Estructura de El Sistema (las tres esferas)

distal void volumes

In order to investigate the hypothesis outlined in Chapter 2, the first step was to decide on a suitable distal void volume. The volume should be of a sufficient size, such that when added to a standard socket, there would be significantly reduced within-gait-cycle fluctuations in in-socket air pressure, compared to the standard socket configuration.

In order to define the distal void volume, a number of assumptions were made. Firstly, it was assumed that the residuum ‘pistons’, i.e. moves up and down within the socket as a result of loading and unloading during gait. As the residuum moves up the empty volume at the distal end of the socket is assumed to increase; conversely, as the residuum moves down, the empty volume at the distal end of the socket should decrease accordingly. A simple model was developed to guide the selection of the volume, as shown in Figure 3.1.

Standard protocol tends to define the relative residuum/socket displacement, under five different loading conditions; correspondingly, we therefore define the relevant variables associated with each condition below:

Table 3.1: Definitions of variables.

Loading condition

Distance from distal end of residuum to distal end of socket

Distal void volume

In-socket air pressure Single Limb Support

(SLS) F0

d0 V0 P0

Double Limb Support (DLS) F1

d1 V1 P1

Un-Loaded (UL) F2 d2 V2 P2

30N tensile force F3 d3 V3 P3

48 Figure 3.1 shows a schematic of a socket and residuum. It was assumed that, at a defined maximum load (SLS, F0) there remains a non-zero distance between the

distal end of the residuum and the interior socket wall and hence a non-zero distal volume.

Figure 3.1: Schematic of residuum displacements relative to socket.

Relevant data relating to the displacement of the residuum within the socket during prosthesis usage was limited although Brunelli et al (2013) (35) presented usable data7 _{on pistoning under relative loads observed in a trans-tibial amputee with a}

SSSS (Figure 3.2 and Figure 3.3). The displacement of the socket relative to the residuum was defined as zero under the SLS condition (see Table 3.1). Relevant data points for displacement at -405 N (DLS) and 90N (F4) were estimated based

on linear fits to the experimental data (Figure 3.2). However, DLS (F1) was calculated from SLS (F0) and UL (F2). Also, 90N tensile load (F4) was extrapolated from UL (F2) and 30N tensile load (F3).

Figure 3.2 shows the amount of residuum displacements while applying different loads and using SSSS in trans-tibial sockets.

49 Figure 3.2: Load-displacement data from Brunelli et al 2013 (35)8_.

Figure 3.3 shows an example of loading conditions during experiment.

Figure 3.3: Loading cases from Brunelli et al 2013 (35). Left – SLS; middle - UL; and right – 30N tensile load.

8 _{In this study, the results of SSSS with sleeve suspension was considered. The reason was}

using the Limb-Logic Communicator will require a sleeve suspension to seal the system, in the following main study.

50

Having identified the displacement of the residuum relative to the socket during key points of the gait cycle, the next stage of the specification process was to develop a displacement-distal void volume relationship.

To begin with, we made a basic assumption that the residuum could be considered as approximately circular in cross section in the distal section of the socket. Therefore, changes in distal void volume during pistoning would be approximately equal to the cross-sectional area of the residuum multiplied by its displacement relative to the socket, outlined in the section above.

As described in Appendix A, models from a laser-based scanner system of 7 previously captured trans-tibial residuums, as well as information on usual prosthetic practice were used to estimate:

a) The average cross sectional area and;

b) The range of initial (unloaded) distal air gaps (V2) built into typical trans-tibial

amputee sockets.

The mean cross-sectional area was 0.006 m2 _{and hence we could assume that the}

change in volume with pistoning could be described as:

∆𝑉 = 0.006 ∗ 𝑑 (2) This relationship allowed for an estimation of distal void volume, as a function of initial distal void volume (V2) and displacement of the residuum within the socket.

The findings described in Appendix A suggest a typical initial (unloaded) air gap volume, V2 is around 0 - 60 ml.

51 Table 3.2: Effects of the initial distal void volume (V2) on the distal void volume

V0,1,3,4 over gait. V2 (mL) V0 (mL) V1 (mL) V3 (mL) V4 (mL) 50 5 27 79 138 60 15 37 89 148 100 55 77 129 188 150 105 127 179 238 200 155 177 229 288

Finally, a known in-socket air pressure value at a specified volume was required. It was assumed that P1 was equal to atmospheric pressure (101 KPa). This

assumption was based on the clinical practice of amputees pressing the manual expulsion valve to equalise in-socket pressure with atmospheric pressure while standing on both lower limbs9 _(DLS).

Assuming adiabatic conditions apply and no air leakage from the system, we can assume that Boyle’s law applies:

𝑃1 𝑉1 = 𝑃0𝑉0 = 𝑃4 𝑉4 (3)

We can therefore use the known pressure P1 and volumes, V1,0,4 (as a function of

V2 and d) to calculate the maximum pressure change (P4-P0) over gait for a range

of values of V2, as shown in Figure 3.4.

Figure 3.4 shows the effects of the initial distal void volume (V2) on the in-socket air

pressure change (ΔP) over gait. ΔP is calculated as the difference between P4 and

P0.

52 Figure 3.4: Effects of the initial distal void volume (V2) on the in-socket air

pressure change (ΔP) over gait.

Based on the above, assuming an original V2 (small) of around 0 - 60 ml 10, then an

additional 100 ml (to make V2 (large) =~100 -160 ml) was selected to give a reasonable

likelihood of a significantly reduced in-socket air pressure change over gait.