Modeling the mechanics of a medical compression stocking through its components behavior: Part 1

Abstract

The goal of this article is to propose practical and scientific explanations about the mechanics of compression by the medical compression stocking (MCS) to the phlebologist and angiologist societies. The first part presents the principle of pressure generated by the MCS. We explain how the surface of MCS fabric is structured from the yarn scale and how each component of the yarn contributes to generate the desired compression. The second part is dedicated to the mechanical behavior modeling of the covered yarn, which is the main yarn component of the elastic knitted fabric of the MCS. The structure analysis shows that the properties of the inlaid yarns reflect significantly the global behavior of the fabric. Therefore, by characterizing the elastic properties of the inlaid yarn, it is possible to predict the mechanical behavior of the entire MCS fabric. We suggest a few approaches to model the covered elastic yarns used in different types of products. The third part describes an identification procedure aiming to calculate the unknown parameters of the mathematical models with the yarn elongation curves. The principle is to divide the general model into several sub-models in order to avoid considering simultaneously a great number of parameters in the identification procedure. The last part presents a set of identification results that compare measured values with simulated data. With a reliable model of the elastic yarns, an efficient strategy can be conducted to define the proper inlaid yarn (for the MCS construction), aiming to treat efficiently vein diseases at different stages according to medical prescription and the patient’s need.

Keywords

covered yarn inlaid knitted fabric constitutive law modeling medical compression stocking

Compression treatment is aimed to exert pressure on the limb with a calibrated pressure. The efficacy of the treatment is based on the control of the compression level corresponding to the dosage of the protocol.¹ The compression level is directly in relation with the pressure P. The usual physical definition of pressure is P = F/S, where P, F and S stand, respectively, for pressure, force and surface. Presently, in medical literature related to the medical compression stocking (MCS),² one can find the ‘medical formula’ P = F/R, where F is expressed in force per cm of material width. This formula is used in the French Norm³ to qualify MCSs. In fact, there are only two standards in the world: the first one in France NF G 30-102B3 and the second one in German RAL-GZG 387. These countries have shown initiative and innovation in compression therapy. In the 1990s, the world of medicine was trying to work out European standards to determine the level of pressure from the MCS; this project⁵ was debated for 15 years with no concrete outcome as of the year 2009. Few standards have been proposed to define this pressure and there has been little work on MCS modeling to understand the physical phenomena related to these standards for medical use.

Few designers present their research for the sake of industrial protection. We cite here the work of Issam Gaieden who developped a mechanical model based on finite element (FE) method in order to asses and visualize the pressure exerted by the MCS on the legs. His mechanical approach consists of analyzing stresses and strains within the MCS in the framework of a continuous orthotropic material. The development of computer codes and the identification of the constitutive law of knitting were the subject of several scientific publications.^7,8 Although Gaied's study is interesting, it is restricted to a linear model.

The first step of our analysis is to highlight that the difference between the physical and medical definitions of pressure is related only to the investigation scale. Instead of referring to the ‘filament model’ of pressure, the community of compression treatment considers the ‘band material model’ to describe the interface pressure generated by an extended textile material applied against a portion of the limb.⁶

The principle of MCS function is stretching an elastic sleeve, with C₁ as the initial circumference, to wrap up a solid cylindrical body with C₂ as circumference. The ratio of the sleeve elongation, $τ %$ , is defined by

τ % = \frac{(C_{2} - C_{1})}{C_{1}}

(1)

The amount of compression is proportional to the degree of elongation $τ %$ ( $τ % > 1$ ) to the material elasticity modulus $E_{tx}$ , and to S (the surface of contact between the sleeve and the cylindrical body), precisely:

P = F / S with F = E_{tx} \cdot τ %

(2)

Let F ′ be the resultant of the forces pulling the sleeve in contact with the leg skin, modeled by a cylinder in Figure 1, and let dS be a small surface element defined by dS = R · dθ · db.

Figure 1.

Interface pressure by the tension band.

If $\vec{N} = \cos θ \cdot \vec{x} + \sin θ \cdot \vec{y}$ denotes the unit normal to dS and P the pressure acting on dS, the sum of all contact forces exerted on the half cylinder is

\int_{S} d \vec{F} = \int_{0}^{b} \int_{0}^{π} \vec{P} \cdot d S = \int_{0}^{b} \int_{0}^{π} P \cdot \vec{N} \cdot R \cdot d θ \cdot db = 2 \cdot P \cdot R \cdot b \cdot \vec{y}

(3)

Furthermore, the equilibrium of the band provides the equation

\int_{S} d \vec{F} = 2 \cdot {\vec{F}}^{'}

(4)

Thus:

P = \frac{F^{'}}{b \cdot R}

(5)

where the resultant

(\int_{S} d \vec{F}) / b

is expressed in cN/cm of band. This change of the investigation scale, from ‘surface model’ to ‘filament model’, shows that the pressure exerted by the MCS on the limb can be solved by modeling the constitutive law of the weft yarns of the MCS.

Modeling the mechanics of the medical compression stocking through its yarns behavior: physical analysis

The textile fabric surface of the MCS is a knitted structure based on two components: the weft yarns and the knitted loops (see Figure 2).^9,10 This specific textile construction is today the only way to engineer reliable medical compressive fabric with adequate comfort for wearers. The weft yarn is a synthetic elastic yarn with textile filaments wrapped around it; this is called covered yarn. This component is inserted between the loops, which constitute the base structure of the fabric. The intrinsic properties of the MCS are determined by the covering knowhow. The amount of the treatment (level of compression) is defined by the weft yarn properties, which are directly related to the modulus of the elastic yarn and its covering parameters.

Figure 2.

Structure of the medical compression stocking (MCS) fabric (weft knit) under different magnifications.

The covering process plays a key role in the ‘active ingredient’ of the ‘compression treatment’, as on the one hand it enables the control of the ‘force/elongation’ characteristics and on the other hand it enables the protection of the elastic yarn. The manufacturing process is aimed to wrap up the natural textile fibers (e.g. cotton or wool) or synthetic fibers (e.g. polyamide, polyester) around the elastic yarn (natural rubber or elasthan). The core elastic yarn can be single or double covered (see Figure 3).

Figure 3.

Yarn-covering process.

MCSs are divided into three main classes, according to their level of compression. Each class is controlled by the specific defined type of yarns in use.¹¹ The model of the MCS dynamics must consider the characteristics of each component of the knitted structure, especially the physics of the weft yarn on the macroscopic scale, that is to say, within the validity domain of the model of elastic yarns.

A general model has been developed by taking into consideration a wider validity domain in order to provide a better understanding of the dynamic effects resulting in the covering process. Nevertheless, two other specific sub-models are also proposed for better characterization of the MCS. The latter models are more suitable for certain MCS performances required by the compression therapy.

General model of the covered yarn

Due to its structure, the general model of the covered yarn is characterized by the combination of the dynamic constitutive law of the ‘elastic’ yarn and the plastic component. The notion of elasticity is quite relative; each material is more or less elastic according its domain of investigation (degree of elongation). Evaluating the elastic properties of a piece of steel does not refer to the same protocol and tools that studying a textile fabric does. Even within the textile field, the elasticity modulus of the Kevlar yarn is totally different from the elasticity of a nylon yarn. The nylon yarn itself is totally different from real elastic yarn, such as Lycra. In our paper we decide to classify the nylon (polyamide) as a ‘non-elastic yarn’ and the elasthan as an elastic yarn. Our mentioned covered yarn is a textile construction combining a core (elastic) yarn with covering (mainly non-elastic) yarns. The maximum elongation ratio of an elastic yarn is around 600%, while the maximum elongation ratio of a usual nylon is only around 200%. On the other hand, comparing yarns with equivalent count (dtex), the elastic modulus of the nylon is much stronger than the elasthan modulus. Figure 3, depicting a covered yarn, shows the core yarn wrapped spirally with nylon. At the beginning of the elongation process, the backward force is mainly related to the (elastic) properties of the core elastic component (the spiraled nylon is not yet elongated at this step of stretch). When reaching 300–400% of elongation on the covered yarn (covering machine settings) the nylon begins to be stretched. From this moment the global behavior of the covered yarn reflects mainly the properties of the nylon, because its modulus is much higher than the elasthan modulus. According to the covering process parameters (type of yarns used and machine settings), the properties of each component are revealed at different stages during the application of a full stretch. This phenomenon can be observed either by the gap of force amplitude or a delayed action between the physical properties of the two components.

Figure 4 shows the theory of the superposition of two yarn models (dashed and dotted curves) in the elongation dynamics, which provides us with the general model (continuous curve). Thus, from the beginning of the elongation process until $ɛ_{0}$ , the pressure is mainly obtained from the elastic yarn (e.g. Lycra with high elastic modulus), as shown by the dashed curve. It is also important to point out that $ɛ_{0}$ has a relatively high degree of elongation for a related force $F_{0}$ . The contribution of the polyamide yarn (with high plastic properties), shown by the dotted curve, occurs progressively, in addition to the elastic component, between a given range of elongation $ɛ_{0}$ and $ɛ_{3}$ , where the determining properties are related to the polyamide yarn. With specific machine settings, the properties of the elastic yarn become dominant at an extreme degree of elongation. The general constitutive law of a material is the sum of the constitutive law of each component of the said material. Basically, to better understand the global model, we have to know each yarn behavior separately; however, such details are not always available.

Figure 4.

General model of the fully elongated covered yarn.

Referring to the state of art in yarn modeling, we consider the approach proposed by Serwatka et al.¹² and Lun,¹³ which suggests dividing the global model into six segments that are characterized by the following equations:

\begin{matrix} F (ɛ) = ξ_{1} [(1 - \frac{F_{1} - F_{0}}{ξ_{1} ɛ_{1}}) ɛ + \frac{2 (F_{1} - F_{0})}{ξ_{1}} - ɛ_{1}] \cdot (\frac{ɛ}{ɛ_{1}}) \\ + F_{0}, ɛ \leq ɛ_{1} \end{matrix}

(6)

F (ɛ) = ξ_{1} (ɛ - ɛ_{1}) + F_{1}, ɛ_{1} \leq ɛ \leq ɛ_{2}

(7)

F (ɛ) = ξ_{1} [1 - (a + d \cdot e^{\frac{- ɛ}{c}})] (ɛ - ɛ_{2}) + F_{2}, ɛ_{2} \leq ɛ \leq ɛ_{3}

(8)

F (ɛ) = ξ_{2} (ɛ - ɛ_{3}) + F_{3}, ɛ_{3} \leq ɛ \leq ɛ_{4}

(9)

\begin{matrix} F (ɛ) = ξ_{2} (ɛ - ɛ_{4}) + F_{4} + ξ_{3} [(1 - \frac{F_{5}}{ξ_{3} ɛ_{5}}) ɛ + \frac{2 F_{5}}{ξ_{3}}] \cdot (\frac{ɛ}{ɛ_{5}}), \\ ɛ_{4} \leq ɛ \leq ɛ_{5} \end{matrix}

(10)

F (ɛ) = ξ_{3} (ɛ - ɛ_{5}) + F_{5}, ɛ_{5} \leq ɛ

(11)

where

ξ_{1}, ξ_{2}

and

ξ_{3}

stand for the slope of each sub-model curve. This multi-segment model must comply with the continuity conditions of order 0 and 1 at each transition.

Core yarn model with plastic trend

This other model^14,15 shows a behavior close to the constitutive law of rigid materials, such as steel. When applying elongation to a textile sample (either yarns or fabric), the usual mechanical reaction is as illustrated in Figure 5. This model reflects mainly the behavior of ‘non-elastic’ yarns, such as cotton, polyester or polyamide. It is not suitable for textiles with high stretch properties (e.g. elasthan).

Figure 5.

Constitutive law of the fully elongated non-elastic yarn.

Like our general model, we can subdivide the curve in Figure 5 into three segments.

① The phase where pre-tension begins to be applied to the yarn. Substantial friction between the fibers occurs in this phase.

② The phase where the fibers/yarn are stretched. The behavior is mainly elastic and linear in this phase. The main slope $ξ_{1}$ of the curve corresponds to the elasticity modulus.

③ The final phase, where the non-linear behavior relates to the damage of the fibers. This step is not very important to us, because it is related to a domain that is totally out of our operating range (our investigations focus on the degree of material elongation when the MSC is worn).

The trend of the curve ② can be associated to a second-degree polynomial equation:

F_{1} (ɛ) = A ɛ^{2} + B ɛ + C

(12)

In the same manner, the trend of the curve in phase ② can be associated to a linear function:

F_{2} (ɛ) = ξ_{1} \cdot (ɛ - ɛ_{1}) + F_{1}

(13)

In Ngo Ngoc,¹⁶ the author uses the following equation for phase ③ description:

F_{3} (ɛ) = ξ_{1} [1 - (a + d \cdot e^{\frac{- ɛ}{c}})] (ɛ - ɛ_{2}) + F_{2}

(14)

Next, applying the continuity conditions to $F_{1}$ , $F_{2}$ , $F_{3}$ leads to

\begin{matrix} F_{1} (ɛ) = ξ_{1} \cdot [(1 - \frac{F_{1} - F_{0}}{ξ_{1} \cdot ɛ_{1}}) \cdot ɛ + (2 \cdot \frac{F_{1} - F_{0}}{ξ_{1}} - ɛ_{1})] \\ \times \frac{ɛ}{ɛ_{1}} + F_{0}, ɛ \leq ɛ_{1} \end{matrix}

(15)

F_{2} (ɛ) = ξ_{1} (ɛ - ɛ_{1}) + F_{1}, ɛ_{1} \leq ɛ \leq ɛ_{2}

(16)

F_{3} (ɛ) = ξ_{1} [1 - (a + d \cdot e^{\frac{- ɛ}{c}})] (ɛ - ɛ_{2}) + F_{2}, ɛ_{2} \leq ɛ \leq ɛ_{3}

(17)

Twisted yarn model with a viscous-elastic trend

As we can see in Figure 4, the function (dashed curve) is far from being linear and can be described by a viscous-elastic material. Such properties are a combination of purely elastic material and purely viscous, which can be described by the Kelvin–Voigt and Maxwell models.¹⁷

A purely elastic material complies with Hooke’s law:

σ = ɛ \cdot E

(18)

where σ, ɛ and E, respectively, denote the internal stress, the elongation (in %) and the Young modulus of the material.

The behavior of a purely viscous material is similar to Newtonian liquid and complies with the following laws of fluid mechanics:

σ = η \cdot \frac{d ɛ}{dt}

(19)

where

\frac{d ɛ}{dt}

, η respectively denote the deformation speed and the viscosity of the material. The rheological model that describes our experiments the best way is the Kelvin–Voigt solid in series connection with the Maxwell solid (see Figure 6(d)).¹⁸ This combination corresponds perfectly to the MCS fabric (knitted structure with weft yarns, see Figure 6(c)), whereas, during the elongation test, the main material response is related to the linear properties of the weft yarn (covered elasthan).

Figure 6.

Rheological models of medical compression stocking (MCS) fabrics.

The constitutive law of Kelvin–Voigt’s model complies with the following relation (see Figure 6(a)):

σ = σ_{1} + σ_{2} = E \cdot ɛ_{1} + η \cdot \frac{d ɛ_{2}}{dt}

(20)

whereas Maxwell’s model can be described by the following law (see Figure 6(b)):

\frac{d ɛ}{dt} = \frac{1}{E} \cdot \frac{d σ_{1}}{dt} + \frac{σ_{2}}{η}

(21)

The elongation test has been performed, where a constant speed leads to impose a constant deformation rate K₀ to the mixed Kelvin–Voigt/Maxwell’s model (see Figure 6(d)):

ɛ = ɛ_{1} + ɛ_{2} + ɛ_{3} = K_{0} \cdot t

(22)

A simple calculus shows that strain linked to the Kelvin–Voigt’s part, precisely $ɛ_{3}$ , is the solution of the following differential equation:

(\frac{1}{ω^{2}}) \cdot \frac{d^{2} ɛ_{3}}{{dt}^{2}} + (\frac{2 \cdot ξ}{ω}) \frac{d ɛ_{3}}{dt} + ɛ_{3} = K

(23)

with

K = \frac{η_{1}}{E_{2}} \cdot K_{0}, ω = \sqrt{\frac{E_{1} \cdot E_{2}}{η_{1} \cdot η_{2}}} and ξ = \frac{1}{2} \cdot \sqrt{\frac{E_{1} \cdot E_{2}}{η_{1} \cdot η_{2}}} (\frac{η_{1}}{E_{2}} + \frac{η_{2}}{E_{2}} + \frac{η_{1}}{E_{1}})

(24)

Solving (23), we get the constitutive law of the mixed Kelvin–Voigt/Maxwell’s model, namely

σ = A^{'} \cdot e^{P_{1} t} + B^{'} \cdot e^{P_{2} t} + K^{'}

(25)

with

P_{1} = ω \cdot (ξ - \sqrt{ξ^{2} - 1}), P_{2} = - ω \cdot (ξ - \sqrt{ξ^{2} - 1})

(26)

and

A^{'} = A \cdot (E_{2} + η_{2} P_{1}), B^{'} = B \cdot (E_{2} + η_{2} P_{2}), K^{'} = E_{2} \cdot K

(27)

On the one hand let us keep in mind that $F = S \cdot σ$ (where S denotes the cross section of twisted yarn) and on the other hand that the experimental conditions (22) impose $t = ɛ / K_{0}$ , so that (25) gives rise to the constitutive law of the twisted viscous-elastic yarn:

F (ɛ) = S \cdot (A^{'} \cdot e^{\frac{P_{1}}{K_{0}} \cdot ɛ} + B^{'} \cdot e^{\frac{P_{2}}{K_{0}} \cdot ɛ} + K^{'}) = λ_{1} \cdot e^{β_{1} \cdot ɛ} + λ_{2} \cdot e^{β_{2} \cdot ɛ} + λ_{3}

(28)

Identification method

Determining manually the constants $ξ_{1}, F_{1}, ɛ_{1}, ɛ_{2}, F_{2}, a, d, c$ of Equations (6)–(11) of the general model is a very difficult task. To solve such problems, we consider the set of constants as a vector of parameters and we optimize the error between the simulated curves and real curves with the non-linear least square method (a function of the Matlab software) to calculate this vector of N parameters $μ = (μ_{0}, μ_{1}, \dots, μ_{N - 1})^{T}$ of the general model. When having to deal with a great number of parameters to identify, modeling segment by segment enables us to progressively perform the identification task by considering a process of the ‘shifting and adaptive window’ to evaluate the error criteria $\sum_{ɛ = 0}^{ɛ_{i}} (y (ɛ) - \overset{\land}{y} (μ_{i}, ɛ))^{2}$ , with the i variable (i = 2–6) representing the number of segments to be identified.

This window is enlarged as the sub-models are integrated as described by the diagram of identification procedure shown in Figure 7. This procedure shows a first step of identification focusing on the curve segment between $ɛ_{0}$ and $ɛ_{2}$ for the related sub-models 1 and 2, described by the first two equations from the general model. The second step of identification is focused on the curve segment between $ɛ_{0}$ and $ɛ_{3}$ for the related sub models 1, 2 and 3, described by the first three equations from the general model. The following steps continue in this manner. This technique allows for progressive refinement of the parameter values previously identified in the preceding step and also for improvement of the continuity conditions, order 0 and 1, between each sub-model.

Figure 7.

Identification algorithm of the general model.

A similar procedure has been used for the core yarn model with a plastic trend to identify the parameter vector $μ = (μ_{0}, μ_{1}, \dots, μ_{N - 1})^{T}$ . This model has N = 8 parameters (see Figure 8). We use also a ‘shifting and adaptive window’ to evaluate the error criteria $\sum_{ɛ = 0}^{ɛ_{i}} (y (ɛ) - \overset{\land}{y} (μ_{i}, ɛ))^{2}$ with the i variable (i = 2, 3) representing the number of sub-models to be identified.

Figure 8.

Identification algorithm of the model of covered yarn with a plastic trend.

Simulation results

For each of our trials, we applied a constant speed of elongation, with the dynamometer (see Figure 9) set at 200 mm/mn (acceleration at the beginning and deceleration at the end of each trial was limited to 3 seconds). The comparison of theoretical curves (dashed line) to the measured values (continuous line) in Figure 10 shows that the general model described by (17)–(22) reflects the dynamic behavior of general covered yarns where both of their components contribute to the entire constitutive law. In some particular applications, only viscous elasticity or plasticity is required . Covering settings enable one to obtain those properties.

Figure 9.

Force–elongation testing equipment.

Figure 10.

Identification results of the general model.

The trials of different material samples have been performed by involving the core yarn model with a plastic trend. The results of the identification process provide us with the following parameters $(ξ_{1}, F_{1}, ɛ_{1}, ɛ_{2}, F_{2}, a, d, c)$ .

• Basic polyamide yarns.

These yarns are used as the outer component of the covered yarn:

Pa 33dtex = (131.4044 4.3530 0.0569 0.3459 41.9028 −0.7269 4.3455 0.4289)

Pa 44dtex = (153.6899 5.2073 0.0717 0.3045 40.7289 −0.9934 3.1453 0.9682)

• Basic elastic yarns.

The following yarns were used as core components of the covered yarn:

Elast 310 dtex = (2.1506 0.1338 0.1952 3.5299 7.3166 −0.3456 1.1970 −9.5089)

Elast 395 dtex = (2.3567 1.3611 0.3371 3.0178 7.9789 −0.9509 1.1950 −5.4124)

Elast 620 dtex = (2.8423 1.4702 0.3776 2.5674 7.9971 2.9020 −3.9079 3.6742)

Some significant curves related to the identification process of our currently used yarns are given as examples in Figures 11 and 12.

Figure 11.

Identification results of Pa 33 dtex.

Figure 12.

Identification results of elasthan 310 dtex.

This plastic-like model is perfectly suited for polyamide yarns (the outer component of the covered yarn) and for covered yarns (within their operational zone), since the parameters $(ξ_{1}, F_{1}, ɛ_{1}, ɛ_{2}, F_{2})$ , related to the beginning of the curve, are quite close to the actual test phenomenon.

However, concerning the identification process of knitted fabrics or elastic yarns, even though the simulated curves are quite close to the measured data (especially at the final phase), the distance between $ɛ_{1}$ and $ɛ_{2}$ corresponds to an important gap compared to the normal use of the product. Nevertheless, this model describes the best complex phenomenon by combining several sub-models.

Such complex models are used exceptionally, because they represent mainly the constitutive law of multi-layer compound materials with significant friction between layers.

The twisted yarn model with a viscous-elastic trend has been involved to test the knitted fabric of the MCS in classes I, II and III. The item used was a calf model of medium size (ankle circumference 22–24 cm). The maximum applied amount of stretch corresponds to the equivalent of deployed 24 cm. The available function Curfit Fit Tool from Matlab software made it possible to identify the parameters $(λ_{1}, β_{1}, λ_{2}, β_{2}, λ_{3})$ of our model. The results are as follows.

• Basic polyamide yarns.

These yarns are used as the outer component of the covered yarn:

Pa 33dtex = (170.2 0.1882 −176 −0.5485 0.9903)

Pa 44dtex = (155.5 0.4285 −160 0.5368 0.9964)

• Basic elastic yarns.

These yarns are used as a core component of the covered yarn:

Elast 310 dtex = (2.316 0.3386 −2.843 −0.795 0.9996)

Elast 395 dtex = (2.272 0.41 −2.184 −1.678 0.9997)

Elast 620 dtex = (1.106 0.929 0.24 0.9188 0.9963)

The superposition of the theoretical curve and the measured curve (see Figures 13 and 14) shows that the viscous-elastic model (continuous line) coincides with the measured values (dashed line) for elastic yarns (e.g. elasthan). However, as we might imagine, this viscous-elastic model is not suitable for polyamide yarn.

Figure 13.

Identification results of elasthan 395 dtex.

Figure 14.

Identification results of Pa 33 dtex.

Conclusion

This article proposed another approach to describe the mechanics of the MCS. We performed the study at the yarn scale for a better understanding of the fabric properties. This enables efficient control of the yarn-covering process.

In this approach, the covered yarn is described by a global model to build the force–elongation curve and to define, on this obtained curve, the location of the ‘operating point of the MCS’. This point corresponds to the degree of applied elongation when the MCS is worn on the leg. It is then possible to determine the level of pressure exerted on the varicose veins by combining this operating point with the elasticity modulus of the material.

The study also highlighted the fact that the dynamic behavior of multi-component yarns can be obtained by the principle of superposition of the dynamic behavior of each component.

Another outcome of this study shows that it is more convenient to define complex models of MCS material by superposing simple sub-models.

However, it is fundamental to consider the operating point of each sub-model, since each component of the compound yarn does not necessarily contribute to the global mechanical property at the same degree of elongation.

In conclusion, in order to design appropriate MCSs for a reliable compression treatment, the key issue is related to the knowledge of the behavior of each component (within the yarn scale) of the MCS materials.

Another important aspect of MCS engineering concerns the settings of the covering process, as it is 'the operating point' of the covered yarns that fixes the pressure level provided to the patients according to their degree of pathology.

Footnotes

Acknowledgements

This paper is based on the outcomes of a PhD Thesis entitled ‘Medical Compression Stockings Characterization’ achieved in the GEMTEX laboratory (Lille University) and sponsored by SIGVARIS. We thank the R&D Department of SIGVARIS France for their contribution.

Funding

This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.

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Modeling the mechanics of a medical compression stocking through its components behavior: Part 1 – modeling at the yarn scale