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### Article

#### Research Article

2020; 13(2): 40-47

Published online April 1, 2020 https://doi.org/10.1016/j.jams.2018.11.005

Copyright © Medical Association of Pharmacopuncture Institute.

## Laser Acupuncture in Open-Angle Glaucoma Treatment: A Retrospective Study of Eye Blood Flow

Marzio Vanzini1, Michele Gallamini2*

1Oculistica Viva Eye Clinic, Via Ugo Lenzi, 1 40122 Bologna, Italy
2Sal. Maggiolo di Nervi, 7 16167 Genova, Italy

Correspondence to:Michele Gallamini

Received: March 20, 2018; Revised: August 17, 2018; Accepted: November 29, 2018

### Abstract

Patients with glaucoma can show blood flow anomalies at the eye vessel level. A causal relationship is reasonably expected, but so far, it has not been demonstrated. Traditional Chinese medicine indicates that acupuncture can promote specific blood perfusion in specific body districts. Ninety-eight patients with open-angle glaucoma were treated with an ultralow light–level laser, according to a specific acupuncture protocol, and their blood flow was measured before and after a six-week treatment cycle. Doppler measurements showed significant modifications in both pulsatility and resistivity indexes. The most relevant outcome of this study is that the applied treatment demonstrated its effectiveness not only in vasodilation but also in perfusion control that seems to restore appropriate functionality. The protocol therefore should be investigated in future controlled studies and perhaps in other blood perfusion–related pathologies.

Keywords: laser acupuncture, eye blood perfusion, open-angle glaucoma, ultra-low-level laser therapy

### 1. Introduction

It is well known that in several eye pathologies, open-angle glaucoma among them, blood flow anomalies can be observed that are deemed to be among concurring factors for the pathology itself [1-4]. Acupuncture treatment, applied according to traditional Chinese medicine, can modify blood flow parameters and is well known [5].

Patients with open-angle glaucoma reporting to the Oculistica Viva Eye Clinic are routinely treated by ultra-low-level laser therapy (ULLLT), according to an acupuncture protocol, and subjected to color Doppler measurement both before and after treatment. Such a measurement, on such tiny vessels, does require a specific skill by the operator, and this study is a special tribute to the skill of the late Dr. Cipriano Ridolfi, who collected the majority of the included data. The present study reports a retrospective analysis of the evidence provided by 98 patients at different glaucoma stages.

### 2.1. The sample

Ninety-eight subjects affected by open-angle glaucoma reported to the Oculistica Viva ophthalmic clinic.

All patients, duly informed, gave their written consent both to the treatment and to the data collection.

It is known that this pathology does not depend on the sex of the patient; all the data were therefore pooled in a single sample.

### 2.2. Laser acupuncture treatment

Within the two weeks after the first measurement, a six-weekly session treatment protocol was started. The treatment was applied by means of the BioliteLP020® (RGMD SpA, Italy). The same operator, a certified acupuncture ophthalmologist medical doctor (MD), performed one treatment session weekly for six weeks.

The device features ULLLT with a square-wave, modulated emission [6] whose effectiveness in acupuncture-derived treatments had been previously demonstrated [7].

The main characteristics of the BioliteLP020® are as follows: laser emission wavelength: λ = 670 nm; radiated power: peak = 5 mW, average = 0.05 mW; spot surface: ≈ 0.13 cm2; and squarewave modulation: frequency = 100 Hz, duty cycle = 1%.

### 2.3. Selected acupoints

The selection is the same that was successfully applied in the treatment of amblyopia [8] and includes the following:

• LI1dadded for its well-known effectiveness in improving blood flow in the cerebral arteries and in the central retina arteries, useful in many eye pathologies.

• LI4dthe master point for the head and neck. It is well known for its effects on blood circulation, namely, in the cerebral and retinal arteries [9,10].

• LI7dselected because we have experienced its support of other LI points in the circulatory functions.

• LI20dselected because it is known for a specific channel to ST1 (stimulating the Qi flow to the face).

• BL1, ST1, GB1, TE23, and EX-HN5dadded because they are known to be specific to eye and vision pathologies.

The acupoint location is described in Table 1 and shown in Fig. 1.

Selected acupoints..

AcupointLocation
BL1JingmingJust above the inner canthus of the eye
LI1ShangyangJust behind the corner of the nail on the radial side of the index ﬁnger
LI4HeguIn the middle of the 2nd metacarpal bone on the radial side
LI 7Wenliu5 cun above the crease of the wrist.
LI20YingxiangIn the nasolabial groove, level with the midpoint of the lateral border of the ala nasi
ST1ChengqiBelow the pupil, between the eyeball and the infraorbital ridge
GB1TongzijiaoSlightly lateral to the outer canthus of the eye in a depression on the lateral side of the orbit
TE23SizhukongIn a depression at the lateral end of the eyebrow
EX-HN5TaiyangAt the temple, in a depression about 1 cun posterior to the midpoint between the lateral end of the eyebrow and the outer canthus of the eye.

Figure 1. The selected acupoints. Image adapted from an original by courtesy of Fremslife, Genoa, Italy.

These criteria were derived from the specifically referenced documents and from several traditional Chinese medicine textbooks listed as general references [11-20]. Unfortunately, some of the latter are out of print or generally not easy to find.

The points were stimulated bilaterally. Each of the selected points was stimulated with 20 half-second flashes (flash repetition rate: 1/sec) using the Biolite®. The tip of the emitting probe was kept at some 30 mm from the skin (spot area: 0.13 cm2) and perpendicular to the selected acupoint.

### 2.4. Color Doppler measurements

The reproducibility of the central retina artery measurement has been demonstrated [21]. Measurements were performed using Antares (Siemens) using a VFX 9-4 probe. According to the Antares manual, its main performances related to our measurement are as follows: flow speed range, 10-600 cm/sec and tolerance on flow (probe at 45°), 10%.

### 2.5. Measurements

The central retina artery measurements performed using Antares have provided the most used indexes [22-24], calculated from the flow speed [(peak systolic velocity, Psv) and (end-diastolic velocity, Edv)]:

• Resistivity index: The resistivity index (RI) (known also as the Pourcelot Index) is defined as the ratio between the difference of the maximum and minimum flow speeds and the maximum (diastolic) speed.

$RI=(Psv-Edv)Psv$

• Pulsatility index: The pulsatility index (PI) is defined as the ratio between the difference of the maximum and minimum flow speeds and the mean flow speed.

$PI=2×(Psv-Edv)Psv+Edv$

Such parameters were measured for the central retina artery [25].

### 2.6. Statistical analysis

The results were analyzed with the assistance of Dr. T. F. Piccinno, PhD (V.I.E. srl, Genoa). Analyses were performed using R statistical software [26] and the lme4 package [27].

### 2.7. Participants

Ninety-eight participants with glaucoma were enrolled in this study. The mean age was 60.71 ± 13.15 (range = 20-84). Women comprised 65% of the sample (N = 64).

PI and RI measures were taken before and after the treatment for each eye. The interval between the first and the second measurements (Δ days) varied between 19 and 1717 days (mean = 209.42 ± 253.86 days). The participants were clustered in five quantiles, according to the values measured at the first measurement. Table 2 shows the PI and RI value ranges for each quantile.

IntervalPulsatility indexResistivity index
Q1PI < 0.85RI < 0.61
Q20.85 < PI < 1.050.61 < RI < 0.71
Q31.05 < PI < 1.280.71 < RI < 0.78
Q41.28 < PI < 1.460.78 < RI < 0.82
Q5PI > 1.46RI > 0.82

PI = pulsatility index; RI = resistivity index..

&md=tbl&idx=2' data-target="#file-modal"">Table 2

Analyzed values' intervals..

IntervalPulsatility indexResistivity index
Q1PI < 0.85RI < 0.61
Q20.85 < PI < 1.050.61 < RI < 0.71
Q31.05 < PI < 1.280.71 < RI < 0.78
Q41.28 < PI < 1.460.78 < RI < 0.82
Q5PI > 1.46RI > 0.82

PI = pulsatility index; RI = resistivity index..

### 3.1. Main evidence

The data with the results of the measurements in Table 3 show only a very small modification of the mean of PI and RI scores. However, a quick look at the plot of the second versus the first measurements shows an unexpected behavior (see Fig. 2). By applying the interocular trauma test (first invented by Joe Berkson at the Mayo Clinic: “Plot the data, and if the result hits you between the eyes, it's significant.”), we could not but be struck by the apparent clockwise rotation of the distribution and by the significant contraction of the standard deviation of the measures. The diagonal line showing the “no change” reference further suggested a sort of normalizing effect that convinced us to deepen the statistical analysis along that line.

Pulsatility indexResistivity index

PretreatmentPost-treatmentPretreatmentPost-treatment
Average1.1671.1430.7130.699
Standard deviation0.3470.2370.1250.083
Median1.1451.1200.7250.700
Reference (*) [25]1.0180.675
&md=tbl&idx=3' data-target="#file-modal"">Table 3

Average values' modifications..

Pulsatility indexResistivity index

PretreatmentPost-treatmentPretreatmentPost-treatment
Average1.1671.1430.7130.699
Standard deviation0.3470.2370.1250.083
Median1.1451.1200.7250.700
Reference (*) [25]1.0180.675

Figure 2. Pulsatility and resistivity indexes, after vs. before treatment. In the two graphs, individual measurements are compared: post-treatment values on the vertical axis versus pretreatment ones on the horizontal axis. The two axes have the same limits, and obviously, the diagonal line from the origin to the upper right corner represents the no change line. By plotting the values while observing that the mean value is almost on the no change line, a rotation of the linear trend regression line toward the horizontal line is apparent. The clockwise rotation, that is confirmed also by the much smaller standard deviation shown by the error bars on the mean value, tells that low pretreatment values were increased by the treatment, whereas high pretreatment values were reduced. This rotation suggests a regulatory effect of the treatment. PI = pulsatility index; RI = resistivity index.

PI and RI are indexes currently used in blood flowmetry proportional to the arteries' compliance and to the blood flow rate. Akarsu and Bilgili [25] demonstrated the normal values for such parameters. The difference between velocities [(peak systolic velocity, Psv) and (end-diastolic velocity, Edv)] probably grows with arterial stiffness, but an excessive artery compliance might affect the blood flow pressure negatively. For this reason, Akarsu and Bilgili [25] set a reference: the measured indexes should not exceed either the upper or the lower limit across the given indications.

It was immediately self-evident that a beneficial effect followed the laser acupuncture treatment (see graphs in Fig. 2); we then decided to examine deeper to make sure that there were no confounding factors. Statisticians, with appropriate tools and methods, demonstrated that age and gender were not introducing any statistically significant difference and that the beneficial effect was not significantly affected by the differences in time difference between the first and second measurements.

For this purpose, we grouped the population into quantiles according to homogeneity indexes (Tables 2 and 3), and we plotted the measurements on a post-treatment versus pretreatment graph (see Fig. 3) (see Fig. 4).

Figure 3. Pulsatility index (PI) and resistivity index (RI) by quantiles, after vs. before treatment. On the same type of graph used in Fig. 2, post-treatment vs pretreatment values that have been grouped by pretratment value intervals of both pulsatility index (PI) and resistivity index (RI) are plotted. The clockwise rotation is even more clear, and data are converging toward the values (hypertension, glaucoma, and control) discussed in the article by Akarsu and Bilgili [25].

Figure 4. Modifications by quantiles. The change of mean values for each quantile is plotted and demonstrates their convergence toward the standard values proposed by the referenced literature. Legend: (*) reference values according to Akarsu C., Bilgili M.Y.K. (2004). PI = pulsatility index; RI = resistivity index.

### 3.2. The statistical evaluation

Two linear mixed models were specified to predict the PI and RI independently. Fixed effects were time of measurement (T1 before treatment, T2 after treatment), interval of the first measurement (Q1, Q2, Q3, Q4, and Q5), the participant's gender (male, female) and age (years), and the time difference (days) between T1 and T2; the participant's ID was the clustering variable. In addition, the interaction between time of measurement and interval was included to test whether changes in the PI and RI scores after the treatment varied between intervals. We hypothesized that the treatment could normalize the scores of the RI and PI, reducing toohigh scores and increasing too-low scores.

Linear mixed models are linear regression models, in which both fixed effects and random effects are specified [28]. A random effect is generally something that can be expected to have a nonsystematic or unpredictable (thus considered random) influence on the outcome variable. Introducing random effects in the model allows generalizing over the idiosyncrasies of single clusters (in this case, participants). In this case, random effects could be different levels of the PI and RI across participants (intercepts) and different effects of the treatment across participants (slopes). Fixed effects, on the other hand, are expected to have a systematic and predictable influence on outcome variables. While fixed effects exhaust all the levels of a factor, random effects sample from the population of interest. If data are clustered, a linear mixed model that properly accounts for clustering provides more power. The intraclass correlation coefficient was computed to determine the proportion of total variance in the PI and RI that was accounted for by the participants' differences. The intraclass correlation coefficients were 0.50 and 0.47 for the PI and RI, respectively; these results suggested that the specification of a linear mixed model was needed because the clustering [28] accounted for more than 5% of the variance of the outcome variables.

Null models, fixed effects with random intercept models, and fixed effects with random intercept and slope models were compared. The latter model had better goodness of fit when indexed by information indices (Akaike information criterion and Bayesian information criterion; smaller values indicate better fit), and therefore, we considered its results. Time and interval were significant predictors of both the PI and RI. The interaction between time and interval significantly predicted the PI and RI; these results support the hypothesis of normalization of the scores after the treatment because higher scores tended to decrease toward normal values, whereas smaller scores tended to increase toward normal values.

Age (RI: β = 0.0006, p = 0.3; PI: β = 0.0003, p = 0.05) and gender (RI: β = 0.013, p = 0.49; PI: β = 0.007, p = 0.121) had no significant effect on the outcome variables. The difference in days between T1 and T2 (RI: β= 0.00002, p = 0.01; PI; β= 0.00005, p = 0.27) had a significantly negative effect on the RI and no significant effect on the PI. Each day produced an expected mean decrease of 0.00002 in the RI score on average, whereas treatment (time) produced, on average, a much stronger increase of RI scores (0.1513) and PI scores (0.417). The same analyses were performed on two reduced samples [Model C included only participants tested twice in two years (Δ days < 730); Model D included only participants tested twice in one year (Δ days < 365)]; the results were consistent across models, confirming that the changes of the outcome variables were not related to the time difference between the two measurements (T1 and T2). Tables 4 and 5 show the results of the analysis.

*p < 0.05..

**p < 0.01..

***p < 0.001..

AIC = Akaike information criterion; BIC = Bayesian information criterion; PI = pulsatility index..

Number of observations: 383, groups: ID, 98..

Model A = fixed effects and random intercept. Number of observations: 383, groups: ID, 98..

Model B = fixed effects, random intercept and slope covariance. Number of observations: 383, groups: ID, 98..

Model C = Model B with Delta days < 730. Number of observations: 363, groups: ID, 93..

Model D = Model B with Delta days < 365. Number of observations: 315, groups: ID, 81..

&md=tbl&idx=4' data-target="#file-modal"">Table 4

Pulsatility index..

PI null modelPI Model API Model BPI Model CPI Model D
Fixed effects
Intercept1.1470.642***0.695***0.700***0.714***
Time0.342***0.417***0.421***0.396***
Interval
Q1 vs Q20.225***0.229***0.225***0.227***
Q1 vs Q30.403***0.409***0.407***0.411***
Q1 vs Q40.642***0.644***0.640***0.643***
Q1 vs Q50.898***0.921***0.921***0.926***
Age0.0010.0010.0010.000
Gender0.0260.0110.0110.013
ΔDays0000
Time*Q1 vs Q2-0.222***-0.260***-0.257***-0.230***
Time*Q1 vs Q3-0.346***-0.415***-0.421***-0.390***
Time*Q1 vs Q4-0.548***-0.642***-0.653***-0.613***
Time*Q1 vs Q5-0.714***-0.892***-0.893***-0.851***
Random effects
Intercept0.0440.0070.0000.0000.000
ID0.0330.0330.031
Corr111
Residual0.0450.0210.0110.0110.011
Goodness of fit
Deviance50.8-311.1-448.4-419.4-352.3
AIC56.8-281.1-414.4-385.4-318.3
BIC68.7-221.9-347.2-319.2-254.5

*p < 0.05..

**p < 0.01..

***p < 0.001..

AIC = Akaike information criterion; BIC = Bayesian information criterion; PI = pulsatility index..

Number of observations: 383, groups: ID, 98..

Model A = fixed effects and random intercept. Number of observations: 383, groups: ID, 98..

Model B = fixed effects, random intercept and slope covariance. Number of observations: 383, groups: ID, 98..

Model C = Model B with Delta days < 730. Number of observations: 363, groups: ID, 93..

Model D = Model B with Delta days < 365. Number of observations: 315, groups: ID, 81..

*p < 0.05..

**p < 0.01..

***p < 0.001..

AIC = Akaike information criterion; BIC = Bayesian information criterion; RI = resistivity index..

Null model. Number of observations: 387, groups: ID, 98..

Model A = fixed effects and random intercept. Number of observations: 387, groups: ID, 98..

Model B = fixed effects, random intercept and slope covariance. Number of observations: 387, groups: ID, 98..

Model C = Model B with Delta days < 730. Number of observations: 363, groups: ID, 93..

Model D = Model B with Delta days < 365. Number of observations: 315, groups: ID, 81..

&md=tbl&idx=5' data-target="#file-modal"">Table 5

Resistivity index..

RI null modelRI Model ARI Model BRI Model CRI Model D
Fixed effects
Intercept0.7060.527***0.529***0.530***0.5279***
Time0.142***0.151***0.148***0.1486***
Interval
Q1 vs Q20.110***0.110***0.107***0.108***
Q1 vs Q30.190***0.189***0.186***0.185***
Q1 vs Q40.249***0.248***0.246***0.246***
Q1 vs Q50.305***0.309***0.303***0.302***
Age00.0000.000*0.000*
Gender0.0050.0070.0070.006
ΔDays0.0000.000*0.000-0.000*
Time*Q1 vs Q2-0.118***-0.121***-0.118***-0.120***
Time*Q1 vs Q3-0.189***-0.188***-0.185***-0.180***
Time*Q1 vs Q4-0.236***-0.242***-0.240***-0.239***
Time*Q1 vs Q5-0.244***-0.284***-0.281***-0.282***
Random effects
Intercept0.0040.0000.0000.0000.000
ID0.0020.0020.002
Correlation1.0001.0001.000
Residual0.0050.0020.0010.0010.001
Goodness of fit
Deviance-828-1312-1431-1365-1174
AIC-822-1282-1397-1331-1140
BIC-810-1223-1330-1265-1076

*p < 0.05..

**p < 0.01..

***p < 0.001..

AIC = Akaike information criterion; BIC = Bayesian information criterion; RI = resistivity index..

Null model. Number of observations: 387, groups: ID, 98..

Model A = fixed effects and random intercept. Number of observations: 387, groups: ID, 98..

Model B = fixed effects, random intercept and slope covariance. Number of observations: 387, groups: ID, 98..

Model C = Model B with Delta days < 730. Number of observations: 363, groups: ID, 93..

Model D = Model B with Delta days < 365. Number of observations: 315, groups: ID, 81..

### 4. Discussion

It is known that open-angle glaucoma bearers generally show poor blood flowparameters. Our study aimed to demonstrate that a specific laser acupuncture protocol could ameliorate both the PI and the RI in patients with open-angle glaucoma.

Restoring appropriate blood flow is obviously beneficial to the eye, but it is hard to demonstrate a therapeutic effect of laser acupuncture over a complex pathology such as open-angle glaucoma.

Given the variability of open-angle glaucoma conditions, the rather large cohort of patients that was examined could afford a significant result only in terms of blood flow. The suggested further analysis of ophthalmic parameters that could support a conclusion in terms of therapeutic indications will be performed on more homogeneous and numerically significant samples.

### 4.1. Ultrasound Doppler measurements

Although the statistical significance is very high for both indexes, the clinical meaning of these is worth a comment. Although there are few doubts about the RI giving the difference between systolic and diastolic flows relative to the systolic flow, the PI that is normalizing the same difference to the average flow enjoys less consensus [23]. The PI is in fact generally applied to larger vessels in which a flow reversal can be observed. It might be worth, however, remarking that in our study, both indexes were behaving the same way.

### 4.2. Observed modifications

Measured values after the treatment show a trend toward standard reference values. If a modification could be expected, as suggested by many acupunctural indications [29-34], toward a higher perfusion or toward a reduction of the intraocular pressure [35] (although there is no formal consensus yet [36,37]), the regulatory effect that our study reports would be in all respects a novelty worth a specific note.

### 4.3. Clinical relevance

Far from expressly conclusive remarks, we wish to propose the possible action of laser acupuncture beyond the vasomotion effect and on the physiological flow control mechanism, even more so because the choroid flow lacks a specific autonomous flow control capable of reacting to blood or eye pressure anomalies, causing flow anomalies.

### 4.4. Therapy implications

The measurements were started to focus on treatment of the possible causes of open-angle glaucoma. The results are rather encouraging because they show a beneficial effect on the blood flow parameters, lasting to the medium-term observation (206 days). It is worth indicating that no adverse effects were observed.

### 5. Conclusion

Far from suggesting a possible therapeutic value of this protocol for open-angle glaucoma, we conclude that the ULLLT acupuncture treatment is an effective way to reduce anomalies of blood flow in the central artery of the retina in patients with open-angle glaucoma.

### Acknowledgments

This study was made possible primarily by the skill and dedication of the late Dr. Cipriano Ridolfi, to whom the authors are indebted for his professionalism and human touch in performing these measurements. The authors join his family and assistants in the memory of a great medical doctor. The authors also thank Professor Carlo Chiorri of Genoa University and VIE Srl for the statistical evaluation and Professor Lorenzo Derchi of Universit a di Genova for advice in support of understanding the clinical meaning of the Doppler measurements.

### Declaration of competing interest

The authors declare no conflict of interests. Michele Gallamini, coauthor of the design of the device, is not holding any right on device production.

### Fig 1.

Figure 1.The selected acupoints. Image adapted from an original by courtesy of Fremslife, Genoa, Italy.
Journal of Acupuncture and Meridian Studies 2020; 13: 40-47https://doi.org/10.1016/j.jams.2018.11.005

### Fig 2.

Figure 2.Pulsatility and resistivity indexes, after vs. before treatment. In the two graphs, individual measurements are compared: post-treatment values on the vertical axis versus pretreatment ones on the horizontal axis. The two axes have the same limits, and obviously, the diagonal line from the origin to the upper right corner represents the no change line. By plotting the values while observing that the mean value is almost on the no change line, a rotation of the linear trend regression line toward the horizontal line is apparent. The clockwise rotation, that is confirmed also by the much smaller standard deviation shown by the error bars on the mean value, tells that low pretreatment values were increased by the treatment, whereas high pretreatment values were reduced. This rotation suggests a regulatory effect of the treatment. PI = pulsatility index; RI = resistivity index.
Journal of Acupuncture and Meridian Studies 2020; 13: 40-47https://doi.org/10.1016/j.jams.2018.11.005

### Fig 3.

Figure 3.Pulsatility index (PI) and resistivity index (RI) by quantiles, after vs. before treatment. On the same type of graph used in Fig. 2, post-treatment vs pretreatment values that have been grouped by pretratment value intervals of both pulsatility index (PI) and resistivity index (RI) are plotted. The clockwise rotation is even more clear, and data are converging toward the values (hypertension, glaucoma, and control) discussed in the article by Akarsu and Bilgili [25].
Journal of Acupuncture and Meridian Studies 2020; 13: 40-47https://doi.org/10.1016/j.jams.2018.11.005

### Fig 4.

Figure 4.Modifications by quantiles. The change of mean values for each quantile is plotted and demonstrates their convergence toward the standard values proposed by the referenced literature. Legend: (*) reference values according to Akarsu C., Bilgili M.Y.K. (2004). PI = pulsatility index; RI = resistivity index.
Journal of Acupuncture and Meridian Studies 2020; 13: 40-47https://doi.org/10.1016/j.jams.2018.11.005

Selected acupoints..

AcupointLocation
BL1JingmingJust above the inner canthus of the eye
LI1ShangyangJust behind the corner of the nail on the radial side of the index ﬁnger
LI4HeguIn the middle of the 2nd metacarpal bone on the radial side
LI 7Wenliu5 cun above the crease of the wrist.
LI20YingxiangIn the nasolabial groove, level with the midpoint of the lateral border of the ala nasi
ST1ChengqiBelow the pupil, between the eyeball and the infraorbital ridge
GB1TongzijiaoSlightly lateral to the outer canthus of the eye in a depression on the lateral side of the orbit
TE23SizhukongIn a depression at the lateral end of the eyebrow
EX-HN5TaiyangAt the temple, in a depression about 1 cun posterior to the midpoint between the lateral end of the eyebrow and the outer canthus of the eye.

Analyzed values' intervals..

IntervalPulsatility indexResistivity index
Q1PI < 0.85RI < 0.61
Q20.85 < PI < 1.050.61 < RI < 0.71
Q31.05 < PI < 1.280.71 < RI < 0.78
Q41.28 < PI < 1.460.78 < RI < 0.82
Q5PI > 1.46RI > 0.82

PI = pulsatility index; RI = resistivity index..

Average values' modifications..

Pulsatility indexResistivity index

PretreatmentPost-treatmentPretreatmentPost-treatment
Average1.1671.1430.7130.699
Standard deviation0.3470.2370.1250.083
Median1.1451.1200.7250.700
Reference (*) [25]1.0180.675

Pulsatility index..

PI null modelPI Model API Model BPI Model CPI Model D
Fixed effects
Intercept1.1470.642***0.695***0.700***0.714***
Time0.342***0.417***0.421***0.396***
Interval
Q1 vs Q20.225***0.229***0.225***0.227***
Q1 vs Q30.403***0.409***0.407***0.411***
Q1 vs Q40.642***0.644***0.640***0.643***
Q1 vs Q50.898***0.921***0.921***0.926***
Age0.0010.0010.0010.000
Gender0.0260.0110.0110.013
ΔDays0000
Time*Q1 vs Q2-0.222***-0.260***-0.257***-0.230***
Time*Q1 vs Q3-0.346***-0.415***-0.421***-0.390***
Time*Q1 vs Q4-0.548***-0.642***-0.653***-0.613***
Time*Q1 vs Q5-0.714***-0.892***-0.893***-0.851***
Random effects
Intercept0.0440.0070.0000.0000.000
ID0.0330.0330.031
Corr111
Residual0.0450.0210.0110.0110.011
Goodness of fit
Deviance50.8-311.1-448.4-419.4-352.3
AIC56.8-281.1-414.4-385.4-318.3
BIC68.7-221.9-347.2-319.2-254.5

*p < 0.05..

**p < 0.01..

***p < 0.001..

AIC = Akaike information criterion; BIC = Bayesian information criterion; PI = pulsatility index..

Number of observations: 383, groups: ID, 98..

Model A = fixed effects and random intercept. Number of observations: 383, groups: ID, 98..

Model B = fixed effects, random intercept and slope covariance. Number of observations: 383, groups: ID, 98..

Model C = Model B with Delta days < 730. Number of observations: 363, groups: ID, 93..

Model D = Model B with Delta days < 365. Number of observations: 315, groups: ID, 81..

Resistivity index..

RI null modelRI Model ARI Model BRI Model CRI Model D
Fixed effects
Intercept0.7060.527***0.529***0.530***0.5279***
Time0.142***0.151***0.148***0.1486***
Interval
Q1 vs Q20.110***0.110***0.107***0.108***
Q1 vs Q30.190***0.189***0.186***0.185***
Q1 vs Q40.249***0.248***0.246***0.246***
Q1 vs Q50.305***0.309***0.303***0.302***
Age00.0000.000*0.000*
Gender0.0050.0070.0070.006
ΔDays0.0000.000*0.000-0.000*
Time*Q1 vs Q2-0.118***-0.121***-0.118***-0.120***
Time*Q1 vs Q3-0.189***-0.188***-0.185***-0.180***
Time*Q1 vs Q4-0.236***-0.242***-0.240***-0.239***
Time*Q1 vs Q5-0.244***-0.284***-0.281***-0.282***
Random effects
Intercept0.0040.0000.0000.0000.000
ID0.0020.0020.002
Correlation1.0001.0001.000
Residual0.0050.0020.0010.0010.001
Goodness of fit
Deviance-828-1312-1431-1365-1174
AIC-822-1282-1397-1331-1140
BIC-810-1223-1330-1265-1076

*p < 0.05..

**p < 0.01..

***p < 0.001..

AIC = Akaike information criterion; BIC = Bayesian information criterion; RI = resistivity index..

Null model. Number of observations: 387, groups: ID, 98..

Model A = fixed effects and random intercept. Number of observations: 387, groups: ID, 98..

Model B = fixed effects, random intercept and slope covariance. Number of observations: 387, groups: ID, 98..

Model C = Model B with Delta days < 730. Number of observations: 363, groups: ID, 93..

Model D = Model B with Delta days < 365. Number of observations: 315, groups: ID, 81..

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