Analysis of Stress and Strain on Rat Bones and Blood Vessels Due to Silicon Intake

Analysis of stress-strain in bones and blood vessels of rats

after silicon intake

The Institute of Electronics, Information and Communication Engineers, IEICE Technical Report

INFORMATION AND COMMUNICATION ENGINEERS MBE2014-7 (2014-5)

Analysis of stress-strain in rat bones and blood vessels due to silicon intake

Yoko Kawamura† Yasunari Yokota†† Fumio Nogata††

Mitsuo Terasawa††† Nakayoshi Kamijo†††Noriki Okada††††

†Gifu University Human Biomedical Engineering Research and Development Center 1-1

Yanagido, Gifu-shi, Gifu, 〒501-1193

††Gifu University Faculty of Engineering 1-1 Yanagido, Gifu-shi, Gifu,Japan.〒501-1193

††Tamagawa University Faculty of Engineering 6-1-1 Tamagawa Gakuen, Machida-shi, Tokyo, Japan.〒194-8610

††††APA Corporation Inc.

E-mail: †,††{yokokawa,ykt}@gifu-u.ac.jp, †††terasawamitsuo@yahoo.co.jp

Summary:

It has been noted that there is a close relationship between silicon intake and bone mineral density (BMD). Additionally, silicon intake is suggested to inhibit arteriosclerosis and improve immune function, though there has been little objective verification to date. In this study, we conducted tensile tests on the bones and blood vessels of 13 rats that consumed silicon and rare sugars, analyzing their stress-strain characteristics and assessing the mechanical strength of the bones and blood vessels. Results showed that the strain (elongation) at maximum stress in the blood vessels of the silicon intake group and the rare sugar intake groups was significantly greater than in the control group. Furthermore, the breaking stress of the burned bones in the silicon intake group and the breaking stress of the ulna and radius in the rare sugar intake group were significantly higher than those in the control group.

Keywords: Silicon intake, Bone, Blood Vessel, Stress-strain, Rare sugar

This article is a technical report that has not undergone peer review; a polished and/or extended version may be published elsewhere.

Copyright ©2014 by IEICE

1. Introduction

Since the 1940s, the "Framingham Study," one of the leading epidemiological studies in the United States, and the "Framingham Offspring Study," which began in the 1970s to study the children of the original participants, have suggested that silicon may strengthen bones more effectively than calcium [1],[2]. A joint research team from the United States and the United Kingdom studied 2,846 participants from the Framingham Offspring Study, measuring bone mineral density (BMD) at four sites, including the femoral neck, trochanter, and lumbar spine, as well as participants' dietary silicon intake. The results showed a strong correlation between silicon intake and BMD, with men and premenopausal women who had higher silicon intake demonstrating greater BMD in the femoral neck. Those consuming the most silicon (over 40 mg/day) had nearly 10% higher BMD than those consuming the least (less than 14 mg/day). Given that the increase in BMD from calcium intake was only up to 5%, it was concluded that silicon has a greater impact on BMD than calcium [1].

Additionally, silicon intake has been suggested to inhibit arterial sclerosis and enhance immune function [3],[4]. A study measuring lymphocyte counts in the spleen and thoracic lymph nodes of rats fed distilled water and water-soluble silicon over a certain period found that rats given water-soluble silicon had increased lymphocyte counts, indicating an improvement in immune function [3].

For rare sugar, D-psicose has been found to show effects similar to silicon, such as inhibiting arterial sclerosis, suppressing body fat accumulation [5], reducing postprandial blood glucose levels [6], and exhibiting anti-obesity properties [7],[8]. Although clinical verification is ongoing, the evaluation of mechanical strength characteristics, such as stress-strain behavior, has been largely unexplored.

In the following sections, Section 2 will outline stress-strain characteristics for evaluating mechanical strength, while Sections 3 and 4 will present the results from tensile tests analyzing stress-strain characteristics of rat blood vessels and bones.

2. Mechanical Strength Evaluation

2.1 Stress-Strain [9], [10]

As shown in Fig. 1, when an external force P acts on a material (object) in a pulling or tensile direction, an internal force that resists this external force P is generated on the cross-section perpendicular to the tensile direction. If the object’s length is sufficiently long and the cross-section is sufficiently distant from both ends of the object, this internal force will be uniformly distributed across the cross-section, and the total internal force will be equal to the external force P. In this case, the internal force per unit area is referred to as the stress σ. If A is the cross-sectional area, then: This relationship is given by equation (1).

In engineering, an external force is often referred to as a "load," and a force that causes tension is called a tensile load. Correspondingly, the stress resulting from a tensile load is called tensile stress.

When an object is subjected to force, it deforms, and the degree of deformation generally varies by location. As shown in Fig. 2, if the initial length of the object is ℓ0ℓ0​, the length after deformation is ℓℓ, and the change in length is ΔℓΔℓ, then strain εε represents the degree of deformation at each location within the object. Strain, defined as the elongation per unit length, can be expressed as follows in equation (2):

Fig.1　Normal stress

 Fig. 2　strain

2.2 Stress-shear strain [11]

A slender rod-like member that bears a bending load is called a beam. In the case of the bone specimens used in this study, a fixture was employed as shown in Fig.3(a), where the beam is supported at both ends and subjected to a concentrated load P at a single point in the middle. The tensile stress in bending, or the Fracture Stress σ_f [N/mm²] , is determined by the bending moment M_f and the Sectional Modulus Z, which depends on the shape of the cross-section, as follows: [N/mm2] (3)

 Here, ℓ represents the span length of the sample, and the bending moment M_f is expressed as follows when a simply supported beam receives a concentrated load at its midpoint: (4)

Therefore, the bending moment M_f can be obtained from the (Load) P using equation (4), and the section modulus Z can be calculated from the physical properties of each specimen, so the fracture stress σ_f can be obtained from equation (3). On the other hand, the deflection of the beam, that is, the shear strain, is given as the angle γ in Fig. 3(b). When the shear strain γ is small, let λ be the amount of deflection caused by tension, as follows: [N/mm2] (5)

Fig. 3 (A)Fixed Beam                    (B)Shearing Strain

2.3 Stress-Strain Diagram

Tensile testing, along with other static tests such as compression, bending, and torsion tests, is widely conducted as one of the material tests to obtain fundamental data on the strength of materials. It involves applying tensile load in the axial direction of the test specimen with parallel sections of circular or rectangular cross-sections and measuring the load and elongation at that time [11].

The load and elongation measured by the tensile test are converted into stress and strain according to 2.1, where stress is plotted on the vertical axis and strain on the horizontal axis to represent the relationship between stress and strain, known as the stress-strain curve. Similarly, by using 2.2, the relationship between stress and strain due to bending stress in beams and shear strain due to deflection of beams can also be represented as a stress-strain diagram.

The stress-strain diagram shows that as stress increases, strain increases proportionally until it reaches the point of maximum stress, after which it leads to final fracture. Generally, the maximum tensile stress, also known as tensile strength, in blood vessels and bones, unlike in metallic materials, is measured simultaneously at the time of fracture.

3. Experimental

3.1 Specimens

The experiment utilized 13 male SPF (Specific Pathogen Free) Sle:Wistar rats (Japan SLC, Inc.) at 10 weeks of age. These rats were divided into distinct groups based on their drinking water and were housed for 50 days. Group 1 (control group, CT, 3 rats) received tap water only, Group 2 (silicon intake group, SI, 3 rats) had 10% silicon added to their drinking water. Group 3 (rare sugar syrup intake group, RS, 3 rats) had 10% commercially available Rare Sugar Sweet added to their drinking water, and Group 4 (silicon and rare sugar syrup intake group, SIRS, 4 rats) had 10% silicon and 10% commercially available Rare Sugar Sweet added to their drinking water. Each rat had unrestricted access to these drinking water sources throughout the housing period.

The silicon used was a water-soluble silicon concentrate solution from "umo Concentrated Solution" (commercial product). This solution contains 8,370 ppm of silicon in 100 ml. Additionally, the ingredients of the commercially available "Rare Sugar Sweet" consist of approximately 44% glucose D-glucose, 31% fructose D-fructose, 19% rare sugars, and approximately 4% oligosaccharides. The breakdown of rare sugars includes about 6% D-psicose, approximately 10% each of D-mannose and D-sorbose, and about 3% each of D-tagatose and D-allose.

Fig.4 Tension Test and Jigs of Bone

In addition to the drinking water, a common feed, "Lab MR Stock" (Japan Agriculture and Industry Co., Ltd.) powder, was provided to each rat at a rate of 30g every other day, with the aim of simplifying the process and aiming for a daily intake of 15g per rat.

After 50 days of housing, blood vessels and bones were extracted from each rat. The blood vessels were taken from the abdominal aorta, and the bones were extracted as follows: from the upper limbs, the humerus; from the lower limbs, the femur, tibia, and fibula. However, during the tensile test, only the tibia was measured, as the fibula was removed.

Each specimen was measured for physical properties such as thickness (t), width (d), and length (distance between chucks, L0) for blood vessels. For bone specimens, the section modulus (Z) was determined based on the cross-sectional shape decided by the measurer, and the required dimensions such as thickness (t), diameter (d), base (b), and height (h) were measured. The cross-sectional shapes of the bones were as follows: triangular for the humerus, rectangular (plate-like) for the ulna, circular for the radius, cylindrical for the femur, and triangular and cylindrical for the tibia, with half of each. The section modulus (Z) for these cross-sectional shapes was calculated using values provided in literature [11]. Additionally, for triangular cross-sections, the section modulus was halved to account for movement of the specimen during measurement, combining the section modulus at the base and at the vertex.

3.2 Experimental Method 

A displacement-controlled tensile testing machine, specifically a small tabletop tester (Little Sencer, model LSC-1/300) with a screw-driven uniaxial testing machine (JT Tohshin Co., Ltd.), was used. The sensor used was a load cell, with a 50[N] load cell for testing blood vessels and a 500[N] load cell for testing bones. The tensile speed was set at 10[mm/min] for both blood vessels and bones, and parameters such as maximum testing force and overload were appropriately configured based on the load cell.

The tensile testing fixture employed parallel-type chucks, and for bones, a fixture specifically designed for bones was used. As shown in Fig.4, a dedicated fixture attached perpendicularly to the lower chuck had a 10[mm] gap in the center and holes with a diameter of 8[mm] at both ends. The bone specimen was placed between these holes and the gap. The upper chuck was equipped with a 2[mm]-thick U-shaped fixture that surrounded the center of the specimen, and the specimen was pulled from the bottom to the top by pulling the upper fixture upwards. For blood vessels, a carbon plate (0.3mm thick) with the test specimen glued on it was attached to the upper and lower chucks.

During each test cycle, parameters such as the testing force (Load) and displacement (Stroke) were recorded, with up to 60,000 data points saved in CSV format per file. The measurement sampling frequency was set at 50[Hz].

Fig. 5 A tipical example of stress-strain curve,

(a)   blood vessel, (b) Ulna, Radius

4. Results and discussion

4.1 Stress-strain diagram

For the specimens described in 3.1 and tested using the methods outlined in 3.2, stress-strain curves were generated using the measurement data files as described in section 2. Specifically, for blood vessels, stress-strain curves were created using the measured load (P) and the length (ℓ) of the specimen after deformation, according to equations (1) and (2) in section 2.1. For bones, stress-strain curves were created using the measured load (P) and the calculated stress (σ) from equation (3) and the measured deflection (λ), which can be used to calculate shear strain (γ) using equation (5) in section 2.2.

An example of a stress-strain curve for blood vessels is shown in Fig.5(a), and an example for the ulna and radius bones is shown in Fig.5(b). The horizontal axis represents strain (ε) or shear strain (γ), while the vertical axis represents stress (σ) in [N/mm2]. The point "o" in the figures represents the maximum strain εmax or γmax and the maximum stress σmax at the time of fracture. Due to limitations in the precision of strain measurement for blood vessels, the values appear discrete, but they demonstrate the typical shape of a stress-strain curve.

From the stress-strain curves, parameters such as the maximum stress σmax [N/mm2] at fracture and strain (εmax) were extracted. These parameters, along with measured values of diameter (d) [mm], cross-sectional area (Z) [mm3], and others, were used to evaluate the presence or absence of significant differences between each group and the control group.

The mean and standard deviation (Mean ± S.D.) of each parameter for the Control (CT), Silicon Intake (SI), Rare Sugar Syrup Intake (RS), and Silicon and Rare Sugar Syrup Intake (SI+RS) groups, as well as the sample size, and the p-values obtained from statistical tests comparing each group with the control group, are summarised in Fig.6-12. A smaller p-value indicates a significant difference between groups.

Fig. 6 Compare strain to the max stress of blood vessels.

4.2 Stress-strain analysis of blood vessels

In the analysis of blood vessels, as shown in Fig.6, the strain (stretch) εmax at maximum stress exhibited significant differences. A higher strain (stretch) εmax at maximum stress indicates better elasticity and softer blood vessels.

Compared to the Control (CT) group, significant differences (P = 0.0391, P = 0.0170, P = 0.0044) were observed in the strain (stretch) εmax at maximum stress for the Silicon Intake (SI) group, Rare Sugar Syrup Intake (RS) group, and Silicon and Rare Sugar Syrup Intake (SI+RS) group, respectively. This implies that the intake of silicon, rare sugar syrup, or both resulted in significantly greater stretching of the blood vessels before fracture compared to the group consuming only tap water. Therefore, it is inferred that the intake of silicon and rare sugar syrup may suppress arterial hardening.

4.3Bone stress-strain analysis
             In the analysis of bones, significant differences were observed in the fracture stress (σmax) of the radius bone (ulna) or the radius bone (ulna) and the radius bone (ulna) at the time of fracture. Since the radius bone (ulna) and the radius bone (ulna) were tested together without separation, the stress-strain characteristics were analyzed by combining the section moduli (Z) of each radius bone (ulna) and radius bone (ulna).

Firstly, as shown in Fig.7, the fracture stress (σmax) of the radius bone (ulna) was significantly greater in the RS group and SI+RS group than in the CT group (P=0.0326, P<10-4), but there was no significant difference in the SI group (P=0.1752). A higher fracture stress (σmax) implies greater strength of the radius bone (ulna). Therefore, the Rare Sugar Syrup Intake group or the Silicon and Rare Sugar Syrup Intake group indicates stronger radius bone (ulna) compared to the group consuming only tap water.

To determine which bone, the radius or ulna, influences the fracture stress (σmax), the fracture stress (σmax) for each section modulus (Z) of the radius and ulna was investigated. For the fracture stress (σmax) obtained only from the section modulus (Z) of the radius bone (ulna), there was no significant difference between the SI group, RS group, SI+RS group, and CT group. Next, for the fracture stress (σmax) obtained only from the section modulus (Z) of the ulna, as shown in Fig.8, the SI group exhibited significantly greater fracture stress (σmax) than the CT group.

Fig. 7 Compare rupture stress of Ulna, Radius.

Fig. 8 Compare rupture stress of Radius.

Fig. 9 Compare the diameter of the Radius.

Fig. 10 Compare rupture stress of Humerus.

 Fig. 11 Compare rupture stress of Femur.

 Fig. 12 Compare rupture stress of Tibia.

The rupture stress σmax at the time of tibia fracture was significantly greater in the RS group and the SI+RS group compared to the CT group (P=0.0039, P=0.0076, P=0.0095, respectively). This means that the groups that ingested silicon or rare sugar syrup had significantly stronger tibiae compared to the group drinking only tap water. Interestingly, as shown in Fig. 9, the diameter of the radius bone in the SI group, RS group, and SI+RS group was significantly smaller than that of the CT group (P < 10-6, P < 10-5, P=0.0037, respectively).

From these results, it can be inferred that the tibia bears a significantly greater rupture stress σmax at the time of fracture.

Influences have been observed despite the significantly smaller diameter of the radius bone, indicating its strength. However, determining only the fracture stress σmax by simply adding up the respective sectional moduli Z of the radius and ulna bones is insufficient. It necessitates the consideration of complex bone structures and mechanisms, bending moments, asymmetric bending, and further analysis of combined stress-strain characteristics.

Moreover, the fracture stress σmax at the time of ulna bone fracture showed significant differences between the CT group and the RS group, as well as between the CT group and the SI+RS group (P=0.0363, P=0.0135), but there was only a slight difference in significance between the CT group and the SI group (P=0.0956).

The fracture stress σmax at the time of femur fracture, as shown in Fig.11, did not reveal any significant differences between the CT group and others. Furthermore, the fracture stress σmax at the time of tibia fracture, as shown in Fig.12, similarly did not show any significant differences between the CT group and others.

From these results, it is indicated that the strain (extension) of the blood vessels at maximum stress in the silicon intake group, rare sugar syrup intake group, and silicon rare sugar syrup intake group is significantly greater than in the control group. This implies that by ingesting silicon, rare sugar syrup, or both, blood vessels extend significantly until fracture compared to the group drinking only tap water. In other words, it was considered that arterial sclerosis was inhibited by silicon intake and rare sugar syrup intake. Additionally, the fracture stress of the radius bone in the silicon intake group was significantly greater than in the control group, and the fracture stress of the radius ulna bones in rats that drank rare sugar syrup was also significantly greater than in the control group. This suggests that the radius ulna bones became stronger due to silicon intake and rare sugar syrup intake.

Significant differences in fracture stress were not found in relatively thick bones such as the femur and humerus but were observed in relatively thin bones such as the radius ulna bones, and notably in pulsating blood vessels. It is speculated that silicon intake and rare sugar syrup intake are absorbed by blood vessels and thin bones that are regularly moved in daily life, leading to the earlier manifestation of their effects. It is presumed that with longer intake periods, effects will also become apparent in thicker bones such as the humerus and femur.

5.Conclusion

In this study, tensile tests were conducted on the bones and blood vessels of 13 rats by ingesting silicon and rare sugar, and the stress-strain characteristics were analyzed to evaluate the mechanical strength of bones and blood vessels. As a result, it was found that the strain (extension) of the blood vessels at maximum stress in the silicon intake group, rare sugar syrup intake group, and silicon rare sugar syrup intake group was significantly larger compared to the control group. In other words, ingesting silicon, rare sugar syrup, or both resulted in significantly greater elongation of blood vessels until fracture compared to the group drinking only tap water, indicating that arterial sclerosis was suppressed by silicon intake and rare sugar syrup intake.

Furthermore, the fracture stress of the radius bones in the silicon intake group was significantly greater than that of the control group, and the fracture stress of the radius ulna bones in rats that drank rare sugar syrup was also significantly greater than that of the control group. In other words, it was shown that the radius ulna bones became stronger due to silicon intake and rare sugar syrup intake. The synergistic effect of inhibiting arterial sclerosis and strengthening bones is expected not only from silicon intake but also from rare sugar intake.

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Note: This paper is translated from the following URL. The content is provided for reference on the scientific research of the raw material only. Whether APA raw materials are used or not, we hope this research will help increase understanding and awareness of body minerals.