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

2.1 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

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

where a₁, b₁, and c₁ are regression coefficients 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 Eq. (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).

Figure 1

Model of a body part with different values of G_i circumferences, where G₁, G₂, ..., G_n are the subsequent body part circumferences, Y₁, Y₂, ..., Y_n are the subsequent distances between the circumferences and the base, F₁, F₂, ..., F_n are the circumferential forces in compression fabric strip of width s for subsequent circumferences, and ΔY_i is the distance between the subsequent circumferences.

2.2 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].

Figure 2

The algorithm for establishing free dimensions of a template for compression garments.

In the first 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 coefficient C (y_C, …, Y_G);

• k_C is set unit pressure reduction factor for the circumference at point C (y_C, …, Y_G).

Figure 3

Illustrative model of a leg with characteristic dimensions.

The Pi 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.

Figure 4

Changes in unit pressure along the leg for class III (series 1) and the hand for class II (series 2).

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 G₁, distance between the circumferences and the base Y_i, and intended values of unit pressure P_i, determined as the quadratic function

Regression coefficients of the relationship between force and relative elongation of the knitted fabric are a₁, b₁, and c₁, accuracy factor of the elongation calculations Δε, and maximum fabric elongation ε_max. The coefficients ε_L. and ε_R. stand for the range within which we search for the relative elongation value ε. At the beginning this range is < 0, ε_max > (ε_max 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 or ε_L or ε_R. As we search for ε with accuracy to a specified 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 first 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, G0i′ and Yi, G0i″ with the program of its control allow automatic template cut, including stitching stocks.

5.1 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 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 final stage of the first 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 insufficiency, the stronger the pressure that should be applied;

4. For the upper limbs, products in compression class I or II are usually sufficient;

5. On the lower limbs, compression classes III and IV are used most often;

6. Knitted fabric from which the garments are made should have relatively high elongation stiffness;

7. Due to skin protection, the material should not cause indentations or rolling;

8. Garments should be worn only during the day;

9. The patient should order two products to allow their daily, uninterrupted use.

The determined values of the coordinates of the G0i′ and G0i″ templates together with the coordinates of their position along the length of the limb are presented in Tables 1 and 2. The free dimensions of the circumferences also include stitch reserves. 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.

Figure 8

Leg sleeve template for lymphoedema treatment together with template coordinates Yi, G0i′ and G0i″ (cm).

Figure 9

Arm sleeve template for lymphoedema treatment together with template coordinates Yi, G0i′ and G0i″ (cm).

Figure 10

Leg sleeve used in lymphoedema treatment.

Figure 11

Arm sleeve used in lymphoedema treatment.

6.1 Experimental verification

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 five 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).

Figure 12

Test results for forces in the knitted fabric for three measuring points B, C, and G for leg (Figure 3). F_calc – intended values of peripheral force, F_exp – measured values of force.

Figure 13

Unit pressure values for three measuring points B, C, and G for the leg (Figure 3). P_calc – intended pressure value, P_exp – determined pressure value based on Laplace's law and measured force values.

Experimental verification of the unit pressure for selected body circumferences confirmed 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 difficulties 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].