**6. Methodology**

**Study design:** Descriptive cross-sectional study.

**Setting:** Anthropometric section of department of Anatomy, ESIC Medical College and Hospital, Gulbarga, Karnataka.

**Duration of study:** 14 months; from 31 October 2017 to 31 December 2018. **Sample size:** 1000 participants included medical, dental and nursing students aged between 18 and 21 years of age.

**Inclusion criteria:** Medical, dental and nursing students aged between 18 and 21 years of age in ESIC Medical College, Gulbarga.

**Exclusion criteria:** Students of NRI quota and students with poorly defined wrist creases, deformities of vertebral column and limbs, contractures, missing limbs, history of trauma to hand and foot, with features suggestive of dysmorphic syndromes, chronic illness and hormonal therapy were excluded from the study.

**Sample selection:** Simple random sampling method [13] as we selected 1000 participants out of total 3000 medical, dental and nursing students in our institute satisfying the inclusion criteria. As subjects belonging to the first to third year, they were easily accessible and also represented the young adult age group.

#### **6.1 Data collection procedure**

**Foot length:** Each subject will stand on a calibrated foot board with his/her back against the wall in such a manner that the posterior most point of the heel will

*Effect of Foot Morphology and Anthropometry on Bipedal Postural Balance DOI: http://dx.doi.org/10.5772/intechopen.92149*

**Figure 1.** *Measurement of foot length.*

postural stability. Very few studies are available on correlation of foot parameters

As the age advances particularly after forties, the muscle mass goes on decreas-

A study was conducted in central population of northern Karnataka on 1000 young adult population in which foot anthropometry was measured and correlated

**Setting:** Anthropometric section of department of Anatomy, ESIC Medical

**Duration of study:** 14 months; from 31 October 2017 to 31 December 2018. **Sample size:** 1000 participants included medical, dental and nursing students

**Inclusion criteria:** Medical, dental and nursing students aged between 18 and

**Exclusion criteria:** Students of NRI quota and students with poorly defined wrist creases, deformities of vertebral column and limbs, contractures, missing limbs, history of trauma to hand and foot, with features suggestive of dysmorphic syndromes, chronic illness and hormonal therapy were excluded from the study. **Sample selection:** Simple random sampling method [13] as we selected 1000 participants out of total 3000 medical, dental and nursing students in our institute satisfying the inclusion criteria. As subjects belonging to the first to third year, they

**Foot length:** Each subject will stand on a calibrated foot board with his/her back

against the wall in such a manner that the posterior most point of the heel will

were easily accessible and also represented the young adult age group.

with stature, weight, body mass index and bipedal posture stability [21].

**Study design:** Descriptive cross-sectional study.

21 years of age in ESIC Medical College, Gulbarga.

College and Hospital, Gulbarga, Karnataka.

aged between 18 and 21 years of age.

**6.1 Data collection procedure**

**148**

ing so does the muscle strength. Muscle fatigue, which is a common condition affecting the elderly population, can result in mobility, postural and gait deficiencies. The state of mind can influence the activity of the muscular system, that is, the muscular tonus. The muscular activation or, in the contrary case, the muscular relaxation influences postures adopted by people. The body height and the lower limb length constitute partly to weight transfer strategy. The trunk-cephalic length does not correlate to the postural sway. Body mass is located above the hips, so it is not the main factor for the mediolateral sway. The weight transfer strategy for men depends on the size of the basis of support and their lean mass, while, for women, only the lengths (whole body and lower limbs) are important. Lower basis of supports leads to higher postural sway in the ML direction (Chiari et al. [11]; Chou et al., [20]), and to control the increase in body sway, it is necessary to increase the lean mass, probably and mainly the muscle mass to be able to generate more muscle force. The increase in body height affects the body mass and soft tissue mass (lean and fat masses) increases the postural sway. The increase in body mass indeed

with unipedal and bipedal postural balance [18].

enlarges the postural sway.

**5. Research study**

*Weight Management*

**6. Methodology**

**4.5 Effect of muscle strength and fatigue on postural balance**

gently touch the wall. A vertical stop was placed against the anterior most point of the foot. The distance between the posterior most point of the heel and the anterior most point of the foot was measured as the foot length [22] (**Figure 1**).

**Foot breadth:** It will be measured as distance between metatarsal tibiale (point projecting most medially on the head of the 1st metatarsal bone) and metatarsal fibulare (point projecting most laterally on the head of the 5th metatarsal bone) [23].

**Height:** Standing height will be measured to the nearest centimeters (cm) using a stadiometer with the subject standing erect on a horizontal resting plane bare footed having the palms of the hands turned inward and the fingers pointing downwards. The height will be measured from the sole of the feet to the vertex of the head as recommended by International Biological Program [23].

**Body weight:** It will be taken using the Mechanical Weighing Balance to the nearest kg according to the standard procedures A. Ibegbu, David et al. [24].

**Body mass index:** It will be calculated by dividing weight by height squared [weight/height squared (kg/m2 )] David et al. [24].

#### **6.2 Data collection tools**

Vernier slide calipers, calibrated foot board, stadiometer, regular weight machine, questionnaire for collection of personal details, academic scores, lead pencils, stationary, etc. Data collected were tabulated, graphically represented and statistically analyzed.

#### **7. Observations**

In our study, mean foot length was observed as 24.34 cm on the right side and 24.32 cm on the left side. Mean body mass index was calculated as 20.97. Correlation between foot length and body mass index was done. No statistically significant correlation between BMI and foot length of the right and left sides (P > 0.05) was observed. For further details, refer to **Table 1**.

In the present study, mean foot breadth was observed as 8.95 cm on the right side and 8.96 cm on the left side. Mean body mass index was calculated as 20.97. Correlation between foot length and body mass index was done. There was a

statistically significant correlation between BMI and foot breadth of the right and left sides (P < 0.01). The observations in the study stated that foot breadth of both sides was considerably more in participants who had higher body mass index. Linear regression coefficient was derived. For further details, refer to **Table 2**, **Figure 2.**

**Variables Minimum Maximum Range Mean SD N Correlation r P value** Height (cm) 135.2 195.2 60.0 161.88 13.45 1000 — —

Height = 71.391 + 4.782 (foot length right)

*Effect of Foot Morphology and Anthropometry on Bipedal Postural Balance*

Height = 49.706 + 4.786 (foot length left)

21.0 28.9 7.9 24.34 1.54 1000 r = 0.428 P < 0.01

21.5 29.0 7.5 24.32 1.50 1000 r = 0.516 P < 0.01

HS

HS

Foot length right (cm)

Foot length left (cm)

Linear regression equation

Linear regression equation

*Correlation of foot length and human stature.*

*DOI: http://dx.doi.org/10.5772/intechopen.92149*

**Table 3.**

**Figure 3.**

**Figure 4.**

**151**

*Correlation between foot breadth and body mass index.*

*Measurement of foot breadth.*

#### **Table 1.**

*Correlation of foot length and body mass index.*

#### **Table 2.**

*Correlation of foot breadth and body mass index.*

**Figure 2.** *Correlation between foot length and body mass index.*

*Effect of Foot Morphology and Anthropometry on Bipedal Postural Balance DOI: http://dx.doi.org/10.5772/intechopen.92149*

#### **Table 3.**

statistically significant correlation between BMI and foot breadth of the right and left sides (P < 0.01). The observations in the study stated that foot breadth of both sides was considerably more in participants who had higher body mass index. Linear regression coefficient was derived. For further details, refer to **Table 2**,

**Variables Minimum Maximum Range Mean SD N Correlation r P value**

**Variables Minimum Maximum Range Mean SD N Correlation r P value**

BMI = 19.306 + 0.168 (foot breadth right)

BMI = 17.214 + 0382 (foot breadth left)

12.22 40.61 28.39 20.97 4.66 1000 — —

21.0 28.9 7.9 24.34 1.54 1000 r = 0.073 P > 0.05

21.5 29.0 7.5 24.32 1.50 1000 r = 0.024 P > 0.05

12.22 40.61 28.39 20.97 4.66 1000 — —

7.5 10.9 3.4 8.95 0.78 1000 r = 0.124 P

7.7 11.5 3.8 8.96 0.68 1000 r = 0.115 P

NS

NS

< 0.05 S

< 0.05 S

**Figure 2.**

Body mass index (kg/m2 )

*Weight Management*

Foot length right (cm)

Foot length left (cm)

Body mass index (kg/m2 )

Foot breadth right (cm)

Foot breadth left (cm)

Linear regression equation

Linear regression equation

**Table 2.**

**Figure 2.**

**150**

*Correlation of foot length and body mass index.*

*Correlation of foot breadth and body mass index.*

*Correlation between foot length and body mass index.*

**Table 1.**

*Correlation of foot length and human stature.*

**Figure 3.** *Measurement of foot breadth.*

**Figure 4.** *Correlation between foot breadth and body mass index.*

#### **Table 4.**

*Correlation of foot breadth and human stature.*

We also observed foot length on both sides. Mean foot length on the right side was observed as 24.34 cm, and on the left side, it was 24.32 cm. Correlation of foot length was conducted with human stature. Linear regression equation was derived for both sides. Statistically highly significant positive correlation was observed between height and foot length of both sides (P < 0.01). **Table 3** reveals that foot length of both sides was also significantly more among those having more height (**Figures 3** and **4**).

Foot breadth was observed on both sides. Mean foot breadth on the right side was observed as 8.95 cm, and on the left side, it was 8.96 cm. Correlation of foot breadth was conducted with human stature. Linear regression equation was derived

for both sides. Statistically highly significant positive correlation was observed between height and foot breadth of both sides (P < 0.01). **Table 4** reveals that foot breadth of the right or left side was significantly more in those participants whose

Postural sway was measured in the participants both male and female in anteroposterior and mediolateral direction (**Figure 9**). Correlation of postural sway with foot length and foot breadth was conducted. Mediolateral postural sway

amplitude was the same, that is, 0.3 cm in both males and females.

Gender-wise comparison of observations was done. We observed very highly significant difference in foot length, foot breadth, height and weight among males and females. The foot length, foot breadth, height and weight were significantly more in males compared to females, whereas body mass index was significantly more in females as compared to males.

*Gender-wise comparison of parameters.*

**Table 5, Figures 7** and **8**.

**Figure 6.**

*Correlation between foot length and stature.*

**Variables Male**

Foot breadth right

(cm)

BMI (kg/m2

**Table 5.**

**153**

**(N = 500) Mean SD**

*Effect of Foot Morphology and Anthropometry on Bipedal Postural Balance*

*DOI: http://dx.doi.org/10.5772/intechopen.92149*

*NS, not significant; S, significant; HS, highly significant; VHS, very highly significant.*

**Figure 5.** *Measurement of human stature.*

*Effect of Foot Morphology and Anthropometry on Bipedal Postural Balance DOI: http://dx.doi.org/10.5772/intechopen.92149*

#### **Figure 6.**

We also observed foot length on both sides. Mean foot length on the right side was observed as 24.34 cm, and on the left side, it was 24.32 cm. Correlation of foot length was conducted with human stature. Linear regression equation was derived for both sides. Statistically highly significant positive correlation was observed between height and foot length of both sides (P < 0.01). **Table 3** reveals that foot length of both sides was also significantly more among those having more height

**Variables Minimum Maximum Range Mean SD N Correlation r P value** Height (cm) 135.2 195.2 60.0 161.88 13.45 1000 — —

Height = 106.01 + 6.240 (foot breadth right)

Height = 96.843 + 7.253 (foot breadth left)

7.5 10.9 3.4 8.95 0.78 1000 r = 0.364 P < 0.01

7.7 11.5 3.8 8.96 0.68 1000 r = 0.367 P < 0.01

HS

HS

Foot breadth was observed on both sides. Mean foot breadth on the right side was observed as 8.95 cm, and on the left side, it was 8.96 cm. Correlation of foot breadth was conducted with human stature. Linear regression equation was derived

(**Figures 3** and **4**).

Foot breadth right

*Weight Management*

Foot breadth left

Linear regression equation

Linear regression equation

*Correlation of foot breadth and human stature.*

(cm)

(cm)

**Table 4.**

**Figure 5.**

**152**

*Measurement of human stature.*

*Correlation between foot length and stature.*

#### **Table 5.**

*Gender-wise comparison of parameters.*

for both sides. Statistically highly significant positive correlation was observed between height and foot breadth of both sides (P < 0.01). **Table 4** reveals that foot breadth of the right or left side was significantly more in those participants whose height was more (**Figures 5** and **6**).

Gender-wise comparison of observations was done. We observed very highly significant difference in foot length, foot breadth, height and weight among males and females. The foot length, foot breadth, height and weight were significantly more in males compared to females, whereas body mass index was significantly more in females as compared to males. The observations have been tabulated in **Table 5, Figures 7** and **8**.

Postural sway was measured in the participants both male and female in anteroposterior and mediolateral direction (**Figure 9**). Correlation of postural sway with foot length and foot breadth was conducted. Mediolateral postural sway amplitude was the same, that is, 0.3 cm in both males and females.

**Figure 7.** *Correlation between foot breadth and stature.*

Anteroposterior sway amplitude was .95 cm in females and .10 cm in males. **It was observed that men exhibited more postural sway compared to females in anteroposterior direction**. The findings were statistically signifi-

**Variables Foot length (cm) r(p) Foot breadth (cm) Angle (°**

*Effect of Foot Morphology and Anthropometry on Bipedal Postural Balance*

*DOI: http://dx.doi.org/10.5772/intechopen.92149*

Mediolateral sway (cm) 0.01 (0.88) 0.01 (0.80) 0.01 (0.89) Mediolateral ampl sway (cm) 0.05 (0.54) 0.01 (0.82) 0.03 (0.70) Anteroposterior sway (cm) 0.07 (0.43) 0.05 (0.53) 0.12 (0.21) Anteroposterior ampl sway (cm) 0.09 (0.35) 0.11 (0.25) 0.95 (0.35) Sway velocity (cm/s) 0.05 (0.56) 0.12 (0.22) 0.11 (0.25)

Mediolateral sway (cm) 0.32 (0.00) 0.02 (0.84) 0.04 (0.68) Mediolateral ampl sway (cm) 0.27 (0.00) 0.02 (0.83) 0.03 (0.69) Anteroposterior sway (cm) 0.29 (0.00) 0.00 (0.94) 0.11 (0.24) Anteroposterior ampl sway (cm) 0.27 (0.00) 0.06 (0.52) 0.10 (0.31) Sway velocity (cm/s) 0.15 (0.13) 0.08 (0.42) 0.09 (0.37)

) 0.67 (0.50) 0.24 (0.80) 0.12 (0.22)

) 0.36 (0.00) 0.02 (0.78) 0.10 (0.32)

**)**

Few studies have worked on the relationship of foot anthropometry with balance. Clarke [25] analyzed the angle of foot. Swanenburg et al., [26] examined static posturography using the center of pressure (COP) oscillation on a force platform.

stabilometric parameters only in the male group. Our study observations matched with those of Alonso et al. [27], Kejonen et al., [19] and Molikova et al., [13]. Previous studies by Alonso et al*.*, [3] and Chou et al., [20] also demonstrated that an

Our study states that neither the foot length nor the foot width influences postural balance. These observations matched with Alonso et al., [28], but they had

contradicted with those of Chiari et al.[12] in which foot width showed positive correlation with postural balance. They conducted the study by bipedal standing balance task. They stated that the increase in lean mass correlates to the decrease of the amplitude of the postural sway. They added that the percentage of fat mass explains part of the anteroposterior postural sway in men, but not in women.

Mainenti et al. [29] showed that elderly women with more fat mass had larger balance sway and Winters and Snow [30] reported that 31% of postural sway variability in premenopausal women was caused by the fat mass. Hence, it can be concluded that the effect of fat mass on the postural control is age dependent.

Our study suggested association between greater foot length and higher

conducted the study using unipedal standing balance task. Our findings

increase in the size of the support base can improve the balance.

cant. Refer to **Table 6** for details.

*Spearman's correlation, \*ρ* ≤ *0.05. ampl, amplitude.*

*Correlation between foot anthropometric measurements and postural balance.*

**8. Discussion**

**155**

**Female**

Sway area (cm2

Sway area (cm2

**Table 6.**

**Male**

**Figure 8.** *Multiple bar diagram represents gender-wise comparison of variables.*

**Figure 9.** *Gender-wise comparison of parameters.*

*Effect of Foot Morphology and Anthropometry on Bipedal Postural Balance DOI: http://dx.doi.org/10.5772/intechopen.92149*

#### **Table 6.**

**Figure 7.**

*Weight Management*

**Figure 8.**

**Figure 9.**

**154**

*Gender-wise comparison of parameters.*

*Correlation between foot breadth and stature.*

*Multiple bar diagram represents gender-wise comparison of variables.*

*Correlation between foot anthropometric measurements and postural balance.*

Anteroposterior sway amplitude was .95 cm in females and .10 cm in males. **It was observed that men exhibited more postural sway compared to females in anteroposterior direction**. The findings were statistically significant. Refer to **Table 6** for details.

#### **8. Discussion**

Few studies have worked on the relationship of foot anthropometry with balance. Clarke [25] analyzed the angle of foot. Swanenburg et al., [26] examined static posturography using the center of pressure (COP) oscillation on a force platform. Our study suggested association between greater foot length and higher stabilometric parameters only in the male group. Our study observations matched with those of Alonso et al. [27], Kejonen et al., [19] and Molikova et al., [13]. Previous studies by Alonso et al*.*, [3] and Chou et al., [20] also demonstrated that an increase in the size of the support base can improve the balance.

Our study states that neither the foot length nor the foot width influences postural balance. These observations matched with Alonso et al., [28], but they had conducted the study using unipedal standing balance task. Our findings contradicted with those of Chiari et al.[12] in which foot width showed positive correlation with postural balance. They conducted the study by bipedal standing balance task. They stated that the increase in lean mass correlates to the decrease of the amplitude of the postural sway. They added that the percentage of fat mass explains part of the anteroposterior postural sway in men, but not in women.

Mainenti et al. [29] showed that elderly women with more fat mass had larger balance sway and Winters and Snow [30] reported that 31% of postural sway variability in premenopausal women was caused by the fat mass. Hence, it can be concluded that the effect of fat mass on the postural control is age dependent.

The increase in body height indeed increases the postural sway. Hence, in our study, the greater height in the male group may have been the reason for the greater influence of this parameter on COP in comparison to the female participants.

**References**

90-95

2007;**53**(5):274-281

[2] Alonso AC, Greve JMDA,

[1] Prado JM, Stoffregen TA, Duarte M. Postural sway during dual tasks in young and elderly adults. Gerontology.

*DOI: http://dx.doi.org/10.5772/intechopen.92149*

*Effect of Foot Morphology and Anthropometry on Bipedal Postural Balance*

Relationship between anthropometric factors, gender, and balance under unstable conditions in young adults. BioMed Research International. 2013;

[9] Rozzi SL, Lephart SM, Gear WS,

neuromuscular characteristics of male and female soccer and basketball players. American Journal of Sports Medicine. 1999;**27**(3):312-319

[10] Lee AJY, Lin WH. The influence of gender and somatotype on single-leg upright standing postural stability in

[11] Ledin T, Odkvist LM. Effects of increased inertial load in dynamic and randomized perturbed posturography. Acta Oto-Laryngologica. 1993;**113**(3):

[12] Chiari L, Rocchi L, Cappello A. Stabilometric parameters are affected by anthropometry and foot placement. Clinical biomechanics. 2002;**17**(9–10):

[13] Molikova R, Bezdickova M, Langovaetal K. The relationship between morphological indicators of human body and posture. Biomedical Papers of the Medical Faculty of the University Palacky, Olomouc, Czechoslovakia. 2006;**150**(2):261-265

[14] Greve JMDA, Alonso AC,

2007;**26**(1):32-38

Bordini ACPG, Camanho GL. Correlation between body mass index and postural balance. Clinics. 2007;**62**(6):717-720

[15] Hue O, Simoneau M, Marcotte J, et al. Body weight is a strong predictor of postural stability. Gait and Posture.

[16] McGraw B, McClenaghan BA, Williams HG, Dickerson J, Ward DS.

**2013**:1-5. Article ID: 850424

Fu FH. Knee joint laxity and

children. Journal of Applied Biomechanics. 2007;**23**(3):173-179

249-252

666-677

Camanho GL. Evaluating the Centre of gravity of dislocations in soccer players with and without reconstruction of the anterior cruciate ligament using a balance platform. Clinics. 2009;**64**(3):163-170

[3] Alonso AC, Luna NM, Mochizuki L, Barbieri F, Santos S, Greve JMDA. The influence of anthropometric factors on postural balance: The relationship between body composition and

posturographic measurements in young adults. Clinics. 2012;**67**(12):1433-1441

[4] Riemann BL, Myers JB, Lephart SM. Comparison of the ankle, knee, hip, and trunk corrective action shown during single-leg stance on firm, foam, and multiaxial surfaces. Archives of Physical Medicine and Rehabilitation. 2003;**84**:

[5] Jo S. Hierarchical Neural Control of Human Postural Balance and Bipedal Walking in Sagittal Plane. Department of Electrical Engineering and Computer Science. Massachusetts institute of

Gulsatitporn S, Aksaranugraha S. Age and gender effects on postural stability and static balance in Thai community dwelling adults. Journal of the Medical Association of Thailand. 2004;**87**

technology; May 2006

(Suppl. 2):S112-S116

1995;**76**:961-965

**157**

[6] Raiva V, Wannasetta W,

[7] Hageman PA, Leibowitz JM, Blanke D. Age and gender effects on postural control measures. Archives of Physical Medicine and Rehabilitation.

[8] Julia Maria D, Greve A, Cug M, Dulgeroglu D, Brech GC, Alonso AC.

In our study, conducted among young adults, without major health diseases or other abnormalities, the anthropometric measurements showed gender-related differences.


*2.1. Instrumentation*

The IR spectra of the polycrystalline samples of *rac*- and (*R*)-diols **1** under investigations in KBr pellets were recorded on a Bruker Tensor 27 spectrometer (Bruker Optic GmbH, Cermany). Optical rotations were measured on a Perkin–Elmer model 341 polarimeter (PerkinElmer, USA). The melting curves were measured on a NETZSCH 204 F1 Phoenix DSC differential scanning calorimeter (NETZSCH-Gerätebau GmbH, Germany) in sealing aluminum pans with the rate of heating of 5 ◦C·min−1. The mass of the samples amounted to approximately ~ 1 mg in determining the enthalpies and temperatures of the phase transitions and ~ 7 mg when measuring the specific heats of the samples and was controlled with Sartorius CPA 2P balance (Sartorius AG, Goettingen, Germany). The heat capacity was measured by a continuous method, subtracting the previously measured heat capacity of the empty cell. Temperature scale and heat flux were calibrated against the data for indium and naphthalene. When measuring the heat capacities, the heat capacity of the corundum sample was used for calibration. HPLC analyses were performed on a Shimadzu LC-20AD system controller (SHIMADZU CORPORATION, Kyoto, Japan), UV monitor 275 nm was used as detector. The column used, from Daicel Inc., was Chiralcel OD (Daicel Chemical Industries, LTD - Chiral Technologies Inc., West Chester, PA, USA), (0.46 × 25 cm); eluent—hexane/2-propanol (7:3), flow rate—1 mL·min−1, column temperature—22 ◦C.


**Fully Automatic Retinal Vascular Tortuosity Assessment Integrating Domain-Related Information †**

**Lucía Ramos 1,2,\* , Jorge Novo 1,2 , José Rouco 1,2 , Stéphanie Romeo 3 , María D. Álvarez 3 and Marcos Ortega 1,2**

#### Published: 21 August 2020

**Abstract:** The fundus of the eye is the only part of the human body that allows a direct non-invasive observation of the circulatory system. Retinal vascular tortuosity presents a valuable potential for diagnostic and treatment purposes of relevant vascular and systemic diseases. This work presents a computational metric for the tortuosity characterization that combines mathematical representations of the vessel segments with anatomical properties of the fundus image such as the vessel caliber, the distance to the optic disc, the distance to the fovea and the distinction between arteries and veins. The evaluation of the prognostic performance shows that the incorporation of the domain-related information allows a reliable characterization of the retinal vascular tortuosity that provides a better representation of the expert perception.

**Keywords:** retinal circulation; vascular tortuosity; fundus images; computer-aided diagnosis; image analysis; clinical knowledge

#### **1. Introduction**

The retinal vascular tortuosity, characterized by an abnormal course of the blood vessels, has relevant potential as a clinical biomarker of a significative number of relevant diseases such as diabetic retinopathy, cerebrovascular disease, stroke, and ischemic heart disease, among others. Several computational approaches to address the assessment of the retinal vascular tortuosity have been proposed in the literature. These metrics are mostly based on mathematical properties of the vessel centerlines to describe the tortuosity according to the curvature, the amplitude, or the number of turns and twists of the vessel segments. However, the specialists, on the basis of their experience, besides the analysis of the vessel course, also consider additional domain-related parameters that are not incorporated in the computational metrics of reference. In particular, a set of anatomical factors, including the vessel caliber, the distinction between arteries and veins, the distance to the fovea, and the distance to the optic disc were identified as relevant for the tortuosity assessment. This work presents a computational methodology that combines mathematical properties of the retinal vessels with relevant domain-related information for a better representation of the expert criteria [1].

#### **2. Methodology**

The proposed computational metric consist of a tortuosity quantification based on a mathematical metric of reference [2] combined with the identified anatomical factors. For this purpose, first, the arterio-venous tree is extracted and decomposed into its constituent vessel segments. Then, a local tortuosity based on the mathematical representation of the vessel course weighted by the anatomical properties is computed for each individual vessel. The optimal configuration to incorporate the anatomical factors was set by means of a multi-objective optimization process. Finally, the local tortuosity values are combined in order to compute the global tortuosity measurement for the whole retina. Figure 1 shows examples of the intermediate steps for the computational tortuosity measuremet.

(a) (b)

**Figure 1.** (**a**) Original fundus image. (**b**) Retinal arterio-venous tree extraction and vessel decomposition. (**c**) Domain-related information including the vessel caliber, the distance to the optic disc, the distance to the fovea and the distinction between arteries and veins.

#### **3. Results and Conclusions**

In order to evaluate the impact of the integration of domain-related information for the tortuosity characterization, the prognostic performance of the proposed metric was compared to the effectiveness of the baseline metric of reference, based exclusively on a mathematical representation of the vessel segments. The evaluation was performed over a dataset composed by 200 fundus images manually annotated by a group of five experts according to the binary relevant/non-relevant classification. The AUC achieved by the proposed metric was 93.8%, whereas the AUC of the baseline metric exclusively based on mathematical properties was 89.8%. The results show that the incorporation of the anatomical factors allows a reliable characterization of the retinal vascular tortuosity that better represents the specialists' perception.

**Author Contributions:** L.R., J.N., J.R. and M.O. made substantial contributions to conception and design of the retinal vascular tortuosity assessment, analysis of data and interpretation of the results. S.R. and M.D.A. were involved in the acquisition of the dataset, the rating procedure and the identification of the relevant domain-related information. L.R. performed the experiments and drafted the manuscript and all the authors participated in its critical revision and final approval. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work is supported by the Instituto de Salud Carlos III, Government of Spain and FEDER funds of the European Union through the DTS18/00136 research projects and by the Ministerio de Ciencia, Innovación y Universidades, Government of Spain through the RTI2018-095894-B-I00 research projects; CITIC, Centro de Investigación de Galicia ref. ED431G 2019/01, receives financial support from Consellería de Educación, Universidade e Formación Profesional, Xunta de Galicia, through the ERDF (80%) and Secretaría Xeral de Universidades (20%).

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**

c 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).