Lateral pressure equalisation as a principle for designing support surfaces to prevent deep tissue pressure ulcers

When immobile or neuropathic patients are supported by beds or chairs, their soft tissues undergo deformations that can cause pressure ulcers. Current support surfaces that redistribute under-body pressures at vulnerable body sites have not succeeded in reducing pressure ulcer prevalence. Here we show that adding a supporting lateral pressure can counter-act the deformations induced by under-body pressure, and that this ‘pressure equalisation’ approach is a more effective way to reduce ulcer-inducing deformations than current approaches based on redistributing under-body pressure. A finite element model of the seated pelvis predicts that applying a lateral pressure to the soft tissue reduces peak von Mises stress in the deep tissue by a factor of 2.4 relative to a standard cushion (from 113 kPa to 47 kPa)—a greater effect than that achieved by using a more conformable cushion, which reduced von Mises stress to 75 kPa. Combining both a conformable cushion and lateral pressure reduced peak von Mises stresses to 25 kPa. The ratio of peak lateral pressure to peak under-body pressure was shown to regulate deep tissue stress better than under-body pressure alone. By optimising the magnitude and position of lateral pressure, tissue deformations can be reduced to that induced when suspended in a fluid. Our results explain the lack of efficacy in current support surfaces and suggest a new approach to designing and evaluating support surfaces: ensuring sufficient lateral pressure is applied to counter-act under-body pressure.


S1 Analysis of pressure distributions
The surface pressure induced when seated on a cushion follows a characteristic shape (Fig   1a): there is a narrow peak directly beneath the ischial tuberosity, occupying only a small region of the contact area. Pressure as a function of angle from the z-axis (Fig 1 b) is adequately described using a gaussian function: where is the swept angle between the vertical and the surface position, controls the spread of the curve and is the peak pressure magnitude. Non-linear least squares fitting (using the curve_fit function of the scipy module) was used to fit the parameters for each of the three cushion types (Table 1).
2 Fig 1. a Each of the cushions modelled in section 2.2 produces a similar pressure distribution at the skin surface: There is a peak directly beneath the ischial tuberosity (θ = 0), which drops to zero at the periphery of contact. Here, pressure is plotted as a function of the swept angle between the vertical and the position. A gaussian function provides a good fit for this distribution. b A schematic showing the lateral and under-body surface pressures. c The surface pressure induced when suspended in a fluid (dotted line) is relatively constant from each direction compared to the pressure profile when seated on a cushion (coloured lines). The magnitude of pressure varies substantially with depth, and even at 6 m below the surface, all surfaces are exposed to a pressure greater than that induced by a stiff cushion. When a pressure field representing 10 m submersion is compared to one representing pressure at the surface, the dilatational stress in the tissue increases (from 17kPa at 0m to 243kPa at 10m), but the deviatoric stresses are unchanged.
d Both pressure re-distribution (increasing α) and applying lateral pressure (increasing P L /P V ) reduces the peak pressure (top). Applying lateral pressure mimics the hydrostatic loading distribution more effectively than redistributing pressure (middle). The effective load-bearing area (area experiencing more than 50% of the peak pressure value) is increased more with lateral pressure than with re-distribution (bottom). e By optimising the magnitude and location of lateral pressure, the pressure profile around the soft tissue can accurately mimic that of suspension in a fluid (hydrostatic pressure).

Pressure distribution while suspended in a fluid
Suspension in a fluid can be regarded as a best-case scenario for load-bearing 20 . In this case, the pressure distribution is given as: where is density (997 for water), g = 9.81 , ℎ 0 is the depth of submersion from the fluid surface to the model centre and is the outer surface radius (130 ). The shape of the distribution remains constant as depth is increased, while the magnitudes of the pressures increase (Fig 1c). The dilatational stress within the soft tissue increases (from 17kPa when h0=130mm to 243kPa when h0=10130mm ). In contrast, deviatoric stresses (von Mises) do not change at all as depth is increased.

Pressure re-distribution vs pressure equalisation
We modelled the introduction of a lateral pressure equalisation device by applying a new gaussian term, offset from vertical by angle 0 . In these equations, and are the vertical and lateral pressure peak magnitudes, and control their spread, and 0 controls the lateral peak location (Fig 1b). Supplementary   figure 1d shows that the ideal pressure profile (that of suspension in a fluid) is best achieved by applying lateral pressure. Taken from a different perspective, an objective of support surface design can be seen as trying to maximise the area of contact between the soft tissue and the cushion. Fig 1b shows that applying a small amount of lateral pressure increases the effective load bearing area 1 far more than redistributing under-body pressure.

Scaling pressure distributions
Once the shape of ( ) was described from any of the sections above, it was scaled such that it exerted a net force in the y-direction of 200 N, i.e. to support body force . The force in the z direction acting on an infinitesimal area of a sphere of radius is = ( ) ⋅ cos( ) , can be parameterised as = 2 sin( ) , where is the polar angle and the azimuthal angle. The total force in the z direction is then: = ∫ ∫ 2 0 2 0 ( ) ⋅ cos sin = 2 ∫ 0 ( )sin(2 ) .