Computer-Assisted Modeling and Design of Compression Garments with Graded Unit Compression


 This article presents a useful algorithm for designing compression products with intended and graded unit pressure along the part of the body covered with the mentioned garments. The algorithm was developed using Laplace's law and a designated experimental function describing the relationship between strength and relative elongation of knitted fabric, and the results of 3D scanning of different body parts. On this basis, two examples of products in the form of a leg sleeve and arm sleeve were designed for the treatment of lymphoedema in compression classes II and III. The presented compression product design procedure facilitates the process of designing compression garments and eliminates some errors related to this procedure.


Introduction
Custom-made, personalized products are among the most useful compression garments used in therapies supporting the external healing process. Such products should be designed using Laplace's law [1][2][3][4]. Designing products based on a fi xed percentage reduction of basic construction dimensions, regardless of the size of the patient's body circumferences, which is often 10% for the fi rst set of compression garments and 15% or 20% for all subsequent products [5][6][7][8][9], usually leads to values of unit pressure that are uncontrolled and noncompliant with the recommendations. Depending on the type of therapy, the unit pressure can have a constant value along the covered part of the body, in the case of burn wounds, postoperative liposuction wounds, and hernias. It can also have a graded value, as in the treatment of lymphoedema and anti-varicose edema. The value of the unit pressure in such cases decreases gradually toward the heart. An important factor in the design procedure is the replacement of manual body part measuring with a 3D scanning technique. Such proceeding shortens the measurement time and eliminates some reasons for the scatter of measurement results associated with the manual method of dimensioning the human body [10][11][12][13][14][15][16][17]. Another important element in the procedure of modeling and designing compression products is the development of a compression knitted fabric assessment method, which should correspond to the assessment of the compression garment in terms of the required pressure value. Therefore, it is important to include the mechanical characteristics of knitted fabric in the form of the relationship of the force F with the relative elongation ε, and various relations between the parameters F and ε -depending on the extent of stretching [18]. In articles [2,19,20], for the purposes of compression garments modeling, a constant value of knitted fabric tensile stiffness is assumed, regardless of the value of relative elongation. However, in the case of designing a product, the real relations between the values of force F and relative elongation ε should be assumed which, depending on the range of relative elongation of compression knitwear, assume different values, as evidenced by nonlinear relationships F = f (ε) [18,21,22]. The compression garments design procedure should also take into account the relationships between the tensile stiffness of the fabric and the size of the body circumferences and the presence of the seam [19], as well as the impact of the body's local susceptibility to changes in the unit pressure [23]. However, in the case of standardized products, an important factor is the selection of tensile stiffness for a given compression class and size, as well as dimensional tolerance of the size range [24].
The research presented in this work aims to develop an algorithm used for the design of a compression product that will allow for determining the free dimensions of the product with the intended and graded value of the unit pressure along the part of the body covered with the compression garment.

Basics of modeling and design of compression products
The basic law used in the modeling and design of compression products is Laplace's law. Depending on the type of therapy, the intended value of unit pressure P i (hPa) can be constant or graded as (1) The second important equation in the design procedure of compression products describes the mechanical characteristics of the knitted fabric in the form of the relationship of force F/cm and relative elongation ε [18] as (2) where a 1 , b 1 , and c 1 are regression coeffi cients and ε is the relative elongation of the knitted fabric, which for the modeling purposes is described by the following equation where G 0i is the i-th circumference of the compression product in the relaxed state. Using Eqs (1)-(3) and their solutions with respect to G 0i , we obtain the required value of G 0i circumferences of the compression product for the declared values of unit pressure P i and G i (cm) body circumferences ( Figure 1).

The algorithm of designing compression garments with graded compression
The algorithm of designing compression garments with graded unit compression along the covered body part, presented in Figure 2, was developed using (1) Laplace's law and (2) the generalized form of the function of the mechanical characteristics of the compression knitted fabric in the form of the relation between force F and the relative elongation ε [18]. The pressure gradient along the limb of the human body complies with the guidelines of the subject standards [25][26][27].
In the fi rst part of the algorithm, the form of the function of pressure gradient on the basis of quadratic interpolation is determined as The output data of this part of the algorithm based on a model leg ( Figure 3) are the following parameters: P śr is the middle value of the unit pressure for a given compression class; Y G is the maximum distance of the circumference from the base; k G is the set factor of unit pressure reduction for the circumference at point G (Y G ); y C is circumference position coeffi cient C (y C , …, Y G );  accuracy factor of the elongation calculations Δε, and maximum fabric elongation accuracy factor of the elongation calculations . The coeffi cients accuracy factor of the elongation calculations . and ε, and maximum . stand for the range within which we search for the relative elongation value ε. At the beginning this range is <0, the range within which we search for the relative elongation > ( the range within which we search for the relative elongation can be equal to 1 or more) and should correspond to the relative useful elongation of the knitted fabric. In the subsequent steps of the calculations by bisection method, we narrow the range by changing of the calculations by bisection method, we narrow the range or of the calculations by bisection method, we narrow the range . As we search for ɛ with accuracy to a specifi ed delta, we divide this range until its size is smaller than the delta. Finally, we choose the value of the relative elongation ε in the middle of the range. In the fi rst part of the algorithm, the values of circumferential forces F i are determined from Laplace's law for the subsequent G i circumferences, and on their basis with the use of fabric characteristic F = f(ε) the values of relative elongations ε are determined. Knowing the values of the relative elongations makes it possible to determine the values of fabric circumferences G 0i in the relaxed state. The next step in the calculations is to determine the coordinates of the free dimensions of the model cross sections, which together with the position coordinates of the subsequent circumferences allows to draw the pattern. The coordinates of the template points in the cutter format Y i , ' 0i G and Yi, " 0i G with the program of its control allow automatic template cut, including stitching stocks.

Measuring body parts using 3D scanning techniques
For measurements of the body part (G i circumferences) and their position along the body (Y i ), a spatial structured light scanner was used ( Figure 5) [23].
The measuring head of the scanner rotates around the scanned object. The scanner confi guration is as follows: -Two 1.3 MPix monochrome cameras; k C is set unit pressure reduction factor for the circumference at point C (y C , …, Y G ).
The P i unit pressure values are described in the function determined from the range of the maximum and minimum pressure values in accordance with the guidelines of PN-ENV 12718: 2002 Medical compression hosiery. For the purposes of modeling, it was assumed that the pressure value in the ankle area is 100%, which then decreases degressively toward the maximum calf circumference (point C) to 70% of the initial value of P śr , and for the circumference at point G to 40% (0.4, …, P śr ).
Similar pressure values were adopted for the arm, that is, 100% P śr for the wrist circumference, 70% for the maximum forearm circumference, and 40% of the P śr value for the arm. Changes in the unit pressure along the length of the leg and arm are shown in Figure 4. After adopting pressure reduction factors k, k max = 1, the developed algorithm also allows calculating free circumferences of the knitted fabric for therapies requiring a constant value of unit pressure along the covered body part.
In the second part of the algorithm, the free dimensions of the compression knitted fabric are determined. This part of the algorithm is consistent with the calculation procedure presented by Kowalski et al. [22,23]. The input parameters for this part of the algorithm are body circumferences G 1 , distance between the circumferences and the base Y i , and intended values of unit pressure P i , determined as the quadratic function Regression coeffi cients of the relationship between force and relative elongation of the knitted fabric are a 1 , b 1 , and c 1,  in Figures 6A and 6B, and its relationship characteristics of strength and elongation are shown in Figure 7.
The mechanical characteristics of the knitted fabric, namely, the relationship between strength and relative elongation in relation to the width of the knitted fabric strip s = 1 cm, are described as whose detailed method of determination and justifi cation based on the rheological model are presented by Kowalski et al. [18]. The method of determining the mechanical characteristics of knitted fabric for the purpose of designing compression products is based on the same principles of determining the force F in function of the relative elongation of the fabric e in terms of the number of stretching and annealing cycles and for various stretching subranges, as in the method of testing compression products [25].
This eliminates the causes of errors in the design of compression products with the intended unit pressure value, as it takes into account the differences in the relationship between the values of F and ε, depending on the extent of stretching and rheological properties of the tested compression knitted fabrics.

Designing a template for a leg sleeve with compression class III and arm sleeve with compression class II
The design procedure for compression products with the intended graded value of unit pressure along the length of the product was carried out on the basis of the developed generalized algorithm for determining the template coordinates and model-experimental research. As mentioned above, the project concerns the development of a male leg sleeve and arm sleeve for a woman, both used in the treatment of lymphoedema. The treatment of lymphoedema with appropriately selected -1,280 x 1,024 DLP projector; -FlexScan3D software version 3.1.
The assessment of the scanning accuracy was based on the VDI/VDE 2634 standard, part 2 "Optical 3D measuring systems -Optical systems based on area scanning." Scans of the leg circumferences were made at every 2 cm along the length of the leg, starting from the line above the ankle.

Research material
Sample products in the form of a leg sleeve and arm sleeve were made of knitted fabric with elastomeric threads, whose construction description and basic parameters are presented  The drawn templates are illustrated in Figures 8 and 9, and the views of the designed and manufactured products are shown in Figures 10 and 11. compression garments should, according to the literature data [28], adhere to the following principles: 1. Compression garments should be custom-made based on measurements of the patient's body in the fi nal stage of the fi rst therapeutic phase, when the limb is free from swelling or the edema is stable; 2. While waiting for the device, the patient must continue to use multilayer bandaging; 3. The greater the lymphatic insuffi ciency, the stronger the pressure that should be applied; 4. For the upper limbs, products in compression class I or II are usually suffi cient; 5. On the lower limbs, compression classes III and IV are used most often;

Experimental verifi cation
Based on the calculation data presented in Table 1, the values of the knitted fabric's relative elongation were determined for three measuring points B, C, and G (Figure 3), in accordance with Eq. (3). For the determined values of relative elongation ε, the force F in the knitted fabric was measured ( Figure 12). For this purpose, samples of knitted fabric from which the stockings are made were taken -for points B, C, and G, according to the standard [25]. Then the samples were subjected to the process of stressing and annealing to the determined values of relative elongations ε. For each value of relative elongation, tests were carried out for fi ve 50-mm wide samples in the form of a 100-mm free loop between the clamps of the tensile machine.
The tests were carried out at a speed of 200 mm/min on the Instron tensile machine, with the use of needles stabilizing the width of the fabric. The value of force F was taken from six hysteresis loops after the end of the stressing phase [18]. According to Laplace's law (1), the value of unit pressure P in hPa was calculated for three values of body circumferences at points B, C, and G ( Figure 13).
Experimental verifi cation of the unit pressure for selected body circumferences confi rmed the correctness of the adopted procedure of designing and manufacturing products with the graded unit pressure. The maximum percentage difference between the intended and experimentally determined values was 7.5% for the circumference at point G (thigh circumference). The differences can be attributed to the sample manufacturing tolerance, which is ±0.2 cm (manual cut and joining by seam) and the difference between the values of the regression function of the mechanical characteristic of the compression knitted fabric in the form of a relationship of strength and relative elongation (Figure 7), and the values determined for analyzed points determined by the value of relative elongation.
It is widely known that there are diffi culties in putting on compression garments in higher compression classes (II-IV) due to the high values of circumferential forces. This problem also appears even for the class I compression for large circumference values, for example, the body trunk in the case of treatment of post-burn scars. In such cases, one of the ways of solving the problem is by putting on two products, each designed with a two-times smaller value of the unit pressure compared with the intended value [8,9].

Conclusions
1. The presented procedure of designing a compression garment with a graded pressure using a computer program and 3D body scanning as well as the procedures for determining the mechanical characteristics of knitted fabric in the form of the function of force F and relative elongation of the knitted fabric ε F = f(ε) improve and eliminate some errors in the design of compression garments.
2. Experimental verifi cation of unit pressures for selected body circumferences confi rmed the correctness of the adopted design procedure. The existing differences between the intended values of the unit pressure and the values from the measurement should be attributed to the band tolerance of ±0.2 cm (manual cut and joining by seams) and the difference between the values of the strength of the regression function of the mechanical characteristics of the compression knit in the form of a relationship of strength and relative elongation ( Figure  7) and the values determined for the analyzed points determined by the value of relative elongation.