The association between carotid blood flow and resting-state brain activity in patients with cerebrovascular diseases

Cerebral hypoperfusion impairs brain activity and leads to cognitive impairment. Left and right common carotid arteries (CCA) are the major source of cerebral blood supply. It remains unclear whether blood flow in both CCA contributes equally to brain activity. Here, CCA blood flow was evaluated using ultrasonography in 23 patients with cerebrovascular diseases. Resting-state brain activity and cognitive status were also assessed using magnetoencephalography and a cognitive subscale of the Functional Independence Measure, respectively, to explore the relationships between blood flow, functional brain activity, and cognitive status. Our findings indicated that there was an association between blood flow and resting-state brain activity, and between resting-state brain activity and cognitive status. However, blood flow was not significantly associated with cognitive status directly. Furthermore, blood velocity in the right CCA correlated with resting-state brain activity, but not with the resistance index. In contrast, the resistance index in the left CCA correlated with resting-state brain activity, but not with blood velocity. Our findings suggest that hypoperfusion is important in the right CCA, whereas cerebral microcirculation is important in the left CCA for brain activity. Hence, this asymmetry should be considered when designing appropriate therapeutic strategies.


Results
Statistical analysis. In our analysis, we used two different statistical approaches, namely, bootstrapping correlation and linear mixed-effect model (LMEM) analysis. Bootstrapping correlation provides information concerning non-directional relationships between two parameters that are not relevant to the causality of the two parameters (i.e. a cause-effect relationship was not considered). In this case, we used the terms ' correlate/ correlation' . LMEM analysis provides information concerning directional relationships between parameters (i.e. a cause-effect relationship was considered). In this case, we used the term 'influence' . We used the terms 'relationship/association' when both were mentioned.
Within-modality association: ultrasonography, MEG, and FIM. To interpret the following results accurately, relationships between parameters within specific modalities were assessed. Concerning the carotid ultrasonography data, six parameters used in daily clinical practice were employed for analysis: diameter of artery (DA), peak systolic flow velocity (PSV), end-diastolic velocity (EDV), mean velocity (MV), the pulsatility index (PI), and the resistance index (RI). Two categories were formed, namely: DA, PSV, EDV, and MV, which were considered local factors of blood vessels; and PI and RI, which were considered downstream factors 23 . The four local factors significantly correlated with each other in both sides of the CCA (Table 1; Fig. 1), whereas the two downstream factors correlated in the left side of the CCA only. Several cross-category correlations were also found: EDV/MV and PI/RI correlated in the left side, and EDV and RI also correlated in the right side.
FIM is an assessment tool for cognitive and motor status during rehabilitation for stroke 22 . It consists of two domains: a cognitive subscale (cognitive-FIM) and a motor subscale (motor-FIM). The correlation between cognitive-FIM and motor-FIM was not significant (r = 0.369, P (FDR) = 0.065). Table 1. Correlation matrix within sided ultrasonographic parameters. DA diameter of artery, CCA common carotid arteries, EDV end-diastolic velocity, MV mean velocity, P (unc.) uncorrected p values of bootstrapping statistics, PI pulsatility index, r average correlation coefficient across bootstrap iterations, PSV peak systolic flow velocity, RI resistance index, P (FDR) p values of bootstrapping statistics with FDR-correction. *A statistically significant correlation after FDR correction.  Table 2; Figs. 1a, 2d,e). The PI and the RI in the left CCA negatively correlated with MF. Although the correlations did not reach the statistical threshold after FDR correction, PI/RI and IAF the RI and SE, and PI/RI and cognitive-FIM also showed mild correlations (P (uncorrected) < 0.05). When the biases from patients' profiles (i.e., age and sex) had been eliminated, the RI continued to mildly influence MF (P (uncorrected) = 0.015; Table 3). No local factor (DA, PSV, EDV, and MV) in the left CCA correlated with or influenced any MEG spectral parameter after considering potential profile biases. Similarly, the associations between PI/RI and cognitive-FIM were not significant after controlling for profile biases (Table 3). After controlling for profile biases, no significant correlations or influences were found between local factors (DA, PSV, EDV, and MV) and cognitive-FIM and between ultrasonographic parameters in the left CCA and motor-FIM (Table 3).
In terms of the right CCA, ultrasonography local factors (DA, PSV, EDV, and MV) were more important ( Table 2; Figs. 1b, 2a,b). DA in the right CCA positively correlated with IAF. The other three haemodynamic parameters (PSV, EDV, and MV) negatively correlated with MF and IAF, but not with SE. Neither of the downstream factors (PI and RI) correlated with any MEG spectral parameter.
EDV and MV in the right CCA significantly correlated with cognitive-FIM (Fig. 3), and the RI showed a mild correlation with cognitive-FIM (Table 2). No significant correlations were found between the other ultrasonographic parameters (DA, PSV, and the PI) in the right CCA and cognitive-FIM. When the biases from patients' profiles had been eliminated, similar results were obtained. DA, PSV, and MV in the right CCA had a significant influence on MF, and PSV had a significant influence on IAF. EDV mildly influenced MF, and DA /MV mildly influenced IAF (P (unc.) < 0.05). No downstream factors significantly influenced MEG spectral parameters ( Table 3). The relationships between right CCA parameters and cognitive-FIM did not persist after controlling for profile biases (Table 3). No significant correlation was found between ultrasonographic parameters in the right CCA and motor-FIM after controlling for profile biases (Tables 2, 3).

Between modality association: MEG and FIM.
To confirm the correlation between resting-state brain activity and cognitive status, we compared the association between MEG spectral parameters and FIM scores.  Figure 1. Schematic descriptions of relationships within/between ultrasonographic parameters and MEG spectral parameters. Lines represent a significant correlation. Blue, red, and yellow boxes represent local factors, downstream factors, and MEG spectral parameters, respectively. Biases in terms of patient age and sex were not considered in the relationships depicted here. CCA common carotid artery, D A diameter of artery, EDV enddiastolic velocity, IAF individual alpha frequency, MEG magnetoencepharography, MF median frequency, MV mean velocity, PI pulsatility index, PSV peak systolic flow velocity, RI resistance index, SE Shannon entropy.

Discussion
There are three major findings in this study. First, ultrasonographic parameters were associated with MEG spectral parameters, and MEG spectral parameters were associated with cognitive-FIM scores. However, ultrasonographic parameters were not directly associated with cognitive-FIM scores. Second, local factors in the right CCA were associated with MEG spectral parameters, whereas downstream factors in the left CCA were associated with MEG spectral parameters. Third, the influences of local factors in the right CCA remained significant even after controlling for patient age and sex. These findings supported our hypothesis, in that there was an asymmetrical association found in relation to the left and right sides of the CCA in terms of brain activity and cognitive status. We initially discuss our results prior to controlling for biases in terms of age and sex. Within-modality correlation analysis confirmed that six ultrasonographic parameters fell into two categories 23 , namely, local factors (DA, PSV, MV, and EDV) and downstream factors (the PI and the RI). All local factors correlated with each other on both sides of the CCA (Table 1; Fig. 1). The two downstream factors correlated in the left CCA, although their relationship was not significant in the right CCA. There were several cross-factor interactions. Both downstream factors correlated with EDV and MV in the left CCA, whereas only the RI correlated with EDV in the right CCA. The asymmetry found in the relationship between ultrasonographic parameters could be due to anatomical differences: the left CCA is a branch of the aortic arch, whereas the right CCA is a branch of the brachiocephalic artery. These results indicate that the two ultrasonographic parameter categories should be considered separately. The local factors represent hypoperfusion and were associated with both MEG spectral parameters (MF and IAF) and cognitive-FIM scores in the right CCA (Table 2; Figs. 1b, 2a,b, 3). However, neither of the two downstream factors in the right CCA correlated with any MEG spectral parameters nor with cognitive-FIM. These results suggest that pathological CCA function in the right CCA impairs brain activity and cognitive status via hypoperfusion, as we anticipated. The downstream factors reflect the state of the cerebral microcirculation. They significantly correlated with atherosclerosis risk scores and the presence of brain infarction 26,27 . The PI reflects the transmission of pulsatile energy into the cerebral microcirculation. It has been shown to be positively associated with the development of stroke 28 , which is a major risk factor of dementia. A higher PI indicates a higher risk of brain microbleeds and lacunar infarcts 28,29 . The RI reflects blood flow from the microvascular bed Table 2. Correlation matrix between sided ultrasonographic parameters, MEG spectral parameters, and FIM. CCA common carotid arteries, Cog. cognitive-FIM score, FIM functional independent measurement, IAF individual alpha frequency, MEG magnetoencephalography, MF median frequency, Mot motor-FIM score, P (FDR) p values of bootstrapping statistics with FDR-correction, P (unc.) uncorrected p values of bootstrapping statistics, PI pulsatility index, r average correlation coefficient across bootstrap iterations, RI resistance index, SE Shannon entropy. *A statistically significant correlation after FDR correction.  3). No local factor in the left CCA significantly correlated with any MEG spectral parameters. These results suggest that pathological cerebral microcirculation, such as microbleeds, lacunar infarcts, and arteriosclerosis (represented by downstream factors in ultrasonographic data), impaired brain activity and cognitive status to a greater extent than hypoperfusion in the left CCA. Neither downstream nor local factors were significantly associated with cognitive-FIM scores in the left CCA. Although there were few significant associations between cognitive-FIM and ultrasonographic parameters, cognitive-FIM was significantly associated with MEG spectral parameters (Fig. 3). This suggests that cognitive status (i.e. cognitive-FIM) was influenced by carotid blood flow (i.e. ultrasonographic parameters) indirectly, which was mediated by brain activity (i.e. MEG spectral parameters). Age and sex are possible confounding factors because they affect cardiac functions 32 , brain activities 33 , and cognitive status 34 . After considering these potential biases, our results changed slightly. The relationship between local factors (EDV and MV) in the right CCA and cognitive-FIM was not significant (Table 3, broken blue arrow in Fig. 3), whereas the relationship had been significant prior to controlling for these profile factors ( Table 2). This suggests that the relationship could be solely explained in terms of age and/or sex. Similarly, the relationships between the downstream factors in the left CCA and the MEG spectral parameter (MF) did not remain statistically significant after controlling for the profile factors (Table 3, broken red arrow in Fig. 3). There are two possible explanations for this finding. As with the relationship between local factors and cognitive-FIM in the right CCA, it could indicate that the relationship was explicable in terms of age and sex. The downstream factors correlated with arteriosclerosis risk factors, which include age 35 . Alternatively, it might have been due to our statistical strategy. Examining the null-hypothesis in which the coefficient of the RI (predictor) for predicting MF was equal to zero, the t-value yielded a statistically significant level in a single test (P (unc.) = 0.015). It is plausible to consider that this significant result was masked due to the FDR correction. Since this study is examining a new field, we acknowledge that the procedure we adopted is exploratory, and that certain significant associations may not have been detected. However, the influence of local factors in the right CCA on MEG spectral parameters remained significant even with strict correction, which at least supported our hypothesis, namely, that the left and right side of the CCA had an asymmetrical association with brain activity.
The observed asymmetry may have important implications for clinical practice. Blood flow in the CCA can be improved through surgical treatment such as carotid endarterectomy or carotid artery stenting. Both techniques have been reported to improve blood flow and cognitive function, although this remains controversial [36][37][38][39] . www.nature.com/scientificreports/ However, our study findings indicated that improvement in the blood flow (i.e. affecting local factors) of CCA may not improve cognitive function, because blood flow was not significantly associated with brain activity in the left CCA. Therefore, consideration should be given to differences in the relationship between the left and right CCA and brain activity and cognitive function when designing a therapeutic strategy for pathological CCA. In our study, we report two further findings concerning the relationships between CCA blood flow, restingstate brain activity, and cognitive/motor status. First, the relationship between carotid blood flow and cognitive status was found to be indirect and mediated through brain activity. We presumed that ultrasonographic parameters would be associated with cognitive-FIM because cerebral hypoperfusion affects cognitive status, measured using MMSE 10 , which has been found to correlate with cognitive-FIM scores 40 . However, our results did not support this presumption. The significant relationships between ultrasonographic parameters and cognitive-FIM scores were not replicated after controlling for profile biases. It is plausible to consider that the previously reported relationship between carotid blood flow (i.e. ultrasonographic parameters) and cognitive status (i.e. cognitive-FIM) was mediated through brain activity (i.e. MEG spectral parameters). This result suggests that MEG spectral parameters comprise more risk factors, which are represented as changes in blood flow in the CCA, than the FIM score, given that both cognitive-FIM and motor-FIM correlated significantly with MF and IAF, whereas correlations between cognitive-FIM and motor-FIM and between motor-FIM and ultrasonographic parameters were not significant. This implies that cognitive-FIM and motor-FIM are more closely linked to resting-state brain activities (i.e. MEG spectral parameters) than carotid blood flow (i.e. ultrasonographic parameters). Concerning the lack of association found between ultrasonographic parameters and cognitive-FIM scores, the ceiling effect and cognitive reserve provide two possible explanations. The cognitive-FIM scores were influenced by the ceiling effect, as evident in Fig. 2c,f 41 . This indicates that cognitive-FIM failed to capture continuous gradients in relation to cognitive status, especially for those patients whose cognitive functions were largely retained; therefore, the lack of association between ultrasonographic parameters and cognitive-FIM scores occurred because the scores did not reflect cognitive status appropriately. However, MEG spectral parameters were not similarly   www.nature.com/scientificreports/ limited, which may explain why they were more sensitive to detecting mild cognitive impairment than FIM. Another explanation involves cognitive reserve, which has often been used to explain variations in severity between pathological brain damage and cognitive impairment 42 . Individual differences in cognitive reserve may explain some of the variation found in this study. Second, SE was less sensitive to the change in resting-state brain activity due to impaired carotid blood flow (Figs. 1, 3). No significant association was found between SE and ultrasonographic parameters ( Table 2, 3). All three MEG spectral parameters (MF, IAF, and SE) were calculated from the same normalised power spectral density (PSDn) of the MEG signals, and within-modality association analysis indicated that they correlated significantly, except between IAF and SE. However, these parameters can behave differently because they represent different properties of the PSDn. MF is an index that summarises the power balance between slow and fast neural oscillations, including alpha oscillations. IAF is another index that represents the peak frequency of alpha oscillations. MF and IAF are slightly overlapping, and we consider it reasonable to suggest that they positively correlated with each other. In contrast, SE provides complementary information to that yielded using MF and IAF, although SE is calculated from the same PSDn. SE quantifies the irregularity of the PSDn and reflects the diversity of neural oscillatory components. Although previous research has shown that all three MEG spectral parameters are sensitive to changes in resting-state brain activity due to cognitive impairment 17,[43][44][45][46][47][48] , most previous studies were conducted involving patients with Alzheimer's disease, not in those with vascular dementia. A previous study using electroencephalography showed that the properties of the power spectral density differ between Alzheimer's disease and vascular dementia 49 . Hence, we speculated that SE was less sensitive to changes in resting-state brain activity due to vascular dementia. This study had some limitations. First, data were acquired from patients who had been admitted to our hospital due to symptomatic cerebrovascular diseases. Patients with right hemisphere stroke tend to show fewer symptoms because the right hemisphere is considered the 'minor hemisphere' in most cases 13 . Moreover, such patients may have had more severe atherosclerosis and stroke at admission, which could have led to the asymmetry observed in our study. Furthermore, no healthy volunteers (i.e. a control group) were enrolled in our study because we focused on the pathological effects of cerebral blood flow rather than the physiological effects. To address these limitations, we have begun another study involving volunteers with no symptomatic stroke. Second, we did not consider arteriosclerosis in the cerebral arteries or other arteries, such as the vertebral arteries. Moreover, we did not consider the side and location of the lesions in the brain because they were heterogenous and often temporally and spatially multiple. Clinical magnetic resonance angiography results occasionally showed severe stenosis in cerebral arteries contralateral to the lesion-affected side. Occasionally, lesions were also located outside of the cerebrum (Supplementary Table 1) and, consequently, determining the affected side of the hemisphere was challenging. However, despite this limitation, asymmetry was apparent. Third, cognitive status was only assessed using cognitive-FIM, whereas other neuropsychological assessments such as the MMSE were not used (see the Methods section). In this retrospective study of clinical data, we did not undertake a cognitive assessment; however, our main findings indicating a correlation between ultrasonographic parameters and MEG spectral parameters and a correlation between cognitive-FIM scores and asymmetry between the left and right CCA were not affected. Fourth, our sample size was limited. Given the retrospective design of this clinical study, identifying patients who had undergone both ultrasonography and MEG was challenging as few patients with cerebrovascular diseases had undergone both examinations due to clinical limitations, such as the capacity of the clinical laboratory, or limitations in the health insurance system. To address this fourth limitation, we used a nonparametric bootstrapping approach for the correlation analysis. Given the high effect sizes (r in the correlation analysis was > 0.3 in terms of absolute value, in the most significant cases) and stable results across  Figure 3. Relationships between ultrasonographic parameters, MEG spectral parameters, and FIM scores. A broken box represents subcategory of each modality. Broken arrows indicate the parameters' significant correlations, whereas solid arrows indicate significant influences after controlling for biases in terms of patient age and sex. Red and blue arrows indicate significant associations regarding the left and right CCA, respectively (i.e., asymmetrical association). Black arrows indicate significant associations not relevant to the asymmetricity of the CCA (left or right). CCA common carotid arteries, DA diameter of artery, EDV end-diastolic velocity, FIMFunctional Independence Measure, IAF individual alpha frequency, MEG magnetoencepharography, MF medianfrequency, MV mean velocity, P I pulsatility index, PSV peak systolic flow velocity, RI resistance index, SE Shannon entropy. www.nature.com/scientificreports/ different statistical techniques (i.e. bootstrapping correlation and LMEM approaches: see "Methods" section for details), the results can be considered reliable. We consider that our study findings may help clinicians understand the importance of ultrasonography and MEG, which may encourage data collection and increase sample sizes in future studies. Finally, carotid ultrasonography measurements, MEG recordings, and FIM assessments had all been undertaken on different days. This was also due to limitations concerning data collection during daily clinical practice. In future studies, a controlled data collection procedure is needed to support our findings.

(unc.) P (FDR) β t P (unc.) P (FDR) β t P (unc.) P (FDR) β t P (unc.) P (FDR)
In conclusion, our study findings showed that pathological CCA on the left and right sides of the brain were differently associated with resting-state brain activity and cognitive status. Resting-state brain activity and cognitive status were associated with downstream factors (i.e. the PI and the RI) in the left CCA whereas, in the right CCA, they were associated with local factors (i.e. DA, PSV, MV, and EDV). This result indicates that hypoperfusion in the right CCA and cerebral microcirculation in the left CCA influenced brain activity and cognitive status. Consequently, therapeutic strategies to prevent cognitive impairment need to be different when targeting the left and right CCA.

Methods
Participants. Carotid ultrasonography and MEG data, and the FIM scores of 23 participants (women, n = 6; mean age ± standard deviation, 67.6 ± 13.6 years [range 35-88 years]) at the Kumagaya General Hospital (Japan) were retrospectively analysed. The patients were admitted to the Department of Neurosurgery at our hospital due to cerebrovascular diseases (ischemic stroke, n = 19; transient ischaemic attack, n = 4). The clinical profile details are shown in Supplementary Table 1. Our investigation was conducted according to the Declaration of Helsinki, in accordance with national and international guidelines. The study was approved by the Ethics Committee of Kumagaya General Hospital (approval number: 47). The committee granted the use of clinical data for this retrospective study unless patients did not agree to our re-use of their data. Written informed consent was obtained if a patient's cognitive/physical condition allowed.
Carotid ultrasonography. Carotid blood flow was evaluated using carotid ultrasonography as part of the clinical practice. The ultrasonography system used was ARIETTA 70 or Noblus (Hitachi, Tokyo, Japan). Six ultrasonographic parameters (DA, PSV, EDV, MV, PI, and RI) of the CCA were measured on both sides (left and right CCA). Following findings from a previous study that showed an association between blood flow velocity in the CCA (but not in the internal carotid artery) and cognitive performance 10 , we chose to evaluate the CCA instead of the internal carotid artery, which is downstream of the CCA and makes contact with the cerebral arteries directly. In each patient, six raw ultrasonographic parameters (DA, PSV, EDV, MV, PI, and RI) for each side of the CCA (left and right) were used for statistical analysis.
MEG scanning. The scanning and analysis procedures of MEG activity followed the procedure applied in our previous study 15 . Spontaneous neural oscillations were recorded for 5 min to screen for epilepsy and evaluate brain state as part of the clinical practice. The MEG system used was a 160-channel whole-head type (RICOH160-1; RICOH, Tokyo, Japan), placed in a magnetically shielded room. During the scan, the patients were asked to remain relaxed in a supine position with their eyes closed. The sensor coils were gradiometers with a diameter of 15 mm and a height of 50 mm. Each pair of sensor coils was separated at a 23-mm distance. The sampling frequency was 2,000 Hz with a 500-Hz low-pass filtering during the recording. MEG data analysis. MEG data were pre-processed offline using the software package SPM-12 (Wellcome Trust Centre for Neuroimaging, London, UK; https:// www. fil. ion. ucl. ac. uk/ spm/). Given that MEG spectral parameters are sensitive to artefacts, they were manually removed through applying a principal component analysis, if necessary. For this task, analysis software provided by the MEG manufacturer was used. Power line noise was removed using a 50-Hz band-stop filter. For ease of analysis, the continuous MEG signals were divided into 10-s segments. The segments in which the magnetic signal exceeded 6,000 fT were discarded, when applicable. Thereafter, different properties of spontaneous neural oscillations were quantified using the following three MEG spectral parameters: MF, IAF, and SE 17,24,25 . These MEG-based parameters were computed from the power spectral density (PSD). The PSD was estimated using the Blackman-Tukey method through utilising nonoverlapping 10-s segments. To obtain the normalised PSD (PSDn), the original PSD was divided by the power in the frequency range of interest, i.e. 1-70-Hz 50 .
The first parameter, namely, MF, quantifies the frequency lying at the midpoint of the PSDn (i.e. the median of the frequency distribution represented by the PSDn). MF is a useful spectral parameter to summarise the slowing of spontaneous neural oscillatory activity in patients with dementia 17 as it reflects the typical increase of low frequency oscillatory components, along with the decrease of high frequency neural activity in patients with cognitive impairment. The second parameter, namely, IAF, provides supplementary information to MF. It is computed as the frequency at which the peak of the PSDn in the alpha band is observed 17 . IAF is the parameter that characterises dominant alpha activity, typically observed in human adults in the eyes-closed resting condition, although it gradually alters during dementia progression 17 . The third parameter, namely, SE, yields a complementary description of the PSDn to MF and IAF. Specifically, SE quantifies the irregularity of the frequency distribution of the oscillatory components represented in the PSDn 17,25 . Hence, it provides an estimation of the irregularity of MEG activity. Interestingly, previous studies have showed that SE can reflect the loss of irregularity associated with the progression of dementia 17,25 .
These spectral parameters were calculated for each 10-s epoch and MEG sensor, after which they were averaged across epochs and sensors to generate three representative MEG spectral parameters for each patient. www.nature.com/scientificreports/ Cognitive and motor status assessment. Patients' cognitive and motor statuses were assessed using the FIM during their admission as a part of the clinical practice. The FIM is an assessment tool for cognitive and motor status during rehabilitation for stroke 22 . The FIM is the most commonly used test in stroke units and rehabilitation departments in Japan to evaluate and monitor a patient's condition, and its use is strongly recommended (and is virtually mandatory) by the Japanese Ministry of Health, Labour and Welfare. The FIM is advantageous when it is used for admitted patients with cerebrovascular diseases because it does not require any patient effort. It can even be used for patients with severe cognitive impairment, paralysis, or aphasia. Most other neuropsychological assessments cannot properly be used for these patients. The reliability and validity of the FIM have previously been well established in the field of rehabilitation 51,52 . The FIM consists of two domains: cognitive-FIM and motor-FIM. The maximum possible cognitive-FIM and motor-FIM scores are 35 points and 83 points, respectively, with a lower score indicating more severe impairment. The date difference between a FIM assessment and a MEG scan was 31.7 ± 27.9 days (range 0-108 days).

Statistical analysis.
To examine the relationship between data modalities (i.e. ultrasonographic parameters, MEG spectral parameters, and FIM scores), a correlation analysis was performed using a non-parametric bootstrapping approach. Bootstrapping statistics have methodological advantages over classical statistical inference (e.g. the Gaussian assumption) 53 . The correlations were examined within modalities and between modalities, separately. For each pair of variables, Pearson's coefficient was calculated through resampling with replacement data across all patients 20,000 times. The percentage of the resampled coefficients, when larger or smaller than 0 (the smaller value), was taken as the significance level (P value). We report the grand mean of the correlation coefficient (r) across bootstrap iterations and P values.
As an extension of the correlation analysis, possible biases in relation to patient age and sex were considered. Bias-free between-modality relationships were examined using an LMEM analysis. An LMEM analysis assesses directional relationships; therefore, we made the following assumptions according to physiological rationales: (1) ultrasonographic parameters (predictor variables) influence MEG spectral parameters and FIM scores (response variables), and (2) MEG spectral parameters (predictor variables) influence FIM scores (response variables). For each pair of variables, the response variable was subjected to LMEM with two fixed covariates, one of which was a predictor variable and the other was patient age. To consider sex differences, a random intercept and random slopes (for both fixed predictors) were entered into the model for each sex. The model was estimated using a maximum likelihood method. Estimated fixed coefficients (β) of fixed predictors were tested for a null hypothesis that the coefficients would be equal to zero, using a t test.
Since the analyses were exploratory and generated matrices (Tables 1, 2, 3) where each of the statistical values were tested against our null hypothesis (that the coefficients would be equal to zero), this series of results was at risk of an increasing Type-I error 54 . To manage this risk, we reported P values controlled for the false detection rate (FDR) using the Benjamini-Hochberg method 55 . Although we considered P (FDR-corrected) < 0.05 as statistically significant, P (uncorrected) < 0.05 has also been reported to indicate mild correlations/influences between tested parameters. Significant values are marked with asterisks in Tables 1, 2  Ethics approval and consent to participate. Reuse of the data for the present study was approved by the ethics committee of Kumagaya General Hospital (#47). Additionally, written informed consents for using data were obtained as far as patients' cognitive/physical condition allowed.