Abstract
Background
The femoral vein diameter is a critical factor when assessing endoprosthetic valve size for the treatment of chronic venous insufficiency. To examine the previously stated correlation between body mass index and femoral vein diameter and to re-assess the anatomical and physiological demands for a valve implant for chronic venous insufficiency treatment, we measured the femoral vein diameter in 82 subjects.
Method
Femoral vein diameters (164 legs) were measured with B-mode sonography both in supine position at rest and in upright position during Valsalva maneuver.
Result
The mean femoral vein diameter differed significantly between supine position (13.6 ± 3.0 mm) and upright position (16.4 ± 2.6 mm). Males possessed a significant bigger diameter than females. A significant positive correlation between femoral vein diameter and body mass index was observed.
Conclusion
Assuming an increased femoral vein diameter due to obesity would further impair valve functionality by increasing distance between both valve cusps. For the development of artificial venous valves, it is crucial to consider patient- and condition-dependent vein dilation.
Introduction
The femoral vein diameter (FVD) is an anatomical parameter with underestimated clinical relevance. Basically, the FVD can be used to estimate the central venous pressure (CVP), 1 but it is also an important predictor of chronic venous insufficiency (CVI)2,3 and a critical factor when assessing endoprosthetic valve size for CVI treatment.4,5
Besides deep venous thrombosis (DVT), dilation of the deep venous system might also play an important role for CVI-causing valve dysfunction. Interestingly, the body mass index (BMI) seems to correlate with an increased diameter of the femoral vein (FV)6–10 which in turn marks adipositas as a potential factor in the development of venous valve dysfunction due to phlebotic dilation.
To assess the vascular diameters in the limbs, sonographic measurement is an efficient method. However, in the last two decades, only a few sonographic studies have contributed to our knowledge of the adult FVD and its correlation with various subject parameters.1–4,6–12 Moreover, physico-anatomical parameters of the FV have been neglected in past approaches developing artificial venous valves for minimally invasive therapy of CVI – attempts which have failed since almost 40 years. 13
To re-assess the anatomical and physiological demands for an artificial valve implant and to examine the correlation between BMI and FVD, we have measured the FVDs of a small representative population sample at various positions and under defined conditions.
Materials and methods
The study was approved by the local ethics committee. Patients (n = 75) and employees of the University Medical Center Rostock (n = 7) gave informed consent to the study protocol. All subjects were Caucasian. Patients have presented at the hospital due to minor ambulatory surgery (e.g. hand surgery, orthopedic surgery, port implantation). None of the subjects had severe diseases exceeding American Society of Anesthesiologists Physical Status (ASA PS) classifications 1 and 2. 14 Varicosis or CVI prevalence was not examined systematically. At least one male patient (61 years) had varicose veins on the right lower leg – his measurement data which featured no outlier and were within the range of the respective sub-cohorts were kept in the statistical analysis to retain representativeness. Measurements were done between 8:00 a.m. and 3:40 p.m. (mean: 12:35 a.m.)
The left and right FV was measured both supine and in upright position by an experienced anesthetist specialized in ultrasound-guided regional anesthesia and focused ultrasound in emergency settings (including venous compression ultrasonography).
Measurements
The supine position promotes (passive) venoconstriction to assess the minimum vein diameter. The measured leg is slightly tilted outwards to minimize the distance between ultrasound transducer and thigh vessels.
The upright position with Valsalva maneuver promotes venodilation to assess the maximum vein diameter. The measured leg is slightly tilted outwards.
The diameter of three positions was assessed for each side: (a) the common femoral vein (CFV; Vena femoralis communis) proximal to the orifice of the great saphenous vein (Vena saphena magna) (“CFV” position; Figure 1), (b) the proximal section of the FV about 1–2 cm distal to the orifice of the deep FV (Vena profunda femoris) (“proximal” position; Figure 1), and (c) the distal section of the FV about 20 cm distal to the orifice of the deep FV (“distal” position). Time between supine position and measurements in upright position plus Valsalva maneuver was about 1 min. To estimate a possible influence of time between supine and upright position on vein dilation, measurements were repeated in upright position combined with Valsalva maneuver after 5 min in three subjects for the right leg.
Spatial relations between measured upper segments (“CFV", “prox”) and anatomical landmarks in the right pelvis region (“distal” position not shown here). 3D reconstructions based on contrast medium enhanced magnet resonance imaging of male volunteer. CFV: common femoral vein; dfv: deep femoral vein; f: femur; fa: femoral artery; gsv: great saphenous vein; il: inguinal ligament. Scale bar = 2 cm.
The ultrasound machine (Sonosite, Bothell, WA, United States) had a 38 mm linear transducer (6–13 MHz).
The mean diameter for each measuring position was calculated by assessing both minimum and maximum diameter (cross measurement) with B-mode sonography (Figure 2). Besides their estimated anatomical location veins were identified by being compressed by brief transducer push and through differentiation with color Doppler sonography. Body height, weight and age were recorded for each subject.
Exemplary sonographic B-Mode image with measurement of the common femoral vein diameter (right to the common femoral artery). Scale bar = 10 mm.
Intraobserver variation was tested under same conditions for six subjects 21 months after the first measurements. Interobserver variation was tested for five subjects by re-measuring the FVD in raw digital ultrasound images (n = 29) with the analyze-tool in the image processing program ImageJ (Fiji). 15
Statistics
Cohort mean, standard deviation, minimum and maximum values are computed based on the single values for left and right leg. Statistics were computed with Microsoft Excel 2007 and R 16 and RStudio, 17 respectively.
Normal distribution was tested using the Shapiro–Wilk normality test (Shapiro.test in R). Variance similarity was assessed using the F-test (FTEST in Excel). For categorical comparisons of two groups without normal distribution, the Mann–Whitney U-test was run (Wilcox.test in R). For two groups with normal distribution, unpaired Student's or Welch's t-test, depending on variance similarity, was run (t.test in R; two-tailed). Bilateral differences between left and right leg were tested with the paired t-test.
P-values of ≤ 0.05 in group comparisons are supposed to represent significant differences between cohorts (0.01 < p ≤ 0.05 = slightly significant; 0.001 < p ≤ 0.01 = significant; p ≤ 0.001 = highly significant). P-value adjustments concerning cumulated alpha errors (familywise error rate) due to multiple testing18,19 were done with the Holm–Bonferroni correction 20 (for number of tests per “family” (k) see Supplementary Tables 1 and 2).
For the statistic tests (except for bilateral differences), the mean FVD (left + right leg) for each subject was used.
Age cohorts (mixed-sex) were classified as the following:
age ≤ 30 yr = “young”
30 < age > 65 = “middle-aged”
age < 65 = pre-65
age ≥ 65 = “old”
Height cohorts (mixed-sex) were classified as the following:
height ≤ 170 cm = “small”
170 cm < height < 180 cm = “medium”
height ≥ 180 cm = “tall”
BMI values (kg/m2) (mixed-sex) were classified according to the WHO 21 :
BMI < 18.5 = underweight
18.5 ≤ BMI < 25 = normal weight
BMI ≥ 25 = adiposity
25 ≤ BMI < 30 = overweight
BMI ≥ 30 = obesity
Male and female cohorts were further divided into approximate equal sub-cohorts according to their median value for each subject parameter (age, height, BMI) and tested for significant differences between sub-cohorts correlated with these parameters (unpaired Student's t-test, Welch's t-test or Mann–Whitney U-test).
Simple and multiple linear regression (Analysis-ToolPak in Microsoft Excel 2007) with subject parameters (age, height, BMI) was done for FVDs of male and female cohort. In the multiple linear regression, variables with non-significant coefficients were excluded in a second step to re-calculate and optimize the linear regression model.
Results
Characteristics and femoral vein diameter for overall, male, and female cohort.
Note: Mean values are given with standard deviation and ranges.
BMI: body mass index; CFV: common femoral vein; FV: femoral vein.
Coherence between FVD and subject position
The FVD differed significantly (p ≤ 0.001; paired t-test) between supine position at rest and upright position during Valsalva maneuver (Figure 3). The mean diameter of the CFV measured 13.6 ± 3.0 mm in supine position (range: 5.6–21.3 mm) and 16.4 ± 2.6 mm in upright position during Valsalva (range: 9.5–24.5 mm), which is a mean diameter increase of 21% in upright position. The mean diameter of the middle position (proximal FV) distal to the orifice of the deep FV measured 9.8 ± 2.3 mm in supine position (range: 3.8–19.8 mm) and 11.3 ± 2.0 mm in upright position during Valsalva (range: 6.0–16.9 mm), which is a mean diameter increase of 15% in upright position. The distal position (distal FV) measured 8.6 ± 1.8 mm in supine position (range: 3.4–13.3 mm) and 9.8 ± 1.7 mm in upright position during Valsalva (range: 4.4–15.2 mm), which is a mean diameter increase of 14% in upright position.
Comparison of the mean femoral vein diameter (FVD) for different subject positions (supine at rest or upright during Valsalva maneuver). Standard deviation and probability indices for paired t-test (comparison for mean value difference) are shown. *** = highly significant (p ≤ 0.001, k = 3). CFV: common femoral vein.
To estimate a possible influence of time between supine and upright position on vein dilation, measurements were repeated in upright position combined with Valsalva maneuver for the right leg in three subjects. The mean difference after 5 min was only minor: minus 0.3 ± 0.5 mm (mean absolute value: 0.4 ± 0.7 mm).
Correlations between FVD and sex
The male cohort possessed a significant bigger diameter than the female cohort for all measured segments and for both subject conditions (Figure 4; Supplementary Table 1). BMI-adjusted differences between males and females remained significant for the CFV in the cohorts with normal BMI (supine; p = 8.39 E-03) and adiposity (upright; p = 2.48 E-02). Age-adjusted differences remained significant for the CFV (p ≤ 0.001) and distal FV (p ≤ 0.05) for both conditions in the “middle-aged” and “pre-65” cohort (Supplementary Table 1).
Comparison of the mean femoral vein diameter (FVD) for male and female cohort and different subject positions (supine at rest or upright during Valsalva maneuver). Standard deviation and probability indices for unpaired t-test (comparison for mean value difference) are shown. ** = significant (0.001 < p ≤ 0.01, k = 6), *** = highly significant (p ≤ 0.001, k = 6). CFV: common femoral vein; dist: distal femoral vein; prox: proximal femoral vein; sup: supine position at rest; up: upright position during Valsalva maneuver.
Correlations between FVD and age
The FVD for all segments increased with increasing age (Figure 5; Supplementary Tables 3 and 4). However, significant mean value differences between the various age cohorts are present for certain segments of the FV in certain subject positions, only (Supplementary Table 1).
Comparison of the mean femoral vein diameter (FVD) for different age cohorts and different subject positions (supine at rest or upright during Valsalva maneuver). Standard deviation and probability indices for unpaired t-test (comparison for mean value difference) are shown. ** = significant (0.001 < p ≤ 0.01, k = 24), *** = highly significant (p ≤ 0.001, k = 24). CVF: common femoral vein; dist: distal femoral vein; prox: proximal femoral vein; sup: supine position at rest; up; upright position during Valsalva maneuver; yr: years.
An age-related FVD increase was observed independent from sex (same-sex cohort comparison) which was significant for the CFV (p = 3.61 E-02) and proximal FV (p = 2.24 E-04) in supine position in males, only (Supplementary Figures 1 and 2; Supplementary Table 2). A positive correlation between FVD and age is also seen in the linear regression models (Supplementary Figures 3 and 4, 9 and 10, 15 and 16) which was significant for male and female CFV in supine and female CFV in upright position.
Differences of mean values adjusted for BMI were not significant after p-value correction (k = 24).
Differences between supine position at rest and upright position during Valsalva maneuver in the different age-cohorts (mixed-sex) indicating age-dependent vascular compliance.
Note: Mean percentage is given with standard deviation.
CFV: common femoral vein.
Correlations between FVD and height
The mean FVD was increased for medium and tall subjects (mixed-sex) compared to small subjects for all measured segments and both conditions (Figure 6; Supplementary Table 5). None of these differences was significant. In the cohorts separated according to sex, FVD differences between smaller and taller same-sex sub-cohorts were marginal or without clear tendency or significance (Supplementary Figures 5 and 6, 11 and 12, 17 and 18).
Comparison of the mean femoral vein diameter (FVD) for different height classes (mixed-sex). Standard deviation is shown. FVD differences between cohorts are not significant (p > 0.05). CVF: common femoral vein; dist: distal femoral vein; prox: proximal femoral vein; sup: supine position at rest; up: upright position during Valsalva maneuver; yr: years.
Correlations between FVD and BMI
A total of 58.5% of subjects (n = 48) had a BMI bigger than 25 (adiposity), 15 (18.3%) of these had a BMI bigger than 30 (obesity). The FVD increased with increasing BMI for all measured segments (Figure 7; Supplementary Tables 6 and 7; Supplementary Figures 21 and 22). Differences were slightly to highly significant for the CFV in supine and upright position both between the cohorts with normal BMI and adiposity (BMI ≥ 25) and between the cohorts with normal BMI and obesity (BMI ≥ 30) (Supplementary Tables 1 and 6). Between normal BMI and overweight cohort, differences were not significant. After adjustment for age, significant differences of the CFV in supine and upright position (p ≤ 0.01) were present in the cohort younger than 65 years (“pre-65”) between sub-groups with “normal BMI” and “adiposity” and between “normal BMI” and “obesity”, respectively (Supplementary Table 1).
Comparison of the mean femoral vein diameter (FVD) for different classes of body mass index (BMI). Standard deviation and probability indices for unpaired t-test (comparison for mean value difference) are shown. ** = significant (0.001 < p ≤ 0.01, k = 24), *** = highly significant (p ≤ 0.001, k = 24). CVF: common femoral vein; dist: distal femoral vein; prox: proximal femoral vein; sup: supine position at rest; up: upright position during Valsalva maneuver.
The FVD likewise increased with increasing BMI independent from sex (same-sex cohort comparison; Figure 8; Supplementary Figures 7 and 8, 13 and 14, 19 to 22, Supplementary Table 7).
Significant correlation between body mass index (BMI) and diameter of the common femoral vein (d CFV) in supine position at rest (a) and in upright position during Valsalva maneuver (b). Mean values for the CFV for each subject and regression lines for both sexes are plotted (males supine: p = 4.68 E-03; females supine: p = 4.02 E-07; males upright: p = 1.82 E-03; females upright: p = 1.43 E-03). Measuring points of males (n = 46) are colored blue, females (n = 36) are colored red.
Multiple linear regression of CFV diameter with age, height, and BMI
In the multiple linear regression of the CFV diameter with age, height and BMI for male and female cohort, non-significant coefficients were excluded and the linear regression model was re-calculated in a second step to optimize the model. An increased BMI had the strongest positive effect on the CFV diameter. Age was only a minor factor. Age had no significant effect on the CFV diameter in males during Valsalva maneuver, while height appeared to be a factor with slight significance in this case (in contrast to the simple linear regression; Supplementary Figure 6).
y = 0.17 × BMI + 0.07 × age + 6.84
R2 = 0.33; p [BMI] = 4.90 E-02; p [age] = 2.76 E-02
y = 0.30 × BMI + 0.07 × age + 1.17
R2 = 0.67; p [BMI] = 7.56 E-07; p [age] = 6.91 E-04
y = 0.26 × BMI + 0.10 × height − 7.61
R2 = 0.27; p [BMI] = 7.34 E-04; p [height] = 4.13 E-02
y = 0.18 × BMI + 0.06 × age + 7.69
R2 = 0.40; p [BMI] = 6.33 E-03; p [age] = 9.23 E-03
A summary of the various tested cohorts (mean value comparison) in this study is shown in Supplementary Tables 1 and 2. The linear regression models for FVD and subject parameters of cohorts separated according to sex are shown in the Supplementary Figures 3 to 20.
Bilateral symmetry/asymmetry
In terms of the diameter, slight bilateral asymmetry was present between left and right FV, but none was significant after p-value adjustment (k = 6; p > 0.05) (Supplementary Figure 23). The diameter of the CFV differed 10.0% in supine and 8.1% in upright position on average between both limbs in the same subject with the right FV being bigger in 63.4% and 59.8% of subjects, respectively. In the proximal segment, the diameter differed 15.0% in supine (R > L in 52.5% of subjects) and 12.1% in upright position (R > L in 48.8% of subjects); in the distal segment, 14.0% in supine (R > L in 59.5% of subjects) and 11.7% in upright position (R > L in 45.6% of subjects).
Discussion
This present study adds new morphometric and epidemiologic data to our knowledge on the FV, including variability of the FV diameter (FVD), FV dilation properties, bilateral asymmetry and cohort differences correlated to sex, age and BMI.
Comparison of the femoral vein diameter (FVD) of the common femoral vein (CFV) with previous studies.
Note: Means are given with standard deviation, if available.
BMI: body mass index.
Valsalva-induced dilation
The Valsalva-induced mean dilation of the CFV in our study (24.6%) is in accordance with previous data of 21.2% to 33.7%.4,6,8,23 Values reaching far beyond these means (up to 149.1% in our measurements), or even decreased diameters for the CFV (down to −15.4% in our measurements) in only one leg might be due to Valsalva-induced changes in muscle tension in the legs or slight positional changes to some extent.
A true dilation by up to 100% (FVD doubling) or above, however, cannot be ruled out: in three of our subjects (23, 27, and 47 years old), the CFV reached such a doubling in both legs. Although such a correlation between age and distensibility has been denied in the past, 23 venous wall compliance decreases with age.24,25 Age-dependent alterations of extra cellular matrix components such as elastic and collagenous fibers in the venous wall might be responsible for the loss of compliance similar to the vascular ageing stated for arterial systems. 26 Possible correlations and causes for the age-related loss of venous compliance in the FV, however, must be further studied.
Bilateral asymmetry
In our study, the overall mean CFV diameter of left and right leg differs less than 1 mm (3.8% supine, 2.5% upright/Valsalva maneuver). This is in accordance with previous studies with differences below 1 mm.2,3,12 Within the same subject, we have found a higher bilateral asymmetry between left and right FV, e.g. 10.0% difference on average in supine and 8.1% for the CFV in upright position. Bilateral differences between leg muscle volumes due to different footedness might contribute to these vascular differences but reliable data are lacking for such a coherence. Anatomical variations such as the May–Thurner syndrome with clinically underestimated prevalence might also play a role in causing bilateral asymmetry of the FVD. 27
Correlations between FVD and sex
According to our data, the FVD is sex-related and males possess a bigger FVD than females, which is significant for the CFV, also after adjustment for age. This finding stands in line with previous studies,6,7,28 while others 8 could not verify such a correlation. Distinct differences in mean body size (height) between males and females might contribute to sex-related differences of the FVD since body height was found to correlate to some degree with the FVD. 6 We have, however, not found an unambiguous sex-adjusted correlation between height and FVD in our cohort. Since the FVD is correlated with the diameter of the femoral artery to some extent, 12 differences in blood flow due to sex-related differences of the lower limbs' muscle mass 29 might play a role for these differences of the FVD.
Correlations between FVD and age
We have observed an age-dependent increase of the FVD in all segments and detected a strong correlation between CFV diameter in supine position and age. An age-related increase of CFV and proximal FVD in supine position was independent from sex and significant for males. In this context, data from previous studies are contradictory. While in the study by Kröger et al., 7 the FVD was not correlating with age, Fronek et al. 6 observed a decrease[!] of the CFV diameter with increasing age 6 – which is opposite to our findings. Such an FVD decrease has been already discussed as being probably affected by age-related changes of blood volume, sympathetic activity and venous compliance. 7 However, we expect the CFV in the elderly to be “worn” due to aging processes within the vascular wall which is congruent with our own preliminary observations on post-mortem material from body donors. This assumption fits to the finding that FV compliance seems to decrease with age.
Correlations between FVD and BMI
The previously observed positive correlation between FVD and BMI6–10 is supported by our data. A BMI-dependent increased diameter has also been observed for the great saphenous vein (V. saphena magna). 7 It remains open what the direct cause for such a BMI-related dilation is. Arfvidsson et al. 30 observed an increased iliofemoral venous pressure which is ascribed to the increased intraabdominal pressure which is usually associated with obesity. The elevated venous pressure enhances the transmural pressure affecting the venous wall – if and how this contributes to an FVD change is unclear and subject to future studies. Sufficient data to test an FVD decrease in subjects with underweight is lacking. Moreover, it is not clear if diameter plasticity for the FV is seen in underweight subjects at all, since the FVD might have its homoeostatic minimum and maximum.
Interestingly, there is some evidence for a positive correlation between femoral arterial and venous diameter. 12 In athletic subjects, the diameter of the femoral artery is significantly increased compared to non-athletic subjects. 31 According to current knowledge, athletic lifestyle does not increase vascular diameter per se, since muscular arteries are subject to changes more than the larger elastic vessels. 31 How an athletic lifestyle affects the FVD is unknown.
Clinical relevance of the FVD
An increased FVD is of clinical relevance for several reasons. An abnormally increased CFV diameter might increase the risk for insufficient venous valve closing leading to venous reflux. According to our observations on post mortem material from body donors, height of CFV valve cusps in elderly is often reduced impairing valve functionality. Assuming an increased CFV diameter due to adiposity or other causes would further impair valve functionality by increasing distance between both cusps.
It has been observed that a CFV diameter bigger than 16 mm provides a higher risk for a phlebodem. 3 Similar to that finding, it has been postulated that females with a CFV diameter bigger than 14 mm have a 15-fold risk being affected by CVI. 2 FVs with acute DVT were found to have a larger diameter than normal veins, while those with chronic DVT have a smaller diameter. 12
If we assume FV plasticity making it possible to increase the FVD coherently coupled to the BMI – either directly or indirectly – the question arises whether or not this process is reversible, e.g. by reducing body weight, and thus the risk for CVI or even the severity of persisting CVI can be reduced.
For the successful development and application of artificial venous valve implants for minimally invasive CVI treatment – something which has failed since almost 40 years for several reasons 13 – it is crucial to consider patient- and condition-dependent FV dilation up to 100%. These temporary FVD changes certainly have an effect on implant fixation and possibly its hemodynamic performance on the one hand, and on implant-tissue interactions possibly promoting adverse fibrotic growth by mechanical irritation of the intimal layer on the other. These physico-anatomical aspects of the FV have been neglected in the past.
Limitations of this study
From a statistical perspective, the number of studied subjects in this study is moderate and in line with similar previous studies on the FVD.1,2,8 Diseases such as diabetes are further potential factors which might influence the FVD. Further data from patient records, however, were not available for this study and statistical validity would require a bigger overall sample size to allow more convincing statements on sub-cohort statistics.
Intraobserver variation was tested 21 months after first measurements and under same conditions for 6 subjects (n = 68 measurements) and resulted in a mean variation of 1.26 ± 1.21 mm for all measurement positions and a variation of 13.9 ± 15.2% for the CFV (n = 24 measurements). Interobserver variation was tested with blinded re-measurement of raw digital ultrasound images (n = 29) from five subjects and resulted in a mean variation of 0.36 ± 0.37 mm for all measurement positions and a variation of 2.8 ± 2.4% for the CFV (n = 10 images). In addition, we were able to test the difference between sonographic assessment and magnetic resonance imaging (MRI) for the CFV in one of our subjects (male, 34 yr, normal BMI; Figure 1). The deviation for the MRI scan (contrast medium-enhanced; XY-resolution = 0.78 mm) compared to the sonography was plus 1.3 mm ( + 11.1%) for the left and minus 0.7 mm (−5.7%) for the right VFC in supine position with a mean deviation of 8.4% for both sides.
Our measurement variations are in accordance with similar studies in which interobserver variability was 8.3 ± 7.2% (n = 20), 1 and in which a coefficient of variation of 13.1% was tested for the CFV diameter during Valsalva for 21 subjects. 6
Supplemental Material
Supplemental material for The femoral vein diameter and its correlation with sex, age and body mass index – An anatomical parameter with clinical relevance
Supplemental material for The femoral vein diameter and its correlation with sex, age and body mass index – An anatomical parameter with clinical relevance by Jonas Keiler, Ronald Seidel and Andreas Wree in Phlebology
Footnotes
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was funded in part by the German Federal Ministry of Education and Research within RESPONSE “Partnership for Innovation in Implant Technology” (FKZ: 03ZZ0902A, 03ZZ0909A).
Ethical Approval
The study was approved by the local ethics committee.
Guarantor
Dr. Jonas Keiler
Contributorship
Conceived and designed the experiments: JK, AW, RS. Performed the experiments: RS Analyzed the data: JK. Contributed materials/analysis tools: RS. Wrote the paper: JK, RS, AW
Acknowledgements
We thank all volunteers for their participation. Teresa Mann is thanked for helpful advices with statistics.
References
Supplementary Material
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