Crus I (ORleft = 0.870, 95%CIleft 0.817–0.927, pleft < 0.0001; ORright = 0.893, 95%CIright 0.839–0.951, pright = 0.0004), VIIIa (ORleft = 0.911, 95%CIleft 0.862–0.962, pleft = 0.0008; ORright = 0.911, 95%CIright 0.863–0.962, pright = 0.0009), left I-IV (OR = 0.853, 95%CI 0.787–0.924, p < 0.0001), right VIIb (OR = 0.892, 95%CI 0.844–0.942, p < 0.0001) lobules as well as right dentate (OR = 0.857, 95%CI 0.808–0.910, p < 0.0001) and interposed (OR = 0.871, 95%CI 0.820–0.925, p < 0.0001) nuclei, were significantly associated with a higher risk of worse 3-month lower-limb motor function (Fig. 1; Additional file 2, Table S6). Additionally, smaller volumes of bilateral Crus I (ORleft = 0.863, 95%CIleft 0.806–0.925, pleft < 0.0001; ORright = 0.857, 95%CIright 0.801–0.917, pright < 0.0001), VIIb (ORleft = 0.905, 95%CIleft 0.854–0.960, pleft = 0.0009; ORright = 0.896, 95%CIright 0.844–0.951, pright = 0.0003), VIIIa (ORleft = 0.893, 95%CIleft 0.841–0.948, pleft = 0.0002; ORright = 0.901, 95%CIright 0.849–0.957, pright = 0.0006), right side of Crus II (OR = 0.891, 95%CI 0.836–0.950, p = 0.0004) lobules, dentate (OR = 0.868, 95%CI 0.813–0.926, p < 0.0001) and interposed (OR = 0.894, 95%CI 0.838–0.955, p = 0.0009) nuclei, were significantly associated with poorer 3-month upper-extremity motor function.

Fig. 1

The forest plot and cerebellar anatomical diagram on multivariable ordinal logistic regression analyses of the association of 39 cerebellar regional volumes with 3-month five-dimensional HRQoL outcomes after SIS. The logistic model was adjusted for age, sex, height, weight, heavy alcohol consumption, current smoking status, cerebral infarct volume, eTIV, TOAST classification, NIHSS and mRS score at admission, as well as medical histories of dyslipidemia, diabetes mellitus, hypertension, heart disease, atrial fibrillation and cancers. Abbreviations: HRQoL, health-related quality of life; SIS, supratentorial ischemic stroke; eTIV, estimated total intracranial volume; TOAST, Trial of ORG 10172 in Acute Stroke Treatment; NIHSS, National Institutes of Health Stroke Scale; mRS, modified Rankin Scale

For physical function at 12 months after SIS, smaller volumes of the left anterior regions, primarily left I-IV lobules (OR = 0.865, 95%CI 0.794–0.943, p = 0.0009), as well as specific left superior and right inferior regions, including left Crus I [OR = 0.885, 95%CI 0.827–0.946, p = 0.0004] lobules, right VIIb (OR = 0.902, 95%CI 0.851–0.957, p = 0.0006) lobules, right fastigial (OR = 0.876, 95%CI 0.821–0.934, p < 0.0001) and bilateral dentate nuclei (ORleft = 0.879, 95%CIleft 0.826–0.935, pleft < 0.0001; ORright = 0.823, 95%CIright 0.772–0.877, pright < 0.0001), were associated with poorer 12-month lower-limb motor ability after Bonferroni correction. Furthermore, adverse 12-month upper-extremity motor function was also significantly associated with smaller volumes of bilateral Crus II (ORleft = 0.886, 95%CIleft 0.829–0.948, pleft = 0.0004; ORright = 0.880, 95%CIright 0.822–0.942, pright = 0.0002), right VIIIa (OR = 0.898, 95%CI 0.843–0.957, p = 0.0009) and vermis VI (OR = 0.860, 95%CI 0.799–0.926, p < 0.0001) (Fig. 2; Additional file 2, Table S7).

Fig. 2

The forest plot and cerebellar anatomical diagram on multivariable ordinal logistic regression analyses of the association of 39 cerebellar regional volumes with 12-month five-dimensional HRQoL outcomes after SIS. The logistic model was adjusted for age, sex, height, weight, heavy alcohol consumption, current smoking status, cerebral infarct volume, eTIV, TOAST classification, NIHSS and mRS score at admission, as well as medical histories of dyslipidemia, diabetes mellitus, hypertension, heart disease, atrial fibrillation and cancers. Abbreviations: HRQoL, health-related quality of life; SIS, supratentorial ischemic stroke; eTIV, estimated total intracranial volume; TOAST, Trial of ORG 10172 in Acute Stroke Treatment; NIHSS, National Institutes of Health Stroke Scale; mRS, modified Rankin Scale

Association Between Cerebellar Regional Volumes and Social Function

The trends for 3-month social function were similar to those observed in the upper-extremity motor model, with the addition of a positive association with the left dentate nucleus (OR = 0.904, 95%CI 0.853–0.958, p = 0.0006) (Fig. 1; Additional file 2, Table S6). For 12-month social function, the positive regions included the left Crus I (OR = 0.856, 95%CI 0.801–0.914, p < 0.0001), bilateral Crus II (ORleft = 0.895, 95%CIleft 0.842–0.952, pleft = 0.0004; ORright = 0.891, 95%CIright 0.837–0.948, pright = 0.0002), right VIIb (OR = 0.883, 95%CI 0.834–0.936, p < 0.0001) and VIIIa (OR = 0.904, 95%CI 0.854–0.958, p = 0.0006) lobules, as well as bilateral dentate (ORleft = 0.883, 95%CIleft 0.831–0.939, pleft < 0.0001; ORright = 0.852, 95%CIright 0.800–0.908, pright < 0.0001) and right interposed (OR = 0.882, 95%CI 0.828–0.940, p = 0.0001) nuclei.

Association Between Cerebellar Regional Volumes and Mental Function

No statistical survival was observed in the 3-month mental function model after Bonferroni testing (Fig. 1; Additional file 2, Table S6). However, the association of smaller volumes of bilateral white matter (ORleft = 0.864, 95%CIleft 0.804–0.929, pleft < 0.0001; ORright = 0.847, 95%CIright 0.789–0.910, pright < 0.0001) and left I-IV lobules (OR = 0.838, 95%CI 0.761–0.922, p = 0.0003) with 12-month anxiety/depression outcome were significant.

Detailed information is provided in Additional file 2, Table S6.

Association Between Cerebellar Regional Volumes and a Comprehensive Index

To comprehensively assess HRQoL, CHI (the weighted sum of five-dimensional variables: MO, SC, UA, PD, and AD) and VAS (the direct sum of these variables at 3 and 12 months) were included in linear regression analyses using Bonferroni correction to examine their relationship with the 39 cerebellar regional volumes (Fig. 3; Additional file 2, Table S8). In the 3-month outcome, smaller cerebellar regional volumes of the left I-IV (\(\beta\)=0.023, p = 0.0005), bilateral Crus I (\(\beta\) left = 0.005, pleft = 0.0007; \(\beta\) right = 0.005, pright = 0.0004), and right VIIb (\(\beta\)=0.008, p = 0.0005) were significantly correlated with worse 3-month CHI. Similarly, smaller volumes of the left I-IV (\(\beta\)=2.375, p = 0.0012) and right Crus I (\(\beta\)=0.564, p = 0.0005) lobules were associated with poor 3-month VAS scores. In the 12-month outcome, smaller volumes of the left I-IV (\(\beta\)=0.025, p < 0.0001), VI (\(\beta\)=0.009, p < 0.0001), Crus I (\(\beta\)=0.005, p = 0.0004), vermis VI (\(\beta\)=0.032, p = 0.0002), and right VIIb (\(\beta\)=0.008, p = 0.0003) lobules, as well as bilateral dentate (\(\beta\) left = 0.033, pleft < 0.0001; \(\beta\) right = 0.040, pright < 0.0001) and right interposed (\(\beta\)=0.157, p = 0.0010) nuclei, aggravated poorer CHI of HRQoL, while the right X (\(\beta\)=−0.075, p = 0.0001) lobule reduced its burden. Volumes of I-IV (\(\beta\) left = 3.002, pleft < 0.0001; \(\beta\) right = 2.017, pright = 0.0005), Crus I (\(\beta\) left = 0.757, pleft < 0.0001; \(\beta\) right = 0.608, pright < 0.0001), Crus II (\(\beta\) left = 0.705, pleft < 0.0001; \(\beta\) right = 0.696, pright < 0.0001) bilaterally, right VIIb (\(\beta\)=0.883, p = 0.0003) lobules, dentate bilaterally (\(\beta\) left = 2.886, pleft = 0.0001; \(\beta\) right = 3.455, pright < 0.0001) and left interposed (\(\beta\)=19.323, p = 0.0004) nuclei were significantly associated with 12-month VAS outcomes.

Fig. 3

The heatmap and cerebellar anatomical diagram on linear regression analyses of the association of 39 cerebellar regional volumes with 3- and 12-month comprehensive HRQoL outcomes after SIS. The linear model was adjusted for age, sex, height, weight, heavy alcohol consumption, current smoking status, cerebral infarct volume, eTIV, TOAST classification, NIHSS and mRS score at admission, as well as medical histories of dyslipidemia, diabetes mellitus, hypertension, heart disease, atrial fibrillation and cancers. Abbreviations: CHI, comprehensive health index; VAS, visual analog scale; HRQoL, health-related quality of life; SIS, supratentorial ischemic stroke; eTIV, estimated total intracranial volume; TOAST, Trial of ORG 10172 in Acute Stroke Treatment; NIHSS, National Institutes of Health Stroke Scale; mRS, modified Rankin Scale