Directional dependent variation in mechanical properties of planar anisotropic porcine skin tissue

Journal Pre-proof Directional dependent variation in mechanical properties of planar anisotropic porcine skin tissue Piyush Lakhani, Krashn K. Dwivedi, Navin Kumar PII:

S1751-6161(19)30972-5

DOI:

https://doi.org/10.1016/j.jmbbm.2020.103693

Reference:

JMBBM 103693

To appear in:

Journal of the Mechanical Behavior of Biomedical Materials

Received Date: 13 July 2019 Revised Date:

23 November 2019

Accepted Date: 9 February 2020

Please cite this article as: Lakhani, P., Dwivedi, K.K., Kumar, N., Directional dependent variation in mechanical properties of planar anisotropic porcine skin tissue, Journal of the Mechanical Behavior of Biomedical Materials (2020), doi: https://doi.org/10.1016/j.jmbbm.2020.103693. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

INDIAN INSTITUTE OF TECHNOLOGY ROPAR Rupnagar, Punjab – 140 001 (INDIA) Dr. Navin Kumar Associate Professor Department of Mechanical Engineering

Phone: +91-1881- 242226 Fax: +91-1881 - 223395 E-mail: [email protected] http://www.iitrpr.ac.in/smmee/nkumar

November 23, 2019 To The Editor-in-Chief, Journal of Mechanical Behavior of Biomedical Materials Sub: Author statement Dear Professor Markus Buehler I would like to confirm that all the authors are fully involved in this research study and preparation of the manuscript. Specific contribution of the individual authors are as follows. Author Name Piyush Lakhani Krashn K Dwivedi Dr. Navin Kumar

Thank you. Sincerely, NAVIN KUMAR

Contribution Conceptualization, Methodology, Validation, Formal analysis, Investigation, Writing - Original Draft Validation, Formal analysis, Writing - Review & Editing Conceptualization, Validation, Resources, Writing - Review & Editing, Supervision

Directional dependent variation in mechanical properties of planar anisotropic porcine skin tissue Piyush Lakhania, Krashn K Dwivedib, Navin Kumara* Department of Mechanical Engineering, Indian Institute of Technology Ropar, Rupnagar 140001, Punjab, India b Center of Biomedical Engineering, Indian Institute of Technology Ropar, Rupnagar 140001, Punjab, India a

Graphical Abstract

1 2 3 4 5 6 7 8 9

Directional dependent variation in mechanical properties of planar anisotropic porcine skin tissue

Piyush Lakhania, Krashn K Dwivedib, Navin Kumara* Department of Mechanical Engineering, Indian Institute of Technology Ropar, Rupnagar 140001, Punjab, India b Center of Biomedical Engineering, Indian Institute of Technology Ropar, Rupnagar 140001, Punjab, India a

ABSTRACT

10

Nonlinear and anisotropic mechanical behavior of skin is essential in various applications such

11

as dermatology, cosmetic products, forensic science, and computational studies. The present

12

study quantifies the mechanical anisotropy of skin using the bulge method and full-field imaging

13

technique. In bulging, the saline solution at 37°C mimics the in vivo body temperature and fluid

14

conditions, and all experiments were performed in the control environment. Assumption of thin

15

spherical shell membrane theory and imaging techniques were implemented to obtain the

16

anisotropic stress strain relations. Further, stress strain relations at an interval of 10° were

17

calculated to obtain the variation in modulus with direction. Histological examinations were

18

performed to signify the role of the collagen fibers orientation on the mechanical properties. The

19

maximum and minimum linear modulus and collagen fiber orientation intensity were found in

20

good agreement. The angular difference between maximum and minimum linear modulus and

21

orientation intensity was found 71° ± 7° and 76° ± 5° respectively, and the percentage difference

22

was 43.4 ± 8.2 and 52.5 ± 6.4 respectively. Further, a significant difference in the maximum and

23

minimum collagen orientation intensity between the untested and tested specimens indicates the

24

realignment of the fibers. Additionally, a cubic polynomial empirical relation was established to

25

calculate the quantitative variation in the apparent modulus with the directions, which serves for

26

the anisotropic modeling of the skin. The experimental technique used in this study can be

1

1

applied for anisotropic quantification of planar soft tissues as well as can be utilized to imitate

2

the tissue expansion procedure used in reconstructive surgery.

3

Keywords: Skin; Bulge; Collagen orientation; Biomechanics; Biomaterials

4 5 6

*

Corresponding Author: [email protected]

1. Introduction

7

Mechanical anisotropy and nonlinearity of planar soft tissue are finding practical applications

8

in the field of medical devices and dermatological practices such as plastic surgery, stabbing

9

mechanics, tissue expansion, and grafting [1, 2]. Skin functioning includes protection against

10

external chemicals, biologic assailants, prevention of excess water loss and thermoregulation.

11

The skin comprises of three layers: epidermis, dermis, and subcutaneous tissue. The dermis

12

dominates the mechanical properties of skin and consists of elastin fibers, collagen fibers and

13

ground substances [3, 4]. Lack of knowledge about the stretching, laxity, and anisotropic

14

properties creates a complication in tissue expansion process used in reconstructive surgeries.

15

Tissue expansion is commonly used for hair transplant, burn cases, traumatic defect, and

16

pigmented strains, etc [5]. Therefore, the quantitative knowledge of anisotropic behavior

17

becomes essential to achieve appropriate surgical perfections.

18

Duputren 1836 [6] observed the noncircular wound formation in the skin, which was

19

punched using round tool. This behavior of skin indicates its anisotropic nature. In sequence,

20

Langer 1861 [7] proposed the particular direction where skin was under most tension. Further,

21

he was defined the lines representing the anisotropic behavior of skin, which are commonly

22

known as Langer’s lines. Moreover, it was observed that the skin tension is the significant aspect

23

that contributes to the scar formation, larger collagen deposition, and uncontrolled wound

24

healing response.

2

1

Nonlinearity and anisotropy of the skin is sensitive to the individual subject and

2

environmental factors such as temperature and humidity[8–11], moisturizer and creams [12–14],

3

body location and position [15–17], age [15, 16, 18], nutrition and skin disease [19] etc. Several

4

in vivo and in vitro studies have been done to investigate the mechanical properties of skin which

5

involve uniaxial [20–23], biaxial [24], multi-axial [25], suction [26–28], indentation [29, 30],

6

shear wave [31, 32] and inflation [9] testing methods. These studies have been reported the

7

mechanical properties of the skin in a particular direction. To the best of the authors knowledge,

8

only a single study is available in the literature for the skin tissue which reported the mechanical

9

properties variation in all the directions [31]. This study was found the change in velocity of

10

shear wave propagation with direction (calculated at 10° interval) using the Reviscometer®,

11

which shows the anisotropic nature of the skin. However, no such study was found, which

12

quantified the anisotropy of skin tissue based on directional dependent variation in the modulus.

13

Further, no empirical relation was found in the literature to predict the variation in the modulus

14

with directions. Langer lines indicate the natural tension direction of skin which directs the

15

natural orientation of collagen fibers. Under the deformation the skin exhibits J-shape stress

16

strain cure with three distinct regions i.e. toe, heal and linear. The J-shape stress-strain curves

17

shows that under the deformation, the collagen fibers start to align in the direction of load. These

18

aligned collagen fibers are responsible for the resistance against the deformation [33] and which

19

dominate the modulus of tissue. Therefore, the higher value of modulus predicts the large

20

number of collagen fibers orientation intensity in particular direction.

21

Direction dependent variation in the mechanical properties of the planar tissues under

22

multidirectional loading can be accomplished by the bulge test when coupled with the imaging

23

techniques. The in-plane stress component was calculated through the equation of membrane

3

1

theory using the fluid pressure and inflated radius at a particular angle [34, 35]. Under the

2

uniform hydrostatic pressure, the stress (due to radius of curvature) and strain were different in

3

every direction due to anisotropic deformation. These variations in the stress-strain relations

4

were further utilized to resolve the anisotropic mechanical properties. Combination of bulge test

5

method with the imaging techniques like Scanning Electron Microscopy (SEM)[36], Small

6

Angle X-ray scattering (SAXS)[37], Atomic Force Microscopy (AFM) [38] and staining[39]

7

may be helpful for further in-depth analysis of deformation mechanics for soft tissues. The

8

combined use of these techniques is useful in understanding the anisotropic nature of biological

9

planar soft tissues like pericardium [40], arteries [41] and skin [9, 42, 43].

10

The bulge test method has several limitations over the other methods. In this method, the

11

strain rate cannot be maintained precisely constant and precision in stress calculation is subjected

12

to the accuracy of the curve fit (radius). Bending stress is neglected in the calculation due to the

13

bending instability of soft tissue [44]. Despite these limitations, the bulge test can apply the

14

strain in 360° direction on the plane, which can couple with the digital image correlation to

15

measure the anisotropic behavior of planar tissue.

16

In this study, the imaging analysis technique DIC had been coupled with the bulge test to

17

measure the full-field displacement of the specimen with inflation. Local strain and circular fitted

18

radius in each direction were calculated from the displacement field, and stresses were derived

19

from the fluid pressure and radius data. Further, the modulus in angular directions at an interval

20

of 10° was calculated using stress strain relations. Histological examination was performed to

21

investigate the correlation between the variation in modulus and collagen fibers distribution.

22

Further, a cubic empirical relation based on experimental observation was established to predict

23

the variation of modulus with the directions.

4

1

The present method is an improvement over existing techniques to mimic the in vivo

2

temperature and body fluid condition by keeping the pressurizing fluid Phosphate Buffered

3

Saline (PBS) at temperature 37°C. Microscopic imaging was performed to study a plausible

4

connection between the modulus and collagen fibers distribution. Mechanical properties derived

5

from the experiment can be helpful in the anisotropic modeling of the skin. This study simulates

6

the tissue expansion techniques used in reconstructive surgery.

7

2. Materials and methods

8

2.1 Sample preparation

9

Samples preparation and experiments were done as per institute ethical guidelines for the

10

nonhuman subjects. Fresh skin samples of the Yorkshire porcine from the slaughterhouse were

11

collected within 2 hours of sacrifice, and the experiments were performed within 1 hour after the

12

sample collection. A total seven samples were taken from the eight to twelve months old and 70

13

to 90 kg weight porcine. Body locations were specified in Table 1. Approximately 150 x 150 mm

14

square piece was procured from the porcine body skin. The subcutaneous tissue and fat were

15

removed very carefully using scalpel and scissor, and hair was removed using shaver and

16

shaving cream. Further, the samples were washed thoroughly with liquid body wash and rinsed

17

in water for 30 seconds. Then it was kept in ambient room condition (30°C and RH 50-70%) for

18

15 minutes. Skin samples with epidermis and dermis were used for further studies. The skin

19

specimen was kept in PBS solution until the experiment started, to avoid any further changes in

20

mechanical properties. The thickness of the tissue was measured using the digital micrometer

21

(Mitutoyo IP-65, 0.001 mm least count) at four different locations on the same specimen and

22

mean value was used for further calculations. The mean value of thickness with standard

23

deviation and body site of the specimens are given in Table 1.

5

1

2.2 Experimental setup

2

Acrylic pressure container of dimensions 100-mm inner diameter, 120 mm outside diameter,

3

37 mm height was used for the experimental setup. The samples were attached to a

4

polycarbonate ring having 140 mm outer and 100 mm inner diameter. O-ring of 108 mm

5

diameter and 4 mm cross-section was used to circumvent any leakages and offer fixed boundary

6

conditions to the specimen. Samples were fixed by eight pan-head M4 bolt and nut at an equal

7

angle, and uniform glue (Low viscosity instant adhesive, Permabond) was applied on the top and

8

bottom side of the specimen in between fixed boundary area. Excessive tissues were trimmed,

9

and all nuts were equally tight in the opposite direction to avoid possible misalignment of the

10

ring. Black India ink was used to make a waterproof nonuniform speckle pattern on the specimen

11

to track it in the imaging technique.

12

As shown in Figure 1, specimens were pressurized by means of four syringe pumps (Harvard

13

apparatus, pump 11 elite) injected PBS at temperature 38˚C (1°C above the required) to

14

accommodate the temperature change due to contact with skin specimen. The saline temperature

15

was measured by a DS18B20 waterproof temperature sensor placed inside the container (Range:

16

-55 to 125 ˚C, Accuracy ±0.5 ˚C). A pressure transducer (Honeywell, USA, range: 0 -15 psig,

17

accuracy: ±0.1%) connected with the computer through the data acquisition system (NI cDAQ

18

9174, module: NI9234) was used to record the pressure in the container. The pressure container

19

was located inside the glass chamber to control the environment. Relative humidity (RH) was

20

controlled by a small fan with a water-soaked sponge. Environment conditions were monitored

21

continuously by the humidity and temperature sensor DHT 22 (Humidity range: 0 to 100% and

22

accuracy: ±2% RH, temperature range -40˚C to 80˚C, and accuracy is ±0.5 ˚C).

6

1

2.3 Digital Image Correlation (DIC)

2

Two stereoscopic cameras (Resolution: 5MP, Flir Systems Inc., Canada) were used to capture

3

the images. It was placed 60 cm above the specimen and 10 cm apart from each other. The

4

camera lens aperture was minimized to maximize the depth of field, which was required to

5

accommodate the out of plane displacement. Full-field image analysis technique DIC was used

6

to measure the displacement. The refractive index of the glass cover affects the displacement

7

field. However, the consistent shift was expected which did not alter the strain. Vic snap 8

8

(Correlated Solutions, USA) and Vic-3D (Correlated Solutions, USA) were used for the image

9

capture and to extract the full-field strain respectively [45, 46]. The error in displacement

10

obtained from the digital image correlation was calculated by taking the four identical images.

11

First was taken as reference and the other three images were generated digitally by translating 2,

12

5, and 10 pixels respectively in the horizontal direction [47]. It simulates the motion in the rigid

13

body. The mean displacement error for the mentioned experimental setup was ±2.105 µm.

14

2.4 Bulge Test

15

The entire system was made air bubble-free to avoid the change in biomechanical properties

16

because of two different contact media. The specimen was 20 mm above the level of pressure

17

transducer port, it was created the pressure of 0.2 kPa in a fully filled condition which was

18

considered as the reference zero pressure. The experiments were performed at a saline

19

temperature of 36 -37˚C (like the human body temperature), 29-31˚C atmospheric temperature

20

and 70 to 75% relative humidity (comparable with the monsoon season). These conditions were

21

maintained for 10 minutes before the experiment to ensure the equilibrium condition for the

22

specimen. A preliminary trial with a constant flow rate shows the strain rate at the beginning was

23

very low. To attained a nearly constant strain rate of 0.0055 - 0.0060 s-1 initially flow rate was

7

1

kept higher then decreased gradually. Saline fluid (90 to 120 ml) flowed inside the container

2

such that maximum pressure should be less than the 100 kPa. Images were captured at a

3

frequency of 0.5 Hz for DIC. Tested specimens were stored at -80°C for further study.

4

The experiments consisted of a single loading and unloading cycle without any pre-stretch.

5

The fluid carried the dead weight of the specimen and tests were performed in controlled

6

humidity and temperature conditions. These experimental protocols minimize the effect of

7

preconditioning on final results.

8

2.5 Data Analysis

9

Stress strain relation is required for the quantification of the anisotropic properties of the skin.

10

Stresses were calculated using the pressure and circular radius (local measure) of curvature in a

11

particular direction. The pressure was recorded in the experiment and the displacement field was

12

used for calculation of local measure of curvature radius. As shown in Figure 2 the deformed

13

coordinates of displacement field were U, V, and W corresponding to the X, Y, and Z-axis

14

respectively. The in-plane coordinates were calculated as L = U 2 + V 2 . α 1 α  2 α 3  M α n

 α 1 2 + β1 2  β1 1   β 2 1  xc ' α 2 2 + β 2 2  β 3 1  zc '  = α 3 2 + β 3 2     M

βn

M  yc ' 1

(1)

M   α 2 + β 2  n   n

15

Here, α n and β n represent the coefficient of L and W coordinate corresponding to the nth data

16

point. The radius of the curvature was calculated from the circular arc data fits using equation

17

(1). Best fitted value of xc ' , zc ' and y c ' were calculated by the Gaussian elimination method

18

using MATLAB (MathWorks inc., USA) programming. Further the center point and radius of

19

the curvature was calculated using equation (2) and (3) respectively. 8

xc = −

xc ' z ' and, zc = − c 2 2

Rθ =

xc + z c − ( yc ' ) 2

2

(2)

(3) 2

1

Where xc and zc are coordinate of the center, Rθ is the radius of curvature in the θ direction. It

2

was found that, use of more than 70% of the diameter for the circular fit from the from the apex

3

point was resulted in a poor fit. Therefore, to ensure accuracy in the results, a 60% diameter in

4

the center region was considered as Region Of Interest (ROI). In Figure 3 the circular arc with

5

(0.4181, -30.36) mm center point and 53.69 mm radius in the range of -30 to 30 mm illustrates

6

the results of data fit. Total 200 data points in each direction were extracted from the deformed

7

coordinates for the data fit.

8

For infinitesimally small deformation, the thickness of the specimen can be assumed constant,

9

however, under the finite large deformation variation in the thickness cannot be omitted. In this

10

study variation in thickness was incorporated in the calculation by considering the thickness

11

variation as shown in Figure 4. The thickness (t) as a function of distance and height of the apex

12

point is given in equation (4) [48].

 x2  t = t0  2 2 x +h 

(4)

13

Where t0 is the initial thickness, x is the half-width of the effective diameter, h is the height

14

of apex point as described in Figure 4 using the schematic cross-sectional view of the deformed

15

shape. Further, for the simplification in stress calculations, the average thickness in the ROI was

16

taken into consideration.

17

9

1

The membrane theory was used for stress calculation with the assumption of uniform

2

distribution of stresses along the thickness. Bending stress is neglected in membrane theory

3

which does not affected significantly on the results of this study due to the bending instabilities

4

of soft tissues [44]. Therefore, the assumption of the plane stress was taken to neglected the

5

bending stress in further calculations. Anisotropic deformation of the specimen leads to the bulge

6

of nonuniform radius sphere. Therefore, stresses on the specimens with the direction were

7

nonuniform. The radius and stresses were calculated at an interval of 10°, as illustrated for angle

8

θ in Figure 5. Stress ( σ θ ) in the direction of angle θ as a function of radius ( R(θ +90) ), thickness

9

(t) and pressure (P) is given in the equation (5) and schematically represented in Figure 4.

10

Variation in the circular arc radius for a specific value of the pressure was found between 2% to

11

10% with the direction.

σθ =

P ⋅ R(θ +90)

(5)

2⋅t

12

Full-field strain calculated from DIC was shown in Figure 6 for the normal strain

13

corresponding to the X, Y directions ( ε x , ε y ) and shear strain on XY planes ( γ xy ). A mean value

14

of 200 data points along a line in the particular direction within

15

calculation of ε x , ε y and γ xy . These strains were calculated on the same lines, which were used

16

for the calculation of stress at an interval of 10°. Further, these values were incorporated in

17

equation (6) to calculate the value of normal strain ε θ in the direction of angle θ [49].

εθ =

εx + εy 2

+

εx −εy 2

cos ( 2θ ) +

γ xy 2

ROI was taken for the

(6) sin ( 2θ )

18

The stress strain relations for skin is nonlinear having two distinct linear regions. The slope of

19

stress and strain curve for the first and second linear regions is known as toe and linear modulus 10

1

respectively. In the present article, the stress strain curve for each direction was based on the

2

directional stresses and directionally averaged strains. Therefore, more precisely, modulus was

3

defined as the apparent modulus. Generalized Hooke’s law equations were employed with the

4

assumptions of transverse isotropy to calculate the linearized coefficient, which represents the

5

apparent modulus of specified directions. Orthogonal principal material coordinates were

6

selected. One principal axis was taken in the direction of angle θ and modulus was defined as Eθ

7

. The plane perpendicular to the direction θ was taken as the plane of isotropy and modulus was

8

defined as Eθ +90 . The slope of first and second linear regions was calculated in each direction.

9

The first linear region was considered up to the stress level of 5.0 ± 0.3 kPa for the calculation of

10

toe apparent modulus [9]. Whereas the second linear region was considered for the final 0.03

11

strain to calculate the apparent linear modulus. The intersection of the two linearly fitted curves

12

was defined as the transition point. These data of toe and linear region were coupled in equation

13

(7) and (8) to calculate the value of ET and EL respectively in each direction.

εθ =

1 ν ⋅σ θ − ⋅ σ θ + 90 Eθ Eθ + 90

ε θ + 90 = −

ν Eθ

⋅σθ +

1 Eθ + 90

⋅ σ θ +90

(7) (8)

14

Where ν is Poison’s ratio, Eθ is modulus in the direction of angle θ . For simplification, the

15

Poison’s ratio was taken as 0.5 independent of the direction [26]. Variation in the apparent

16

modulus is expected due to anisotropy of skin, which comes from the collagen fibers directional

17

distribution intensity.

11

1

2.6 Histology

2

The orientation of collagen fiber for untested and mechanically tested specimens was

3

examined by Hematoxylin and Eosin (H&E) (Sigma-Aldrich, USA) staining [39, 50]. To avoid

4

the location dependent nonuniformity in collagen distribution, all specimens of skin were taken

5

from the ventral region. The permanent deformation in the tested specimens S2 and S3 were

6

induced using the relaxation experiment in bulge, where specimens were relaxed at approximate

7

15% constant strain for 3 hours. This procedure ensured the permanent deformation of collagen

8

fibers. The strips of 8 mm x 8 mm dimensions were cut from the center of the tested and untested

9

specimen. Further, it was embedded in Optimal Cutting Temperature (OCT) medium and froze

10

at -80 °C. Total 21 (7 from each tested and untested) sections of 5 µm thickness were cut parallel

11

to epidermis using cryostat (Leica CM1850 UV, Germany), which was maintained at -30 °C

12

working temperature. The standard protocol was followed for the H&E staining as discussed in

13

the literature [39, 50, 51]. Later it was covered with a coverslip using the mounting media.

14

Digital images were acquired for all the sections oriented in the same direction using the manual

15

mode of the microscope at the magnification of 10x and 20x.

16

The objective of staining was to determine the directional distribution intensity of collagen

17

fibers. This information was required to determine the plausible relation between the collagen

18

fibers orientation and mechanical properties. Image processing software ImageJ (NIH) with

19

OrientationJ plug-in was used to determine the local orientation of collagen distribution based on

20

a 2-pixel size gaussian window on the entire image [52]. A total 10 images (2 from each section)

21

for each specimen at the magnification of 10x and 20x were analyzed to determine the average

22

fiber orientation.

12

1

3. Results

2

The objective of this study was to quantify the anisotropy (occurred due to variation in the

3

directional intensity of collagen fibers) of the skin. It was accomplished by calculating the

4

apparent linear modulus and performing the histological analysis. Variation in the apparent linear

5

modulus and fiber orientation was analyzed in the planar directions parallel to the epidermis.

6

3.1 Mechanical Testing

7

In this study, the variation in apparent modulus with the direction at an interval of 10° was

8

calculated to quantify the anisotropy of the skin. The accuracy for the maximum and minimum

9

modulus was found to be ±5°. Therefore, additional values near the maximum and minimum

10

points were calculated to increase the accuracy up to ±1°. The maximum value of EL

11

represented the direction of the preferential orientation of the collagen fibers under

12

multidirectional loading conditions. The value of the maximum and minimum modulus for

13

collagen dominated (linear) region was 43.36 ± 11.80 MPa and 17.78 ± 6.03 MPa respectively.

14

These results were found in good agreement with the value of modulus obtained for the porcine

15

dermis in the literature [53]. Maximum and minimum modulus for the toe region was 0.3727 ±

16

0.1690 MPa and 0.3068 ± 0.1501 MPa respectively. These results were found to be consistent

17

with the modulus 0.12 - 0.85 MPa in previous in-vivo and in-vitro studies [21, 53, 54]. The ratio

18

of maximum to minimum linear modulus was 2.71 ± 1.32, which was found similar to the

19

reported values [55]. The angle differences between the maximum and minimum modulus in the

20

toe and linear region were found 64° ± 17° and 72° ± 7° respectively. The minimum and

21

maximum value of transition strains were observed as 0.13 ±0.04 and, 0.14±0.05 respectively.

22

These values were in good agreement with the reported values of 0.11 and 0.18 in the literature

23

using the bulge test experiment [9].

13

1

3.2 Staining

2

Histological images were analyzed to examine the directional intensity of the collagen fibers

3

and the effect of mechanical loading. Representative images of H&E staining for untested and

4

mechanically tested specimens are shown in Figure 7(A) and (B) respectively. Eosin bind with

5

the proteins and hence collagen appears pink, and Hematoxylin binds with nuclei which appears

6

blue. As shown in Figure 7(A) the gap between two adjacent fiber families in the untested

7

specimen (a gap between pink color fiber bundle) was less as compared to the tested specimen as

8

shown in Figure 7(B), this increase in gap indicates the damage of collagen fibers after the

9

loading. Moreover, from the same results, straighten in collagen fibers was also observed in the

10

tested specimen.

11

The orientation of the collagen fiber in the tested (20 images from 2 specimens) and untested

12

(10 images) specimen images were analyzed using ImageJ. The mean and standard deviation was

13

calculated and normalized with respect to the maximum value. The maximum value of the

14

orientation intensity was taken as 100% in the direction of 0°. Percentage variation in the

15

collagen fibers orientation for the untested and tested specimen is shown in Figure 7(C) and (D)

16

respectively. The angle difference between maximum and minimum fibers orientation intensity

17

was found to be 87° ± 6° for untested and 76° ± 5° for a tested specimen. These results were

18

found to be in good agreement with the tested specimens angle difference between the maximum

19

and minimum apparent linear modulus (72° ± 7°), which indicates the significant effect of

20

collagen fiber orientation intensity on the modulus.

21

3.3 Role of collagen fibers orientation on mechanical properties

22

The stresses and strains calculated from equation (5) and (6) respectively were plotted at an

23

interval of 10° for specimens S1 and S2. Comparison for specimen S1 (dorsal) and S2 (ventral)

14

1

were shown in Figure 8(A) and Figure 8(B) respectively. Natural tension line and pretension

2

state play a major role in the mechanical anisotropy. It was reported that the level of anisotropy

3

is significantly lower for the dorsal skin as compared to the ventral porcine skin [53, 56].

4

Therefore, it was expected that for S2 (ventral) a large number of collagens are oriented in the

5

preferential direction. Wide-span width in Figure 8(B) indicated the higher difference in the

6

modulus variation and higher level of anisotropy. A similar trend was observed for the specimen

7

S3 (shoulder), S4, S5 (ham) and S7 from the ventral. The ratio of maximum to minimum

8

modulus for the specimen having a similar level of anisotropy (specimens S2, S3, S4, S5, S7)

9

was 2.37 ± 0.33. Variations in the modulus with the angle were found consistent for specimens

10

S2, S3, S4, S5 and S7 defined as Major Group (MG) for further study.

11

The narrow span width for S1 (dorsal) in Figure 8(A) indicated the less difference in modulus

12

variations. The ratio of maximum to minimum modulus was 1.56, which indicates a lower level

13

of anisotropy as compared to other specimens. It was because of the more uniform distribution of

14

the collagen fibers. Schematic representation in Figure 8(A) and Figure 8(B) shows the

15

directional distribution intensity of the collagen fibers, which was predicted based on the

16

variation in the modulus. Table 2 shows the analysis of variation in the mean value of apparent

17

modulus ET and EL with standard deviation for all specimens, whereas Figure 8 (C) shows the

18

graphical representation of modulus ET and EL with the angle for specimen S2.

19

Further, results were normalized for the MG to represent the relative variation in the modulus

20

with the direction. The maximum modulus was taken in 0° direction and considered as 100%.

21

Variations were rearranged in such a way that the angle for minimum modulus was ≤ 90°. The

22

percentage variation with the angle was calculated for each specimen of MG. Further, the mean

23

and standard deviation was calculated for MG. Cubic polynomial fit was taken for the linear (R2

15

1

= 0.9972) and toe (R2 = 0.9847) region modulus percentage variation. These results were plotted

2

with mean and standard deviation error bars in Figure 9 to show the variation in the value of EL

3

and ET with the direction. Similarly, the percentage variation of collagen fibers orientation

4

intensity observed in the histological study is shown in Figure 9. Variation in the collagen

5

orientation intensity for the untested specimen was 68.4% ± 7.1%, which signifies the role of

6

natural tension line on collagen alignment. For tested specimen, it was reduced to 52.5% ± 6.4%,

7

this indicates the realignment of collagen fibers under the multidirectional loading.

8

The comparison shows a similar trend for the directional distribution intensity of collagen

9

(from histological analysis) and percentage variation in the apparent linear modulus (from the

10

mechanical testing). The percentage variation for the collagen directional intensity and modulus

11

was 52.5± 6.4 and 43.4 ± 8.2 respectively. This similarity in the variation signifies the role of

12

collagen fibers orientation intensity on the mechanical properties for the skin.

13

4. Discussion

14

The method presented in this article was performed under in vivo like environment conditions

15

to overcome the several limitations of in vitro studies. Mechanical properties were found in the

16

same range of in vivo and in vitro mechanical properties presented by several authors [21, 53,

17

54, 57], which supports the appropriateness of the present experimental method. Radius,

18

thickness, and strain in all 360° were calculated from full-field displacement. Which overcomes

19

the limitation of global strain by calculating the average strain in each local subset.

20

Inhomogeneous stresses were calculated based on radius in each direction. The variation in the

21

stress and strain relations with the direction shows the anisotropic nature of the skin.

22

The available literature is limited to the properties of skin tissue in the parallel and

23

perpendicular direction of the Langer lines [20, 21, 53]. The variation in the modulus with the 16

1

directions as well as the angle difference between the maximum and minimum modulus is

2

important to understand the soft tissue biomechanics. Histological analysis shows that the

3

directional intensity of collagen fiber orientation was different in untested and tested specimens.

4

The nature of collagen distribution can be different under the various types of loadings.

5

Consistency in the mechanical properties and collagen distribution intensity will be helpful to

6

understand the plausible relation between collagen fiber distribution and mechanical properties

7

obtained through uniaxial, biaxial and multidirectional loadings.

8

This study shows that the collagen fibers remain oriented in the preferred direction even after

9

the excision. These results were found to be consistent with the literature [58]. The probability of

10

the collagen alignment in a preferential direction was purely depended on the natural tension for

11

the untested condition. The schematic diagram in Figure 10 (A) shows the reduced number of

12

collagen fibers and the qualitative probability of directional intensity for the unstretched

13

condition. Under uniaxial load, most of the fibers are reoriented in the stretched direction (Figure

14

10 B) and start resisting the load. The probability of orientation intensity for the collagen

15

alignment shows a single peak [37, 43] (Figure 10 B), as the reorientation of collagen fiber takes

16

place through rotation and stretching in the loading direction [59]. Under the biaxial loading,

17

fibers became oriented in two directions. Therefore, the probability of collagen fiber orientation

18

intensity shows the two peaks (Figure 10 C) [37, 43, 60].

19

The multiaxial loading tends to straighten the collagen fibers in all stretching directions, as

20

shown in Figure 10 (D). The probability distribution intensity plotted in Figure 10 (D) is based

21

on the histology and modulus variation found in the present study. From the above discussion, it

22

can be concluded that the different types of loading conditions lead to different levels of

23

anisotropy.

17

1

Histological analysis shows that the angular difference between the maximum and minimum

2

collagen fibers orientation intensity for untested specimens was significantly higher than the

3

tested specimen. This discrepancy between tested and untested specimens indicates the

4

reorientation of the collagen upon stretching. Based on the observation it can be hypothesized

5

that the stretching of collagen fibers takes a path in the direction where overall minimum

6

displacement (minimum change in position) occurs. This direction may be identified by taking

7

the linear fit of the fibers profile shape. Further investigation may require using in-situ imaging

8

techniques with the multidirectional loading to validate the hypothesis.

9

In this study, the generalized formula to calculate the linear modulus with the angle is

10

introduced as given in equation (8). This empirical relation is valid for the selected anatomical

11

site where pre-tension conditions are similar to the MG (ventral). This formula was derived from

12

the mean percentage and standard deviation of the variation in apparent linear modulus with the

13

direction. The goodness of the correlation (R2) for the cubic polynomial equation with the

14

experimental data points was 0.9972.

Eθ = Er ⋅ (−0.0386) ⋅θ 3 + (0.3479 ± 0.0091) ⋅θ 2 − (0.7120 ± 0.0215) ⋅θ + (1.0000 m 0.0151) 

(8)

15

Where, θ is the angle in radian, Eθ is modulus at angle θ direction, and Er is reference value

16

of modulus in the direction of Langer lines. Literature has reported the range of modulus in the

17

linear region ( Er ) as 3 - 150 MPa [21, 53, 54, 57, 61].

18

Observations of the present study may become a benchmark to explore the anisotropy of

19

planar soft tissue in all the directions. The given empirical relation for the variation in the linear

20

modulus will be helpful in computational studies for structure based anisotropic modeling of

21

skin. The present testing method mimics the tissue expansion technique which is widely used in

22

clinical applications. Tissue expansion is an anisotropic process accomplished by mainly square, 18

1

rectangular, circular or crescent shaped tissue expanders [62].

This technique has several

2

complications like mechanical failure, flap failure, and implant extrusion [63]. Nonuniform

3

expansion takes place based on the selection of expander. The knowledge of mechanical

4

properties and anisotropy will be helpful to place the expander and to optimize the expansion

5

rate [51]. The expander orientation should be chosen in such a way that the direction of

6

maximum expansion should be parallel to the direction of minimum modulus. The method

7

presented here will help to study the tissue expansion for different shapes expander and to

8

optimize the tissue expansion rate.

9

Future scope includes improvement in the bulge test technique by controlling the flow rate to

10

make the strain rate constant, calculate the bending stress, and determine the hyperelastic and

11

viscoelastic properties of skin in all the directions. In-situ studies with the imaging technique can

12

allow a more in-depth look at collagen fibers deformation. It may be required to validate the

13

hypothesis for the rotation of collagen fibers under uniform loading conditions.

14

5. Conclusion

15

The present in vitro study for the directional dependent variations in the mechanical properties

16

can be incorporated for almost all kinds of planar soft tissues. The bulge test overcomes some

17

limitations of in vitro studies by keeping the 37 °C saline temperature to mimic the natural body

18

temperature and fluid. The angle difference between maximum and minimum collagen fibers

19

orientation intensity for tested and untested specimens indicates the realignment of fibers under

20

the multidirectional loading. This observation is helpful to propose the hypothesis on the

21

collagen fibers deformation mechanics for multidirectional loading.

22

Acknowledgment:

19

1

The IIT Ropar is highly acknowledged for providing facilities and infrastructure and used in

2

the current research. One of the authors (Piyush Lakhani) thanks the Ministry of Electronics and

3

IT for providing the Visvesvaraya Ph.D. scheme research fellowship.

4

Conflict of interest

5

The authors declare that they have no conflict of interest.

6

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26

1

Table 1. Skin specimen thickness and location on the body. Sample

Thickness (mm)

Body site

S1

2.601 ± 0.081

Baby Back Ribs

S2

3.745 ± 0.109

Spare Ribs

S3

4.286 ± 0.061

Picnic Shoulder

S4

3.266 ± 0.054

Spare Ribs

S5

2.743 ± 0.048

Ham

S6

3.641 ± 0.085

Pork Chops

S7

2.781 ± 0.091

Spare Ribs

2 3 4 5 6

Table 2. Statistics of the experimental results plotted in Figure 8. (∆θ )T and (∆θ )L represent the angle

7

between the maximum and minimum value of modulus in toe region and linear region respectively, for

8

>90° angle difference in counterclockwise represented by an angle in a clockwise direction. Toe region modulus E T

Sample

Linear region modulus E L

Maximum

Angle

Minimum

Angle

(MPa)

(Degree)

(MPa)

(Degree)

(∆θ )T

Maximum

Angle

Minimum

Angle

(MPa)

(Degree)

(MPa)

(Degree)

(∆θ )L

S1

0.3224

2

0.2438

64

62

36.12

4

23.12

76

72

S2

0.4062

116

0.3401

16

80

49.77

102

19.81

0

78

S3

0.3562

10

0.2872

96

86

33.74

8

12.49

74

66

S4

0.2206

64

0.1821

100

36

28.36

100

13.16

170

70

S5

0.6595

100

0.5568

34

66

62.51

56

23.65

136

80

S6

0.1546

46

0.1126

98

52

50.86

62

9.16

140

78

S7

0.4937

92

0.4248

24

68

42.13

53

23.08

114

61

Mean

0.3727

64

43.36

0.3068

17.78

72

27

Std. dev.

0.1690

0.1501

17

11.80

6.03

7

1 2 3 4

Figure Captions:

5

Figure 1. Schematic diagram (left) and photograph (right) of the experimental setup. A-

6

syringe pump, B- glass chamber for control volume, C- fan for humidity control, D- computer

7

for image and data acquisition, E- pressure transducer, F- Arduino for temperature and humidity

8

monitoring, G- digital camera, H- temperature and humidity sensor, I- pressure chamber, J- light

9

source.

10

Figure 2. Full-field displacement obtained through DIC. (A) displacement in X-axis direction

11

(B) displacement in Y-axis direction and (C) out of plane displacement indicated as U, V, and W

12

respectively.

13 14

Figure 3. Comparison of experimental data (reduce number of points) from the deformed

shape and corresponding circular fit obtained through Gaussian elimination method.

15

Figure 4. Schematic diagram for the cross-sectional view of the specimen having a peripheral

16

fixture. It represents the thickness variation near the apex point and tangential stress acting at

17

particular section.

18

Figure 5. Represent the in-plane X and Y axis, the shaded area shows the region of interest,

19

which has a 30 mm radius. The dashed line represents the direction at angle θ, which was used

20

for the calculation of average strain and radius for θ angle direction.

28

1

Figure 6. Full-field Lagrangian strain calculated from the displacement field obtained through

2

the DIC. (A) normal strain in X-axis direction (B) normal strain in Y-axis direction (C) shear

3

strain on XY-plane.

4

Figure 7. Histological examination of the dermis section using Hematoxylin and Eosin

5

staining of untested (A) and mechanically tested specimen (B). Pink color shows the collagen

6

fibers. Black arrow with lines represents the increased gap between collagen fibers in tested

7

specimens compared to untested. Percentage variation in the fibers directional intensity with

8

mean and standard deviation for untested and tested specimen is shown in (C) and (D)

9

respectively. The maximum value was taken as 100% and 0° direction.

10

Figure 8. (A & B) represent stress vs. engineering strain measured from the experiment at

11

each 10° angle with the positive X-axis (0° angle direction was considered on positive X-axis)

12

and in the counter-clockwise direction. Wide-span width of stress strain curve for specimen S2

13

(ventral) in (B) indicates the preferential direction distribution of collagen fibers as compared to

14

narrow span width in (A) for specimen S1 (dorsal). The variation in the apparent elastic modulus

15

for the toe region and the linear region with the direction angles for the specimen S2 is shown in

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(C).

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Figure 9. shows mean percentage variation of elastic modulus in the linear region and toe

18

region with experimental data and standard deviation error bar. Maximum values were taken as

19

100% and in the 0° direction. The line presented for modulus was cubic polynomial fitted.

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Histological analysis (dashed dot line) shows the percentage variation in the directional

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distribution intensity with angle.

29

1

Figure 10. Shows the schematic diagram of reduced number of collagen fibers (upper) and

2

qualitative probability distribution (p) versus direction angle in degree (lower). Unstretched

3

condition (A) shows the curved fibers with the preferential orientation probability distribution in

4

natural tension direction. The Uniaxial loading (B) aligned the collagen fibers along the stretched

5

direction and the probability shows single valley. Biaxial (C) stretching makes collagen aligned

6

in two directions, and the probability curve has two valleys. Representative schematic for multi-

7

directional loading in (D) shows the realignment of the collagen fibers, which was resulted in the

8

probability distribution with the shift at the valley.

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Directional dependent variation in mechanical properties of planar anisotropic porcine skin tissue

Figure 1. Schematic diagram (left) and photograph (right) of the experimental setup. Asyringe pump, B- glass chamber for control volume, C- fan for humidity control, D- computer for image and data acquisition, E- pressure transducer, F- Arduino for temperature and humidity monitoring, G- digital camera, H- temperature and humidity sensor, I- pressure chamber, J- light source.

Figure 2. Full-field displacement obtained through DIC. (A) displacement in X-axis direction (B) displacement in Y-axis direction and (C) out of plane displacement indicated as U, V, and W respectively.

Figure 3. Comparison of experimental data (reduce number of points) from the deformed shape and corresponding circular fit obtained through Gaussian elimination method.

Figure 4. Schematic diagram for the cross-sectional view of the specimen having a peripheral fixture. It represents the thickness variation near the apex point and tangential stress acting at particular section.

Figure 5. Represents the in-plane X and Y axis, the shaded area shows the region of interest, which has a 30 mm radius. The dashed line represent the direction at angle θ, which was used for the calculation of average strain and radius for θ angle direction .

Figure 6. Full-field Lagrangian strain calculated from the displacement field obtained through the DIC. (A) normal strain in X-axis direction (B) normal strain in Y-axis direction (C) shear strain on XY-plane.

Figure 7. Histological examination of the dermis section using Hematoxylin and Eosin staining of untested (A) and mechanically tested specimen (B). Pink color shows the collagen fibers. Black arrow with lines represents the increased gap between collagen fibers in tested specimens compared to untested. Percentage variation in the fibers directional intensity with mean and standard deviation for untested and tested specimen is shown in (C) and (D) respectively. The maximum value was taken as 100% and 0° direction.

Figure 8. (A & B) represent stress vs. engineering strain measured from the experiment at each 10° angle with the positive X-axis (0° angle direction was considered on positive X-axis) and in the counter-clockwise direction. Wide-span width of stress strain curve for specimen S2 (ventral) in (B) indicates the preferential direction distribution of collagen fibers as compared to narrow span width in (A) for specimen S1 (dorsal). The variation in the apparent elastic modulus for the toe region and the linear region with the direction angles for the specimen S2 is shown in (C).

Figure 9. shows mean percentage variation of elastic modulus in the linear region and toe region with experimental data and standard deviation error bar. Maximum values were taken as 100% and in the 0° direction. The line presented for modulus was cubic polynomial fitted. Histological analysis (dashed dot line) shows the percentage variation in the directional distribution intensity with angle.

Figure 10. Shows the schematic diagram of reduced number of collagen fibers (upper) and qualitative probability distribution (p) versus direction angle in degree (lower). Unstretched condition (A) shows the curved fibers with the preferential orientation probability distribution in natural tension direction. The Uniaxial loading (B) aligned the collagen fibers along the stretched direction and the probability shows single valley. Biaxial (C) stretching makes collagen aligned in two directions, and the probability curve has two valleys. Representative schematic for multidirectional loading in (D) shows the realignment of the collagen fibers, which was resulted in the probability distribution with the shift at the valley.

Research Highlights The bulge test method coupled with the digital image correlation enabled the finding of the variations in the mechanical properties of the planar tissue. Empirical relation for the variation in apparent modulus with the direction will be helpful for the computational modeling of skin. The significant angle difference between orientation intensity from histology and mechanical testing for tested and untested specimen indicates the novel hypothesis on collagen deformation mechanics.

INDIAN INSTITUTE OF TECHNOLOGY ROPAR Rupnagar, Punjab – 140 001 (INDIA) Dr. Navin Kumar Associate Professor Department of Mechanical Engineering

Phone: +91-1881- 242226 Fax: +91-1881 - 223395 E-mail: [email protected] http://www.iitrpr.ac.in/smmee/nkumar

November 23, 2019 To The Editor-in-Chief, Journal of Mechanical Behavior of Biomedical Materials Sub: Conflict of Intrest Declaration Dear Professor Markus Buehler I hereby submit the revised manuscript entitled “Directional dependent variation in mechanical properties of planar anisotropic porcine skin tissue” for your consideration to publish it in “Journal of Mechanical Behavior of Biomedical Materials”. I would like to confirm that we authors (Piyush Lakhani, Krashan K Dwivedi, Dr. Navin Kumar) have no conflict of interest. I would like to confirm that all the authors are fully involved in this research study and preparation of the manuscript and that the material within has not been and will not be submitted for publication elsewhere. I confirm that all the authors have made substantial contributions to the conception and design of the study, acquisition, analysis and interpretation of data, drafting of the article or revising it critically for important intellectual content and final approval of the version to be submitted. I also confirm that the manuscript, including related data, figures and tables has not been previously published and that the manuscript is not under consideration elsewhere. Thank you. Sincerely, NAVIN KUMAR