Introduction: Ventral hernia repair, a challenging procedure. We consider rubber bands, evaluating the strength of bands of differing length and thickness to see how changes in these parameters affect the elastic materials to try to mimic how abdominal muscle get affected by tensile forces.
Methods: Four sets of six rubber bands were evaluated: A) thick, medium length, B) thick, longest length, C) thin, medium length and D) thin, short length. Thickness and length of rubber bands were measured using a Vernier caliper. Each rubber band was attached to a string attached to a stabilized paper clip. Increasing weight was applied until each rubber band broke. The maximum weight was converted to maximum tensile strength by dividing the weight in Newton's by the cross sectional error. Effects of width and length upon maximal tensile strength were analyzed by statistical two pair analysis and log gamma regression.
Results: Log Gamma regression revealed an interaction between thickness and length; the coefficients for an increase in width by 1 mm (-0.63) and length by 1 cm (-0.53), which decreased maximum strength were countered by a strengthening from a combined increase width by 1 mm and length by 1 cm (0.13). The initial observations showed that a thicker elastic material (red rubber band) holds more weight than a thinner one (yellow) despite similar length (P<0.0001).
Discussion: The effects of increasing muscle strength and the circumference of the abdominal wall cannot be considered in isolation. The muscle component of the ventral hernia is one of many variables affecting the abdominal wall. In this paper we focus on that issue understanding the complexity of the pathology. Our goal is to show how stress force act on any material and assuming that they do the same on the human body. We can hypostasize the notion that hernia is secondary to shear forces and because of this repair of the entire abdominal wall therefore is the only solution.
Ventral Hernia Repair (VHR) has been a challenging surgery during years. Matters moved to mobilizing muscle and closing the abdominal wall. Component Separation Repair (CSR), which required dissection of the fascia of the rectus muscle and closure of the midline linea alba [1]. The goal of ventral hernia repair is to restore abdominal muscle strength and abdominal wall function [2,3]. The muscle component of the ventral hernia is one of many variables affecting the abdominal wall to contribute to ventral hernia. In this paper we focus on that issue understanding the complexity of the pathology. We hypothesized that evaluating the maximal stress on a set of artificial tensile structures, rubber bands, might open a different view on the effects of daily forces affecting the strength of varied abdominal walls.
Four sets of six rubber bands were evaluated (Table 1).
Rubber Band A (Red) - thick and medium length | ||||||
Dimensions= 0.1 x 0.35 x 4.2 | Cross sectional area = 0.035 cm^{2} | |||||
Mass hung at failure (kg) | Force (N) | Stress (N/cm^{2}) | Stress (lbs/in^{2}) | |||
Trial 1 | 3.75 | 36.82 | 1051.91 | 1525.15 | ||
Trial 2 | 3.84 | 37.69 | 1076.86 | 1561.32 | ||
Trial 3 | 3.72 | 36.5 | 1042.94 | 1512.15 | ||
Trial 4 | 3.32 | 32.52 | 929.15 | 1347.15 | ||
Trial 5 | 3.72 | 36.44 | 1041.26 | 1509.71 | ||
Trial 6 | 2.24 | 21.97 | 627.84 | 910.29 | ||
Mean | 3.43 | 33.66 | 961.66 | 1394.3 | ||
STD | 0.61 | 6.00 | 171.38 | 248.48 |
Rubber Band B (White) - thick and longest length | ||||
Dimensions = 0.l x 0.35 x 7 cm | Cross sectional area = 0.035 cm^{2} | |||
Mass hung at failure (kg) | Force (N) | Stress (N/cm^{2}) | Stress (lbs/in^{2}) | |
Trial 1 | 2.72 | 26.66 | 761.82 | 1104.55 |
Trial 2 | 2.36 | 23.17 | 662.03 | 959.87 |
Trial 3 | 2.26 | 22.13 | 632.32 | 916.8 |
Trial 4 | 3.23 | 31.65 | 904.2 | 1310.99 |
Trial 5 | 3.12 | 30.56 | 873.09 | 1265.88 |
Trial 6 | 2.95 | 28.94 | 826.84 | 1198.83 |
Mean | 2.77 | 27.19 | 776.72 | 1126.15 |
STD | 0.4 | 3.91 | 111.6 | 161.81 |
Rubber Band C (Yellow) - thin and medium length | ||||
Dimensions = 0.1 x 0.1 x 4.7 (cm) | Cross sectional area = 0.01 cm^{2} | |||
Mass hung at failure (kg) | Force (N) | Stress (N/cm^{2}) | Stress (lbs/in^{2}) | |
Trial 1 | 0.88 | 8.66 | 866.22 | 1255.92 |
Trial 2 | 0.74 | 7.29 | 728.88 | 1056.8 |
Trial 3 | 1.18 | 11.61 | 1160.52 | 1682.62 |
Trial 4 | 0.9 | 8.86 | 885.84 | 1284.37 |
Trial 5 | 0.98 | 9.64 | 964.32 | 1398.16 |
Trial 6 | 1.1 | 10.79 | 1079.1 | 1564.57 |
Mean | 0.97 | 9.47 | 947.48 | 1373.74 |
STD | 0.16 | 1.56 | 155.68 | 225.72 |
Rubber Band D (Blue) - thin and shortest length | ||||
Dimensions = 0.1 x 0.1 x 2.0 cm | Cross sectional area = 0.01 cm^{2} | |||
Mass hung at failure (kg) | Force (N) | Stress (N/cm^{2}) | Stress (lbs/in^{2}) | |
Trial 1 | 2.65 | 26 | 742.76 | 1076.91 |
Trial 2 | 3.15 | 30.9 | 882.9 | 1280.1 |
Trial 3 | 2.45 | 24.03 | 686.7 | 995.63 |
Trial 4 | 3.05 | 29.92 | 854.87 | 1239.46 |
Trial 5 | 3.25 | 31.88 | 910.93 | 1320.74 |
Trial 6 | 2.85 | 27.96 | 798.81 | 1158.19 |
Mean | 2.9 | 28.45 | 812.83 | 1178.51 |
STD | 0.31 | 3.02 | 86.39 | 125.26 |
In the first comparison, we matched rubber band based on their thickness of 0.1x0.35 cm: A) short (4.2 cm), high strength rubber bands (red bands) (modeled the young person with much muscle strength and flexibility, B) long (7 cm), high strength rubber bands of longer length (white bands) modeled abdominal walls with fully stretched muscle, but with similar strength, such as occurs after pregnancy or with obesity. In the second comparison, we match the length (4.2 cm) and change the thickness: A) thick (0.1x0.35 cm), rubber bands (red bands) as above and C) thin (0.1x0.1 cm), rubber bands (yellow bands) modeled elderly or protein deficit patients, obese patient who had experienced an operation. We then use for final comparison a D) thin and short band (0.1x0.1x2 cm).
Thickness, width and length of the bands were measured using a vernier caliper. The four bands were then stressed with progressively increasing weights at 20 g increments. Weight at the time of failure was recorded for each of six trials of each band type (Table 1).
The Tensile strength was measured in force per cross-sectional area. All the data is reported and compared in table 1. The units of force were derived by multiplying mass (kg) by the acceleration of gravity (9.81 m/sec2) per Newton's second law of motion (F=m x a). This results in a force unit of Newton. The tensile strength was measured by taking the weight (Newton) and dividing it by the cross-sectional area (cm^{2}). Tension and shear forces were summarized to create the condition to apply the log regression (Tables 2 and 3).
Force and Stress Analysis | ||||
Dimensions = 0.1 x 0.1 x 2.0 cm | Cross sectional area = 0.01 cm^{2} | |||
Mass hung at failure (kg) | Force (N) | Stress (N/cm^{2}) | Stress (lbs/in^{2}) | |
Trial 1 | 2.65 | 26 | 2599.65 | 3769.19 |
Trial 2 | 3.15 | 30.9 | 3090.15 | 4480.36 |
Trial 3 | 2.45 | 24.03 | 2403.45 | 3484.72 |
Trial 4 | 3.05 | 29.92 | 2992.05 | 4338.12 |
Trial 5 | 3.25 | 31.88 | 3188.25 | 4622.59 |
Trial 6 | 2.85 | 27.96 | 2795.85 | 4053.66 |
Mean | 2.9 | 28.45 | 2844.9 | 4124.77 |
STD | 0.31 | 3.02 | 302.36 | 438.39 |
Table 2: Force and stress analysis.
Coefficient | Exp(est) | Estimate | SE | T | P | |
Intercept | 12078.5 | 9.39918 | 0.1779 | 52.834 | < 2e-16 | *** |
Width↑1 mm | 0.53181 | -0.63147 | 0.08546 | -7.389 | 3.89E-07 | *** |
Length↑1 cm | 0.58299 | -0.53959 | 0.04676 | -11.54 | 2.70E-10 | *** |
Width↑1 mm & Length ↑1 cm | 1.14153 | 0.13237 | 0.01789 | 7.398 | 3.82E-07 | *** |
Table 3: Results of log gamma regression.
Experimental procedures: Cross sectional area was the product of the width and thickness in centimeters. Units of force were the product of the maximum mass (kg) and the acceleration of gravity (9.81 m/sec2) per Newton's second law of motion (F=m x a), measured in Newton's. Tensile strength was the number of Newton's divided by the cross-sectional area (cm^{2}).
Statistical analysis: T-test for two independents (non-pooled standard error) was used to compare the bands two at the time. All statistical measures included 6 data points for each band. Log gamma regression was used to evaluate the effect of changes in width and length upon maximum tensile strength.
Rubber band measurements, mass hung at failure measurements and calculated maximal tensile strength measurements are recorded in table 1. We notice that the thicker and short rubber band was the strongest (red), the longest rubber band was the weakest in regards to the tensile stress (Newton/cm2). The Red and White bands had a significant difference at alpha = 0.10 since the p value was 0.055. The Yellow clearly held much less weight and was significantly different than the other three P = 0.000. The yellow band held much less than the other two the mean mass held by the red was 3.43 kg and the yellow was 0.97 kg. Failure is most often occurred at either the top or the bottom of the band. One of the challenges was to load the masses in a careful manner without adding additional forces due to dropping the weights abruptly onto the hook that held the weights. By repeating the same experiment with thinner cross-sectional area of 0.01 cm^{2} between Yellow and Blue band we confirm the data that when the thickness is the same the factor that contribute to hold more weight is shorter length in this case the blue (2.0 cm) vs the yellow (4.7 cm).
All rubber bands broke in a similar fashion, nearly always at the top or the bottom of the rubber band. Results of log gamma regression are recorded in tables 2 and 3, with each of the coefficients being highly statistically significant (P<0.0001 for each assessment). No violations of generalized linear methods were seen. No important outliers were observed.
The regression equation estimated by log gamma regression is: Maximum strength = log (12078.47 - 0.63 x Width (mm) - 0.53 x Length (cm) + 0.13 x Width x Length). Note that the relationship is logarithmic. An increase in width of 1 mm without a change in length is associated with a maximum tensile strength that is 53% of the thinner rubber band. An increase in length of 1 cm without a change in width is associated with a maximal tensile strength that is 58% of the shorter rubber band. An interaction is present, such that each 1 cm longer and 1 mm wider rubber band is associated with a maximal tensile strength that is 14% greater than the thinner, shorter rubber band, apart from the differences imparted from the changes in length and width themselves.
The effect of changes in length and width thus depend upon the length and the width. Examples best illustrate this. The result of decreasing a 3 mm wide 5 cm long band to a 1 mm wide 5 cm long band is: (1-3) x -0.63 + (1 x 5-2 x 5) x 0.13 =-0.96; a 1 mm wide 5 cm band has exp (-0.06) = 94% of the maximum stress of a 3 mm wide 5 cm long band. The result of increasing a 3 mm wide 5 cm long band to a 3 mm wide 6 cm long band is: (6-5) x -0.53 + (3 x 6 - 3 x 5) x 0.13 = -0.14; a 3 mm wide 6 cm long band has exp (-0.14) = 87% of the maximum stress of a 3 mm wide 5 long cm band. The result of changing a 3 mm wide 5 cm long band to a 1 mm wide 6 cm long band is: (1-3) x -0.63 + (6-5) x -0.53 + (1 x 6 - 3 x 5) x 0.13 = -0.46; a 1 mm wide 6 cm long band has exp (-0.46) = 63% of the maximum stress of a 3 mm wide 5 long cm band.
In this experiment, we tried to focus on material and showed the breaking point of it. We are very aware that muscle is not a material and cannot be directly compare to it. Our goal is to show how stress force act on any material and assuming that they do the same on the human body. Looking at our result we can hypostasize the notion that hernia is secondary to shear forces affecting the muscle and fascia. Repair of the entire abdominal wall therefore is the only solution.
Citation: Frezza EE, Cogdill C, Wacthell M, Frezza EGP (2017) A Physic Tensile Forces Experiment to Possible Explain the Reason of Failing Ventral Hernia Repair. J Gastroenterol Hepatology Res 2: 007.
Copyright: © 2017 Eldo E Frezza, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.