Determination of leg cross-sectional curvatures and application in pressure prediction for lower body compression garments

Abstract

It has been recognized that the cross-sectional curvatures of lower extremities directly influence pressure magnitudes and distributions exerted by compression garments. In the practice of compression therapy, higher peak pressures produced by compression shells occurred at anatomic sites with smaller radius of curvatures and led to side effects and discomfort perception. An effective and operational method to determine leg curvature properties in order to predict pressure performances is desirable to improve comfort and mechanical function of compression garment. By employing three-dimensional (3D) digital anthropometry and two-dimensional (2D) digital image simulation, the curvatures and radius of curvatures of a total of 300 cross-sectional slices involving 1200 anatomic sites along the lower limbs were determined onto the ten healthy female subjects when they were and were not wearing compression stockings. Based on the determined cross-sectional characteristics, the skin pressures were calculated using the circumference-based and the radius of curvature-based Laplace’s equations, respectively, which were further validated against the experimental skin pressures measured by a PicoPress transducer. This study provided quantitative evidence in the exploration of the working mechanisms of uneven pressures produced by compression garments, and established a standardized method to determine cross-section-related curvature characteristics for pressure assessment and prediction, which will contribute to improving user compliance of compression garments in long-term wear.

Keywords

compression garment compression therapy cross-sectional curvature lower body skin pressure

Elastic compression stockings (ECSs) have become the cornerstone in preventing and treating venous or lymphatic diseases of the lower extremities (e.g. edema, varicose veins, ulceration, etc.).^1,2 Their applications have been also increasingly extended to athletic sports for reduction of cumulative fatigue and promotion of physical recovery.^3,4 The mechanical function of ECSs compression is to provide controlled pressure to the skin, underlying tissues and vein systems to reduce venous hypertension and promote venous return.^5,6 However, high non-compliance has affected their wearing frequency and effectiveness in practice.^7,8 Uneven skin pressures (e.g. excessive or peak focal pressures) around and along the lower extremities have caused side effects, including ischemia, necrosis and even ulcerations,^9–13 especially at bony prominence for the elderly with thin and fragile skin.^10,11

The pressures by ECSs generate homogeneous or heterogeneous distributions, largely depending upon leg morphologies and local anatomic structures where the pressures are applied (Figure 1). When external pressure is applied to a cylinder with uniform radius of curvatures, the pressures at all points are consistent (or homogeneous) over the entire surface area reflecting the calculated average pressure. However, the human lower extremities exhibit marked differences in curvatures at various anatomic sites along the leg perimeters, which lead to unequal (or heterogeneous) pressure beneath the ECSs. Effective pressure determination and prediction are essential to prevent side effects from excessive focal pressures prior to application. Currently, numerous studies have been conducted to study the clinical effects of ECSs,^6,8,14–17 but few studies were reported on how the leg geometries govern the skin pressure magnitudes and how to determine leg geometries for pressure prediction.

Figure 1.

(a) Circular limb cross-section: homogeneous pressure generated by compression garment; (b) non-circular limb cross-section (e.g. ankle cross-section); (c) heterogeneous pressure generated by compression garment at specific limb cross-section; (d) heterogeneous pressure generated at various cross-sections along the lower extremity.

In 1805, Pierre-Simon Laplace described a formula that defined the pressures exerted on curved surfaces,^17,18 which explained the relationship between the pressure gradient across a closed elastic membrane or liquid film sphere and the tension in the membrane or film. However, this formula did not take into account the adaptations that may occur in human legs. A modified Laplace’s equation was further introduced to include the pressure materials’ width, tension and the number of layers applied to calculate skin pressure in clinical practice.¹⁹ The modified formula can be summarized as below,

P = \frac{T \times n \times 4620}{CW}

(1)

where P is pressure in millimeter of mercury (mmHg), T is sub-bandage tension in kgf, n is the number of layers applied, C is the circumference (cm) of the limb and W is the width of the sub-bandage (cm). The constant 4620 is derived from the conversion of the units of measurement. However, this modified equation ignores the varying curved surfaces of the lower extremities, which emphasizes the “average” pressure around a limb with known circumference rather than “focal pressure” at specific regions. To date there are few available data to demonstrate cross-sectional curvatures of lower limbs, although these curvatures are recognized to be a decisive factor influencing focal pressures by compression garment. Pressure transducers have been employed as a direct measurement tool to detect skin pressures beneath ECSs. Whether the sensor-measured pressures are consistent with the ones calculated by Laplace’s equation aforementioned has not been fully elucidated.^17,20

Three-dimensional (3D) digital body scanning techniques including white light phase-based image capture, laser-based image capture and radio-wave linear array image capture, etc., have become the cornerstone in capturing anthropometry of human body with satisfactory accuracy and reliability.^21,22 Studies on lower body anthropometries and related body shape categorization have been conducted using 3D digital body scans.^23,24 However, among all these investigations, the circumferences and corresponding heights were the major measurements of human body. The quantitative data on cross-sectional morphologies and curvature characteristics of lower extremities cannot be directly collected. We are short of quantitative evidence on the impact of interventions of compression garments on cross-sectional morphologies including variations of curvatures and radii of curvatures. Therefore, this study aims to quantify cross-sectional geometric properties (circumference, curvature and radius of curvature) of lower extremities and their spatial variations under situations with and without intervention by compression garment; and to apply the determined cross-sectional characteristics to predict skin pressures via both circumference-based and curvature-based pressure algorithms. The prediction results were further validated against the experimental pressures measured by pressure transducers. The detailed research questions in this study are itemized as follows:

how to quantify cross-sectional curvature characteristics of lower extremity using an operable and efficient methodology

how to apply the determined cross-sectional curvatures in the prediction of skin pressures induced by elastic compression materials

how to validate the predicted skin pressures with experimental data, and to assess the practicability of the proposed methodology.

The developed determination methods on cross-sectional curvatures of lower limbs and the obtained quantitative results will provide valuable evidence to guide studies on working mechanisms of compression garments and also will facilitate the selection, assessment and prediction of pressure dosages for compression garments in practical use.

Methodology

Acquisition of anthropometric data of lower extremities

The younger populations are increasingly applying compression garments to enhance functional performance of the body. In this study, ten healthy female volunteers aged 22–39 years (height: 162.0 ± 6.04 cm; weight: 55.3 ± 15.12 kg; body mass index: 23.4 ±3.07 kg/m²) were recruited. Prior to measurement, each subject was informed about the purpose and the whole procedure of the test to ensure the accuracy and consistency of data collection.

The manual tape measurement was commonly used in traditional anthropometric study, but its measurement result was largely influenced by operators’ skills and tape placement. Therefore, A VITUS^Bodyscan scanner (Human Solutions of North America, Cary, NC) was applied in this study to produce non-contact and true-to-scale 3D body measurement model. The measurement principle of this scanner system is based on optical double triangulation. Eight sensor heads are set on the four columns around the tested subject in scanning booth, which generates contact-free 3D recording of body measurements with fast scanning process (12 seconds), and high accuracy (the average circumference error <1 mm).^25–27 This type of scanner complies with the DIN EN ISO 20685 international standard, and has been applied in epidemiological²⁸ and anthropometric tests²⁹ for medical³⁰ and clothing fitting purposes.³¹

During scanning, the subjects were required to wear their fitting bras and briefs with white or light colors and stand still with their feet placed at two standardized distance-apart footprints on the platform, looking forward and maintaining normal breathing. The geometric dimensions of the right legs of all the subjects were digitally scanned with and without wearing thigh-high Class I (18–21 mmHg) ECS. The ScanWorX software was used for 3D visualization and automatic extraction of the recorded cross-sectional images in the body scanning. Along each leg, the 15 cross-sectional slices were defined at the five major segmental regions (ankle B: ankle with minimum circumference; ankle brachial B1: the level at which the Achilles tendon changes into the calf muscles; calf C: the calf region at the maximum circumference; knee E: the level across the middle of kneecap; and mid-thigh F: the level between the kneecap and the top of thigh) following German standard RAL 387/1³² (Figure 2(a)) and measurement guidance of clinical practice.³³ The heights of each cross-sectional slice were defined separately for every participant. At each segmental region, the three sequential cross-sectional slices with intervals of 1 cm between each other were determined (Figure 2(d)). The curvature related properties at the four key directions (anterior, posterior, medial and lateral) around each cross-sectional slice were defined along the legs (Figure 2(e)). To ensure the measurement precision for each circumference slice of each participant, double checking to the defined position was taken simultaneously. The average values on the circumferences and curvature-related parameters along the five major segmental regions (B, B1, C, E and F) were adopted to characterize cross-sectional geometries along lower extremities. In general, a total of 1200 anatomic sites at the 300 leg cross-sectional slices were investigated onto the ten healthy subjects under with and without ECS conditions.

Figure 2.

Illustration of the normalized digital anthropometry of lower leg by 3D body scanning system (a) the 15 determined cross-sectional slices along the five key cross-sectional segments of lower limb; (b) VITUS^Bodyscan booth; (c) anatomic sites around the four directions of each key cross-sectional segment; (d) three sequential cross-sectional slices at each key segment; (e) summary of the key cross-sectional segments and anatomic sites along the different height levels along the lower limb.

Characterization of leg cross-sectional geometries

Around the leg cross-sections, the anatomic sites with maximum curvatures ( ${Curva}_{max}$ ) are subjected to peak focal pressures being applied by the compression garment, which could impair users’ tolerance and compliance in long-term wear. In this study, a minimum bounding was set as a two-dimensional (2D) (x,y) coordinate system to determine the anatomic sites with ${Curva}_{max}$ around the four directions of the lower limb cross-sections (Figure 3). In this 2D coordinate system, the four “tangent points” (i.e. the anatomic sites with ${Curva}_{max}$ ) positioned at posterior, medial, anterior and lateral aspects of each cross-sectional slice were denoted as P1 $(a_{1}, b_{1})$ , P2 $(a_{2}, b_{2})$ , P3 $(a_{3}, b_{3})$ and P4 $(a_{4}, b_{4})$ , respectively.

Figure 3.

Digitalized cross-sectional curves of lower limb (a) a coordinate system and the defined multiple scattering points along the four directional segmental curves (H1: posterior curves; H2: medial curves; H3: anterior curves; H4: lateral curves); (b) an example of the simulated curve at the posterior side of ankle cross-section. The units shown on the x and y axis of the coordinate system represented the resolution (pixels) of the scanned images shown in the GetData Graph Digitizer (GGD) graphic processing interface.

The cross-sectional images in JPEG format captured by 3D VITUS^Bodyscan system were further digitally characterized via GetData Graph Digitizer (GGD, version 2.26.0.20, Digital River, Germany) to quantify the curvature properties of the cross-sectional outlines. GGD is a powerful program for professionally digitizing the scanned graphs and scientifically plotting to obtain coordinate data (x, y) from the scanned graphs. By using this tool, at least 13 splattering points were defined at each directional outline around per cross-sectional slice (Figure 3(a)) of lower limbs. Based on the splattering points, the segmental outline curves (H1, H2, H3 and H4) were further simulated by applying polynomial curving algorithms via Matlab analysis system (Figure 3(b)). Table 1 depicts an example of the simulated outline curves around one cross-sectional slice of the one tested subject (e.g. ankle). It can be seen that the simulated four directional outline curves (H1: posterior curve, H2: medial curve; H3: anterior curve and H4: lateral curve) presented a high consistency with the outlines determined by the 3D digital body scanning with coefficients of simulation close to 1.

Table 1.

The simulated polynomial curving models of the four segmental lines (H1–H4) around ankle cross-section of lower limb

Segmental Lines	Simulated polynomial curving models	Adjusted R^2*
H1 (Anterior)	Y = 735.9x⁹ – 31122.0 x⁸+ (5.846 e + 5) x⁷ – (6.401e+6) x⁶ + (4.504 e + 7) x⁵ – (2.111 e + 8) x⁴ + (6.594 e + 8) x³ – (1.323 e + 9) x²+ (1.548 e + 9)x – 8.045e + 8	0.9985
H2 (Lateral)	X = 62.4y⁹ – 2270.0y⁸+ 36666.0y⁷ – (3.448 e + 5) y⁶ + (2.082 e + 6) y⁵ – (8.37 e + 6) y⁴+ (2.24 e + 7)y³ – (3.85 e + 7) y²+ (3.853 e + 7) y – 1.712 (e + 7)	0.9994
H3 (Posterior)	Y = 7.849x⁹ –306.9x⁹+ 5302.0x⁷ - 53122.0x⁶+ (3.397 e + 5) x⁵ – (1.437 e + 6) x⁴ + (4.012 e + 6) x³ – (7.124 e + 6) x²+ (7.279 e + 6) x – (3.25 e + 6)	0.9991
H4 (Medial)	X = 23.59 y⁸ – 798.0 y⁷+ 11800.0 y⁶ – 99588.0 y⁵+ (5.247e + 5) y⁴ – (1.768 e + 6) y³+ (3.718 e + 6) y² – (4.464 e + 6) y + (2.342 e + 6)	0.9989

The adjusted R² was employed as a corrected goodness of fit (model accuracy) measure for the simulated curve models, in which the highest adjusted R² was considered to be the optimum one for precisely determining curvature properties of the tangent points along leg cross-sectional outline. The closer the R² was 1, the higher the degree of the simulated curve.

Based on the established polynomial curving models, the curvatures ( ${Curva}_{max}$ ) of the four “tangent points” (P1, P2, P3, P4) around leg cross-sectional slices can be further determined in terms of equation (1) and equation (2). As shown in Figure 3(a), the curvatures of the defined tangent points P1 (Kp1) and P3 (Kp3) positioned at posterior and anterior regions around the scanned leg cross-section can be calculated according to equation (2),

K (p 1, p 3) = | \frac{y ″}{(1 + y^{' 2})^{3 / 2}} |

(2)

where y′ is the first-order derivative of y with respect to x; and y″ is the second-order derivative of y with respect to x.

The curvatures of the defined tangent points P2 (Kp2) and P4 (Kp4) at medial and lateral regions around the scanned cross-sectional image can be calculated via equation (3),

K (p 2, p 4) = | \frac{x ″}{(1 + x^{' 2})^{3 / 2}} |

(3)

where x′ is the first-order derivative of x with respect to y; and x″ is the second-order derivative of x with respect to y. The calculated K (p1, p3) and K (p2, p4) indicated the maximum curvatures (

{Curva}_{max}

) around the four directions of one specific lower limb cross-sectional slice.

According to the “similarity” principle,³⁴ the curvatures of the corresponding tangent points around the real biologic leg cross-section (K₀) can be calculated via equation (4),

K_{0 (p 1, p 2, p 3, p 4)} = \frac{tC \times K_{(p 1, p 2, p 3, p 4)}}{{tC}_{0}}

(4)

where the tC₀ and tC indicate the circumferences of the actual biologic leg and the scanned leg image, respectively. The tC₀ can be directly obtained via digital body scanning, and the tC can be calculated by the approximate sum of multi-segmental lengths formed by the sequential scattering points (

x_{i}, i = 1, 2, \dots, n)

along the scanned cross-sectional outline via equation (5),

\begin{matrix} tC \approx \sqrt[2]{\sum_{i = 1}^{n} (x_{i + 1} - x_{i})^{2} + (x_{n} - x_{1})^{2}} \end{matrix}

(5)

For example, the resolution of the scanned ankle cross-section image was 1280 × 1024 (Figure 4). A coordinate system with the x-axis ranging from 0 to 12.79 and the y-axis ranging from 0 to 10.23 can be built up in the GGD working interface. A total of 68 points denoted by $S_{1}, S_{2}, S_{3} \cdot \cdot \cdot S_{68}$ can be determined evenly along the outline of the scanned ankle cross-sectional image. Then the tC value can be calculated as 3.7426 using equation (5), i.e., $t C \approx \sqrt[2]{\sum i_{= 1}^{68} {(x_{i + 1} - x_{i})}^{2} + {(x_{68} - x_{1})}^{2}} \approx 3.7426.$

Figure 4.

The simulated circumference obtained by the approximate sum of multi-segmental lengths via linking the sequential scattering points ( $S_{i}, i = 1, 2, \dots, 68)$ along the scanned ankle cross-sectional outline.

The corresponding radii of curvatures ( ${RoC}_{0}$ ) of the defined tangent points P1, P2, P3 and P4 around the real leg cross-section can be further calculated by the reciprocals of their curvature values via equation (6),

\begin{matrix} {RoC}_{0} (_{p 1, p 2, p 3, p 4)} = \frac{{tC}_{0}}{tC \times K_{(p 1, p 2, p 3, p 4)}} \end{matrix}

(6)

By applying the same methodology, the cross-sectional characteristics at other height levels (ankle brachial, calf, knee and thigh) along the lower limbs can be determined.

Pressure prediction of compression garment – an application of curvature properties

Pressure calculation via Laplace’s Law

Laplace’s Law explains the pressure delivered onto a limb of known radius of curvature by a fabric under known tension.⁵ However, it is seldom utilized in practice largely due to the shortage of evidence-based curvature data. The modified radius of curvature-based and circumference-based Laplace’s equations were suggested to predict pressure performance,^35,36 although their applicability in elastic continuum compression have not been fully investigated till now. Based on the obtained curvature data from digital body scanning and cross-sectional curve simulation of legs, the derivation of a radius of curvature (RoC₀)-based Laplace’s formula that used coherent units of practical measurement was developed in this study as shown in equation (7),

\begin{matrix} P_{skin} (Pascals) = \frac{T (N) \times n}{{RoC}_{0 mean} (m) \times W (m)} \\ = \frac{T (N) \times n \times 10^{4}}{{RoC}_{0 mean} (cm) \times W (cm)} \end{matrix}

\begin{matrix} P_{skin} (mmHg) = \frac{T (N) \times n \times 10^{4} \times 0.0075 (mmHg)}{{RoC}_{0 mean} (cm) \times W (cm)} \\ = \frac{T (N) \times n \times 75}{{RoC}_{0 mean} (cm) \times W (cm)} \end{matrix}

(7)

where P_skin is skin pressure in mmHg, T is tension of compression shell in Newton (N), n is number of layers of compression garment (n = 1), W is the width of the applied compression shell in centimeter (cm), RoC_0mean is the average RoC₀ value (cm) of the three sequential tangent points at the same direction along the three sequential cross-sectional slices (Figure 2(a)) of the real leg, and 75 is a constant for unit conversions (i.e. 1 meter = 100 centimeter; and 1 Pascal = 0.0075 mmHg). The establishment of equation (7) referenced the formulas used in both compression therapy^35,37 and textile material studies.³⁸ Based on equation (7), the circumference (

{tC}_{0}

)-based Laplace’s equation can be expressed in equation (8),

\begin{matrix} P_{skin} (mmHg) = \frac{2 π \times T (N) \times n \times 75}{2 π \times {RoC}_{0 mean} (cm) \times W (cm)} \\ = \frac{T (N) \times n \times 471}{{tC}_{0 mean} (cm) \times W (cm)} \end{matrix}

(8)

where tC_0 mean is the average circumference of the three sequential cross-sectional slices at one specific cross-sectional segment along the real leg (Figure 2(d)), and 471 is a constant for unit conversion. To apply equation (7) and equation (8) in pressure calculation, the tension of compression fabrics need to be further identified through material mechanical assessment.

Determination of tension properties of compression fabrics

In this study, the ECS samples in length of 60 cm were fabricated by Lycra-based double covered polyamide elastomers, including the ground elastic yarns with 40/40D (denier) and the inlay yarns with 265D/20D using 3D circular medical stocking knitting unit (Lonati LA-45ME) (Figure 5(a)). To form a degressive gradient pressure profile in terms of standard RAL-GZ387/1,³² the knitting densities of the laid-in structures from the ankle to the thigh presented gradient variations along the ECS tubes (Figure 5(b)). The looped fabric specimens in 50 mm width and 160 mm looped gauge length (i.e., two specimens in lengths of 80 mm were stitched) were directly obtained from the five major cross-sectional segments (i.e. ankle B, ankle brachial B1, calf C, knee E and thigh F) along the tested ECS samples. The dimensions, densities and thickness at the each tested cross-sectional segments of the ECS samples are determined as shown in Figure 5(b). The fabric tensions in the course directions were measured by using Instron 4411 tensile tester (Norwood, MA, USA) times according to the experimental procedure of EU 3392 standard (Figure 5(c)). The fabric loops were stretched from 0 to 80% at a constant rate of 300 mm/min simulating the general range of horizontally stretching when ECS is mounted onto the subjects’ lower limbs. The corresponding tension forces (N) of each specimen were halved to give the load for one side of the fabric loop, and the third cycle of tension-stretch curves with improved elongation stability was recorded for each tested segment along the stocking tubes (Figure 5(d)). The obtained tension forces of the fabric specimen with known width (i.e. 50 mm) were used to calculate the skin pressure via Laplace’s equations (7) and (8).

Figure 5.

Tension assessment of the fabric specimens in course directions along the compression stocking, (a) the tested elastic compression stockings (ECS) tube with laid-in knitting structures; (b) basic characteristics of the tested specimens; (c) fabric specimens at unstretched and stretched conditions; (d) the third cycle of the tension-stretch curve plots of the tested specimens along different height levels of ECS tube.

Skin pressure measurement

To validate the prediction capability of the circumference-based and radius of curvature-based calculation equations, an objective skin pressure evaluation was conducted via PricoPress pneumatic pressure sensor (Microlab Elettronica Sas, Italy) (Figure 6(d)). The circular air-filled pressure sensor, measuring 5 cm in diameter, was successively placed at the 20 anatomic sites with most maximum curvatures around the four directions (anterior, posterior, lateral and medial) and along the five major cross-sectional regions (ankle, brachial, calf, knee and thigh) of the lower limbs (Figure 2(c)). In each pressure test, the operator pushed on an embedded syringe to introduce 2 cubic centimeters of air to the sensor. The resultant expansion in thickness was constrained by the stocking shell, and the skin pressure in mmHg was recorded by a built-in manometer. This pressure sensor is an ultrathin probe with thickness of 0.2 mm in deflation, which has been widely employed in experimental studies and clinical assessments.^39–41 Partsch and Mosti conducted comparative analysis on the linearity, variability and accuracy of three portable pressure instruments (Kikuhime, SIGaT tester and PicoPress), and indicated that PicoPress transducer was a reliable instrument for measuring pressure under a compression device. In our earlier studies, the stability and repeatability of PicoPress pressure sensor were investigated by comparing pressure data of five repeated tests at the same testing point of a standard wooden leg model (rigid surface and round cross-section) when it was exerted by ECS with matching dimension. Before the test, the ECS fabric was placed at a controlled condition (temperature of 21° ± 2° and a relative humidity of 65% ± 2%) following a minimum of 24-hour equilibrium. The results indicated that the deviations of the pressure values at the same testing regions were within ±1 mmHg. In this study, the pressure sensor with 5 cm in diameter fully covered the three anatomic sites of the three sequential cross-sectional slices at one specific direction (Figure 6(a) and 6(b)). The average values of circumferences, curvatures and radius of curvatures of the three sequential cross-sectional slices at one key cross-sectional segment (Figure 6(c)) were adopted in skin pressure calculations, which were compared with the experimentally measured pressure values.

Figure 6.

Objective evaluation of skin pressure (a) three cross-sectional slices involved at one major segment (e.g. ankle brachial B1); (b) a PicoPress pressure probe with 5 cm in diameter inserted between the skin and elastic compression stockings (ECS) fabric shell to detect practical interface pressure; (c) the average value on radii of curvatures of the three sequential cross-sectional slices were adopted to calculate skin pressure at the one directional anatomic region (e.g. B1); (d) PicoPress pressure transducer and testing system.

Data analysis

In this study, numerical descriptive statistics including the mean and standard deviation were applied to describe curvature-related characteristics. The spatial variations of curvatures and radii of curvatures by the intervention of ECS were examined using paired-t test (2-tailed). The effects of leg anatomic structures on the studied leg shape parameters as well as the comparisons among the studied anatomic parameters were analyzed using Analysis of Variance (ANOVA) with post-hoc multiple comparisons method based on Tukey’s Honestly Significant Difference (HSD) test. The alpha values were set at the three significant levels of 0.05, 0.005 and 0.001, indicating to be highly significant (p < 0.001), moderately significant (0.001 ≤ p < 0.005) and weakly significant (0.005 ≤ p < 0.05), respectively, which were used to reflect impact and difference degrees of anatomic structures on the studied parameters. The data were analyzed by using Statistical Package of the Social Sciences (SPSS) Version 24.0 (SPSS Inc., Chicago, IL).

Results

Circumferences of legs and variations induced by ECS compression

The paired-t test results indicated that the intervention of compression stocking significantly reduced the circumferences of the studied cross-sections by ranging from 0.19 to 0.66 cm, especially at the calf region (p < 0.001) (Table 2). More variances on the circumferences occurred at the thigh with soft tissue dominated structures.

Table 2.

Variations of leg circumferences at different cross-sectional segments

Cross sections	Without ECS (cm)		With ECS (cm)		Comparison between with and without ECS
Cross sections	Mean ± SD†	Variance	Mean ± SD	Variance	Difference mean ± SD	t-value	Sig.
Ankle (B)	21.34 ± 1.08	1.16	21.08 ± 1.04	1.11	0.25 ± 0.20	3.489	0.010*
Brachial (B1)	28.10 ± 1.41	1.99	27.91 ± 1.38	1.98	0.19 ± 0.17	3.146	0.016*
Calf (C)	34.98 ± 2.28	5.19	34.73 ± 2.19	4.93	0.24 ± 0.11	6.340	0.000***
Knee (E)	35.29 ± 1.84	3.37	34.77 ± 1.79	3.30	0.52 ± 0.41	3.576	0.009*
Thigh (F)	47.99 ± 3.52	12.37	47.33 ± 3.34	11.49	0.66 ± 0.46	3.7840	0.007 *

p < 0.05; **p < 0.005; ***p < 0.001; †Standard deviation. ECS: elastic compression stockings

Cross-sectional curvature properties and variations induced by ECS compression

It can be seen that the higher values of cross-sectional curvatures (e.g. from 0.24 cm⁻¹ to 0.56 cm⁻¹) existed at the ankle region with the smallest circumferences (Table 3(a)), especially at posterior (0.39 ± 0.12 cm⁻¹) and anterior sites (0.56 ± 0.18 cm⁻¹). The cross-sectional curvatures at the thigh region were relatively low ranging from 0.14 cm⁻¹ to 0.17 cm⁻¹, where there were higher values in leg circumferences. Compared with the control condition, the intervention of ECS significantly reduced the cross-sectional curvatures at anterior sites of the calf (p = 0.016) and the ankle brachial (p = 0.028), as well as medial site of the thigh (p = 0.034).

Table 3(a).

The curvatures with Curva_max along lower limbs with and without elastic compression stockings (ECS)

Cross sections	Directions	Curvatures without ECS (cm⁻¹) Mean ± SD†	Curvatures with ECS (cm⁻¹) Mean ± SD	Difference mean ± SD between with and without ECS	Paired-t test
Cross sections	Directions	Curvatures without ECS (cm⁻¹) Mean ± SD†	Curvatures with ECS (cm⁻¹) Mean ± SD	Difference mean ± SD between with and without ECS	t-value	Sig.
Ankle (B)	Posterior (BP1)	0.56 ± 0.18	0.53 ± 0.06	0.03 ± 0.14	0.617	0.557
	Medial (BP2)	0.24 ± 0.04	0.25 ± 0.48	−0.01 ± 0.04	−0.878	0.409
	Anterior (BP3)	0.39 ± 0.12	0.34 ± 0.05	0.05 ± 0.13	0.975	0.362
	Lateral (BP4)	0.28 ± 0.07	0.25 ± 0.02	0.03 ± 0.06	1.357	0.217
Brachial (B1)	Posterior (B1P1)	0.28 ± 0.13	0.21 ± 0.02	0.08 ± 0.13	1.594	0.155
	Medial (B1P2)	0.29 ± 0.08	0.23 ± 0.06	0.06 ± 0.08	2.159	0.068
	Anterior (B1P3)	0.31 ± 0.06	0.23 ± 0.04	0.07 ± 0.07	2.753	0.028 *
	Lateral (B1P4)	0.21 ± 0.05	0.19 ± 0.03	0.02 ± 0.07	0.762	0.471
Calf (C)	Posterior (CP1)	0.17 ± 0.02	0.18 ± 0.03	−0.01 ± 0.04	−0.642	0.542
	Medial (CP2)	0.26 ± 0.07	0.23 ± 0.03	0.03 ± 0.06	1.517	0.173
	Anterior (CP3)	0.30 ± 0.04	0.24 ± 0.04	0.06 ± 0.05	3.156	0.016 *
	Lateral (CP4)	0.16 ± 0.03	0.17 ± 0.02	−0.01 ± 0.03	−0.493	0.637
Knee (E)	Posterior (EP1)	0.18 ± 0.07	0.19 ± 0.08	− 0.01 ± 0.10	−0.321	0.758
	Medial (EP2)	0.29 ± 0.17	0.26 ± 0.09	0.03 ± 0.15	0.498	0.634
	Anterior (EP3)	0.21 ± 0.10	0.28 ± 0.05	−0.06 ± 0.11	−1.629	0
	Lateral (EP4)	0.20 ± 0.07	0.22 ± 0.05	− 0.03 ± 0.09	−0.754	0.475
Thigh (F)	Posterior (FP1)	0.15 ± 0.04	0.18 ± 0.03	−0.03 ± 0.04	−1.839	0.109
	Medial (FP2)	0.17 ± 0.05	0.12 ± 0.02	0.05 ± 0.048	2.624	0.034 *
	Anterior (FP3)	0.15 ± 0.02	0.13 ± 0.02	0.02 ± 0.03	1.305	0.233
	Lateral (FP4)	0.14 ± 0.03	0.14 ± 0.20	−0.00 ± 0.03	−0.213	0.838

p < 0.05; **p < 0.005; ***p < 0.001; †Standard deviation.

Table 3(b).

The RoC₀ at defined anatomic sites with Curva_max along legs with and without elastic compression stockings (ECS)

Cross section	Directions	RoC₀ without ECS (cm) Mean ± SD†	RoC₀ with ECS (cm) Mean ± SD	Difference mean ± SD between with and without ECS	Paired-t test
Cross section	Directions	RoC₀ without ECS (cm) Mean ± SD†	RoC₀ with ECS (cm) Mean ± SD	Difference mean ± SD between with and without ECS	t-value	Sig.
Ankle (B)	Posterior (BP1)	1.98 ± 0.67	1.92 ± 0.24	0.06 ± 0.48	0.320	0.758
	Medial (BP2)	4.40 ± 0.88	4.22 ± 1.07	0.17 ± 0.83	0.579	0.581
	Anterior (BP3)	2.79 ± 0.91	2.98 ± 0.48	−0.19 ± 1.11	−0.408	0.695
	Lateral (BP4)	3.76 ± 1.00	4.01 ± 0.44	−0.26 ± 1.05	−0.652	0.535
Brachial (B1)	Posterior (B1P1)	4.12 ± 1.48	4.87 ± 0.54	0.06 ± 0.51	−1.643	0.144
	Medial (B1P2)	3.76 ± 1.14	4.79 ± 1.52	−1.05 ± 0.85	−1.652	0.143
	Anterior (B1P3)	3.41 ± 0.86	4.32 ± 0.61	−0.93 ± 1.11	−2.305	0.055
	Lateral (B1P4)	5.19 ± 1.23	5.45 ± 0.78	−0.30 ± 1.80	−0.433	0.678
Calf (C)	Posterior (CP1)	5.89 ± 0.80	5.64 ± 0.99	0.17 ± 1.37	0.467	0.655
	Medial (CP2)	4.04 ± 1.09	4.43 ± 0.60	−0.34 ± 0.98	−1.088	0.313
	Anterior (CP3)	3.31 ± 0.42	4.19 ± 0.68	−0.85 ± 0.78	−2.868	0.024*
	Lateral (CP4)	6.34 ± 1.60	5.94 ± 0.82	0.39 ± 1.75	0.637	0.545
Knee (E)	Posterior (EP1)	6.40 ± 2.46	5.94 ± 1.95	0.41 ± 2.61	0.467	0.655
	Medial (EP2)	4.96 ± 3.42	4.18 ± 1.10	0.85 ± 3.56	0.612	0.560
	Anterior (EP3)	5.56 ± 1.79	3.74 ± 0.66	1.79 ± 1.75	2.674	0.032 *
	Lateral (EP4)	5.82 ± 2.02	4.75 ± 1.14	1.05 ± 2.45	1.104	0.306
Thigh (F)	Posterior (FP1)	7.19 ± 2.14	5.78 ± 1.00	1.39 ± 1.71	2.087	0.075
	Medial (FP2)	6.85 ± 2.86	8.83 ± 1.70	−2.00 ± 2.41	−2.182	0.065
	Anterior (FP3)	6.80 ± 0.67	7.73 ± 1.41	−1.00 ± 1.61	−1.502	0.177
	Lateral (FP4)	7.45 ± 1.86	7.04 ± 1.03	0.32 ± 1.87	0.547	0.602

p < 0.05; **p < 0.005; ***p < 0.001; †Standard deviation.

Table 3(c).

Multiple comparisons on ${Curva}_{max}$ and RoC₀ among the four directions of lower limbs

Post-hoc test on RoC₀ among four directions under ECS condition							ANOVA analysis
Cross-sections	P1 vs. P2	P1 vs. P3	P vs. P4	P2 vs. P3	P2 vs. P4	P3 vs. P4	F	P (Sig.)
Ankle (B)	.000***	0.026	0.000***	0.006**	1.000	0.031	19.435	0.000***
Brachial (B1)	1.000	1.000	1.000	1.000	1.000	0.182	1.754	0.179
Calf (C)	0.028	.008**	1.000	1.000	0.004**	0.001**	9.240	0.000***
Knee (E)	0.097	0.021	0.545	1.000	1.000	0.984	3.801	0.021
Thigh (F)	0.001**	0.052	0.460	0.646	0.079	1.000	7.044	0.001**

ECS: Elastic compression stockings; ANOVA: Analysis of Variance. *p < 0.05; **p < 0.005; ***p < 0.001.

Table 3(b) further analyzed the radii of curvatures (RoC₀) of the 20 defined anatomic sites with ${Curva}_{max}$ along lower limbs under two wearing conditions. It can be seen that the RoC₀ values increased from the ankle (1.98–4.40 cm) to the thigh (6.80–7.45 cm) for the bare legs. The intervention of ECS significantly increased the RoC₀ values at anterior calf (p = 0.024), and significantly reduced the RoC₀ at anterior knee (p = 0.032) as compared with the control. It implied that the intervention of ECS could deform contacting interfaces, and even flatten the surface curves of leg cross-sections. Meanwhile the use of ECS may also potentially increase the prominence of bony region (e.g. kneecap) as compared with the control.

The post-hoc test indicated that among the four directions around lower limbs, highly significant differences on cross-sectional curvatures occurred at the ankle with irregular ellipse shape (p = 0.000), and the calf with peach shapes (p = 0.000) (Table 3(c)). Meanwhile, the curvatures at the anterior tibia crest around the calf and posterior Achilles’ tendon at ankle produced significant differences with other directional sites within the same corresponding cross-sectional slices, implying that anterior calf and posterior ankle regions would be at high risk of experiencing peak focal pressures with pressure application.

Influence of anatomical structures on leg curvature characteristics

In general, the curvatures and radii of curvatures were more significantly influenced by the cross-sectional levels (B, B1, C, E and F), directions (P1, P2, P3 and P4) and their interactions under ECS compression (Table 4). The varying curvatures at local sites may cause corresponding variations of skin pressures beneath compression shells in terms of Laplace’s principle. The data derived from this study provided an important quantitative evidence to explain mechanisms behind uneven skin pressures generated by compression garment in practice.

Table 4.

Impact of anatomic structures on curvatures and radii of curvatures of lower limbs

Influencing items	Dependent variables	Degree of freedom	Without ECS		With ECS
Influencing items	Dependent variables	Degree of freedom	F-value	P (Sig.)	F-value	P (Sig.)
Cross-section levels	${Curva}_{max}$	4	24.561	0.000***	78.736	0.000***
Cross-section levels	${RoC}_{0 max}$	4	22.628	0.000***	57.176	0.000***
Directions	${Curva}_{max}$	3	5.625	0.001**	15.046	0.000***
Directions	${RoC}_{0 max}$	3	4.056	0.008**	5.219	0.002**
Interactions of cross-section and direction	${Curva}_{max}$	12	5.798	0.000***	15.937	0.000***
Interactions of cross-section and direction	${RoC}_{0 max}$	12	1.737	0.065	6.622	0.000***

p < 0.05; **p < 0.005; ***p < 0.001. ECS: elastic compression stockings

Determination of tension properties for skin pressure calculation

To verify the pressure prediction capability of Laplace’s algorithms (equations (7) and (8)), the fabric tensions at each cross-sectional level along the lower limbs were determined. As shown in Table 5, the use of ECS squeezed the leg volume, resulting in reduced leg circumferences (tC₀ values) compared with the control (bare leg), which led to the reduced fabric tension due to the decreased fabric stretching in course direction. In this study, a single-layered ECS fabric (n = 1) of width (W) 5 cm was adopted in the pressure calculations using Laplace’s equations. This standardized fabric width conformed to the area covered by the 5 cm-diameter of circle-shaped pressure sensor in the pressure measurements.

Table 5.

Fabric tension variations with leg girths

Cross-sections	Girth of ECS (cm)	Girth of leg (cm)	Height (cm)*	Fabric stretch (%)	Fabric tension (N)
Without ECS condition (mean ± SD†)
Ankle (B)	16.00 ± 0.45	21.34 ± 1.08	10.64 ± 0.34	33.38 ± 6.64	5.07 ± 0.45
Brachial (B1)	20.40 ± 0.42	28.10 ± 1.41	19.71 ± 0.74	37.75 ± 5.98	4.43 ± 0.67
Calf (C)	22.00 ± 0.40	34.98 ± 2.28	28.97 ± 1.53	58.98 ± 10.20	6.48 ± 0.34
Knee (E)	21.00 ± 0.55	35.29 ± 1.84	42.73 ± 2.87	68.04 ± 8.61	7.13 ± 0.52
Thigh (F)	30.20 ± 0.65	47.99 ± 3.52	61.25 ± 3.11	58.91 ± 11.46	6.22 ± 1.01
With ECS condition (mean ± SD†)
Ankle (B)	16.00 ± 0.45	21.08 ± 1.04	10.64 ± 0.34	31.80 ± 6.49	4.90 ± 0.65
Brachial (B1)	20.40 ± 0.42	27.91 ± 1.38	19.71 ± 0.74	36.79 ± 6.78	4.42 ± 0.53
Calf (C)	22.00 ± 0.40	34.73 ± 2.19	28.97 ± 1.53	57.87 ± 9.94	6.36 ± 0.93
Knee (E)	21.00 ± 0.55	34.77 ± 1.79	42.73 ± 2.87	65.56 ± 8.51	6.75 ± 0.48
Thigh (F)	30.20 ± 0.65	47.33 ± 3.34	61.25 ± 3.11	56.73 ± 11.05	5.42 ± 0.89

ECS: elastic compression stockings. *The distance between floor level to the defined circumference level along leg; †Standard deviation.

Validation of calculated skin pressures against the measured ones

Figure 7 illustrates the comparative results between the measured and the calculated skin pressures at the five key height levels and 20 major anatomic sites along the original 10 volunteers’ lower limbs. The predicted skin pressures were respectively calculated by using circumference-based (tC₀-based) and radius of curvature-based (RoC₀-based) Laplace’s equations. It can be seen that a consistent varying trend existed between the measured and the calculated “average skin pressures” along the five key height levels, especially at ankle brachial (B1) and thigh (F) regions (Figure 7(a) and 7(b)), indicating that the developed methodology to determine cross-sectional curvatures would be reliable to predict average skin pressure in practice.

Figure 7.

Comparison between the measured and predicted skin pressure calculated by tC₀-based and RoC₀-based Laplace’s algorithms along different height levels and at 20 anatomic sites of the original 10 subjects’ lower limbs.

However, the tC₀-based skin pressure calculations inadequately reflected focal pressures of different directions of legs, especially for the irregular cross-sections. Compared with this, the RoC₀-based pressure calculations sensitively reflected the consistent variations of the “peak local pressures” with the measured ones (Figures 7(c)–(g)). It can be seen that the bony prominence regions (e.g. anterior tibia crest and knee patella) increased differences between the measured and calculated skin pressures (Figure 7(c) and Figure 7(f)), yet the relatively roundish or soft-tissue dominant cross-sections (e.g. ankle brachial and thigh) showed the approximated values between the calculated and the measured pressures (Figure 7(d) and Figure 7(g)).

Discussion

New method of determining curvature properties of lower limbs

Clear defining geometric features of lower limbs would contribute to the provision of comfort fitting and pressure performances by compression devices. In traditional practice, the entire lower limb shape of the user was measured mainly in terms of conventional items, e.g. leg circumference, height, length and body mass index, etc., which is based on the presumption that the lower limbs are uniform with some addition or subtraction allowances for size. However, in reality the shapes of patients’ legs are highly irregular, with rather random variations in sizes. There is evidence that the irregularity of leg cross-sections is one of the critical factors leading to uneven pressures induced by compression textiles.¹ Curvatures and radius of curvatures are typical variables that quantitatively reflect surface geometries of complex objects. However, there is scant literature on quantitative data and their influences on skin pressures, as well as their applications in design of compression garments.

A study conducted by Bruniaux et al., regarded human limb as a cylindrical body with uniform radius of curvatures,⁴² and applied this presumption to develop constitutive law. Kowalski et al. simulated the body curvatures based on the three neighboring points near the tangent points of human torso for design of an after-burn therapeutic compression garment.⁴³ However, this study adopted a manual approach to select sample points, and did not indicate how to build and adjust the 2D coordinate system for each calculation. A subsequent study⁴⁴ further applied more neighboring points (up to five) to minimize the mean square error in calculation of radius of curvature. However, it was confined to the human trunk with relatively even and symmetrical shape. The studies on lower limb curvatures and their applications in ECS design have not been reported.

This novel study constructed a minimum bounding rectangle frame as the basic coordinate system to determine the tangent points with maximum curvatures around the lower limb cross-section, which provided an intuitive approach to reflect peak focal pressures by compression textiles along leg morphology. The tangential curvature of a smooth curve is defined as the curvature of its osculating circle at a tangential point, and its radius of curvature is equal to the reciprocal of its curvature. Smaller osculating circles bend more sharply, and hence have greater curvatures but smaller radii of curvatures.⁴⁵ On this basis, a new curvature formula (equation (4)) with statistical treatments has been proposed to directly determine cross-sectional curvatures of a real leg with specific limb girths via a digitally scanned cross-sectional image. And a standardized and efficient method to predict skin pressures has been further introduced by employing the determined curvature data and the modified Laplace’s algorithms. This study provided an evidence-based and easily operable solution to detect leg surface geometry and predict their impact on skin profiles by elastic compression textiles.

Using finite element models (FEM) is a growing domain to simulate geometric morphology and pressure function by compression interventions.^46–49 However, building a patient-specific FEM is usually delicate⁵⁰ and time consuming, including the processing of imaging examinations (e.g. Computed Tomography or Magnetic Resonance Image scanning), discretization (mesh) and boundary definition, and system calculation, etc. It may not be feasible in daily clinical use for individuals. Compared with FEM, this proposed method largely shortened the scanning process (i.e. the whole leg scanning only takes 12 seconds) and the curvatures can be directly calculated using the established algorithms for immediate pressure prediction.

To reduce the deviations in the measured curvatures at specific tangent points, the curvature values at certain cross-sectional regions were derived from the average values of the three sequential cross-sectional slices at intervals of 1 cm (Figure 2(d), Figure 6(c)), to decrease the potential random deviations caused by a single tangent point in calculation. Meanwhile, more compact sample points were evenly and automatically determined between the four key directional tangent points around the cross-sectional outlines (Figure 3), where the minimum intervals between the sample points were set using the GGD software. Based on the established equations (4) and (5), it can be demonstrated that the properly increased sample points along the limb cross-sectional outline would contribute to the increase of precision in simulation of cross-sectional circumferences, thus increasing precision of curvature data of the tested biologic lower limbs.

An advanced 3D body scanner has the capability to capture 3D body dimensions of the tested subjects, but it cannot directly read out the surface curvatures. Gaussian curvature is the product of the two principal curvatures reflecting 3D surface properties of the object. It is not suitable to directly calculate the radius of curvature (RoC₀) at a specific tangent point. Therefore, our current study converted the 3D surface into 2D curve through digital body scanning and curve simulation. Through this, the two curvatures were reduced to one, which can be conveniently used to calculate RoC₀ via derivative algorithm (equations (2) and (3)), and then to predict skin pressure using RoC₀-based Laplace’s equation (equation (7)). Apart from the tested younger population, this new method can also be applied to subjects encompassing a wide age range for pressure prediction of lower body compression garment, e.g., women aged over 40 years as the main users of ECSs for the treatment of varicose veins.

Practicality of Laplace’s equation in pressure prediction

Thomas addressed calculation of Laplace’s equation for predicting sub-bandage pressure in clinical practice.^35,37 The layers, materials tension and width were introduced. Al Khaburi et al.^51,52 further studied effects of fabric thickness on pressure magnitudes of multi-component compression systems, and established a mathematical model involving bandage thickness based on thick wall cylinder theory for interface pressure prediction. However, Hegarty-Craver et al.⁵³ pointed out that as the limb is not a solid and uniform cylinder, the material friction and creep characteristics could influence the amount of applied pressure using Laplace’s Law in practice of compression therapy. Following that, Sikka et al. further developed a pressure prediction model based on conical limb geometry,⁵⁴ but the model did not cater to the change of tension in a dynamic situation. In addition, the accuracy of Laplace’s algorithms in pressure prediction remains controversial. Macintyre et al. evaluated effects of cylinder circumference variations, fabric structures, and reduction factor by pressure garment.⁵⁵ They found that Laplace’s Law predicted accurate pressures for most of the fabrics except for the “powernet” structure. However, Laplace’s Law was considered to have significantly overestimated the exerted pressure on small-circumference cylinders in their extended study.⁵⁶ Compared with this, Gaied et al. reported that Laplace’s Law underestimated the experimental values by 20–30% through testing ECSs on a rigid mannequin leg;⁵⁷ and Yildiz demonstrated that there was a consistency on pressure values between the theoretical and experimental assessment using trilaminated composite fabrics on five different sized mannequin legs.⁵⁸ Up to now the practicality of Laplace’s equations in pressure prediction of a continuum elastic compression shell (e.g. ECS) has not been thoroughly explored, and no consistent testing device and experimental protocol are available to guide pressure assessments in practice. The results of the present study showed an agreement in pressure variation trends between the measured and the calculated pressure values, which demonstrated the applicability of the proposed methodology and the used Laplace’s algorithms for an elastic compression continuum. Considering its practical application, four aspects required be further elaboration below.

Firstly, two wearing conditions, i.e., with and without wearing ECS, were involved in this study to determine the effects of intervention of compression shell on leg geometric morphologies and curvature properties. It was found that that the intervention of ECS shell significantly reduced the perimeters of legs by 0.19–0.66 cm, which may result in a “slender look” of the leg as claimed by some commercially “slim legging” products; whereas the reduced circumferences by use of stocking did not significantly influence the curvature properties for most of the tested anatomic sites, which indicates that the curvature data of the bare legs determined by 3D body scanning can be directly used for pressure prediction of ECS in practice.

Secondly, the elastic fabric of ECS commonly presents bi-axial stretch properties in wale and course directions; that is, the pressure induced by stocking shell is largely dominated by the horizontal stretch along the course direction of elastic fabric. The horizontal stretched fabric produces encircling forces through constraining lower limb expansion during calf muscle contraction and relaxation, which plays an import role in delivering centripetal mechanical forces to squeeze the underlying venous system to facilitate venous return. In this study, the longitudinal stretch of the developed ECS was controlled less than 10% lengthwise but the transverse stretch was up to approximately 30–60% horizontally from the ankle to the thigh. Therefore, the tension caused by transverse stretch of stocking shell was, as one of major fabric properties, taken into account in the pressure calculation in this study.

Thirdly, both the circumference-based and radius of curvature-based Laplace’s algorithms demonstrated reliabilities in prediction of skin pressures at ankle brachial, calf and thigh where the cross-sectional contours close to be round and soft tissues are dominated. The tC₀-based algorithm presented more consistent trends in “average skin pressures” compared with the measure ones. The RoC₀-based algorithm showed more sensitivities to reflect peak focal pressures around the leg surface, especially at the bony prominence regions (e.g. ankle and knee), which would be a useful indicator to assist users or physicians to adjust or select appropriate pressure dosages to avoid excessive peak pressures or deficient pressures in long-term use.

Fourthly, an optimum pressure measurement interface should be free of any intervention of pressure sensor at contacting area. Such a pressure testing technology and device are still immature. In this trial, the pressures by elastic stocking shell produced recoiling forces towards the sensor surface to restrict its expansion during the tiny air (2 cubic centimeters) was filled. The deformation of sensor shell was restrained under the action of collaborative pressures from two opposite directions by skin surface and inside of fabric shell. Therefore, the presence of the used pressure sensor could exert a limit influence on the contact interface and body surface curvature in the measurement. To further explore the underlying mechanisms, more comparative studies will be carried out to estimate its testing effect and reliability onto contacting surfaces with diverse tissue elasticity and stiffness in our future study.

Effects of cross-sectional curvatures on pressure performance

The International Compression Club (ICC) consensus document proposes that location B1 should always be included in pressure measurements, with the exact location of the sensor situated at the segment that shows the most extensive enlargement of the leg girths of ankle activities and position changes.⁵⁹ In compression therapy, the stiffness of a medical compression device is defined as the pressure change (in mmHg) that occurs with an increase in limb girth of one centimeter (ΔP/ΔC),⁶⁰ which effectively indicates the dynamic pressure function of compression shell in practical treatment.⁶¹ The stiffness at the B1 region is considered to be adequate to assess stiffness of a medical device in vivo. This study’s results provide significant evidence that using the cross-sectional curvatures or circumferences at the B1 region in pressure calculation would be a reliable and time-saving approach to predict pressures by compression shells, thus predetermining medical effectiveness of compression therapy.

The interaction between lower limbs and compression garments are complex. The contact interface conditions are not only determined by surface curvatures of lower bodies but also tissue elasticities and stiffness at the contact areas. Placing the compression shells with known tension properties onto the regions with larger curvatures but lower stiffness may produce lower interface pressure due to deformed tissue volume under squeezing forces by compression materials. The results implied that the use of ECS may flatten the local tissue surface and make the soft tissue-dominated cross-sections more roundish (e.g. anterior calf), and may allow the bony region more angular (e.g. kneecap). Adjusting fabric tensions could be another solution to vary focal pressure magnitudes according to Laplace’s Law.

The current study has some limitations. The detection of biomaterial properties of the subjects’ tissue structures was not conducted. Indentation techniques⁶² or shear wave ultrasound elastography⁶³ could be applied in our following study to quantitatively detect tissue properties at different anatomic segments (e.g. from ankle B to thigh F). The determined tissue properties will be involved as one of parameters in Laplace’s algorithms to enhance their application in pressure assessment and prediction. Moreover, the assessment onto a total of 300 cross-sectional slices and 1200 anatomic sites of subjects’ lower limbs was considered an appropriate size for statistics and verification in current study. However, the results could not be generalized to populations with diverse shapes and sizes of lower limbs. In addition, some other factors including interface frictions between human skin and compression garments, age and gender of subjects, and fabric tension in different directions could also influence the correlation coefficients of Laplace’s algorithms. These aspects will be explored in our future studies.

Conclusion

A new curvature formula with statistical analysis has been developed to determine cross-sectional curvature characteristics of human legs based on digital body scanning and image simulation; and an efficient and operable approach to apply the determined curvature data to predict skin pressure profiles has been proposed and validated against the experimental test. This novel study demonstrated the practicability of the proposed methodology in the determination of leg cross-sectional curvatures and pressure pre-assessment. The results would enhance our understanding on underlying mechanisms of uneven pressure distributions by compression garments and facilitate physicians and users to adopt proper measures to avoid occurrence of excessive or peak focal pressures prior to use, thus improving user compliance and treatment efficacy of compression therapy in practice. In our future studies, the curvatures of diverse body shapes will be determined and the improved Laplace’s algorithms involving biomaterial properties of the anatomic structures as well as more influencing factors will be developed to further promote their practicalities in pressure assessment and prediction.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study is funded by the Hong Kong Polytechnic University through research grants 1-ZE7K and 1-ZVLQ, and ITF project ITS/031/17.

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