Purpose: To perform activities of daily living (ADL) , people with lower limb amputation depend on the prosthetic socket for stability and proprioceptive feedback. Poorly fitting sockets can cause discomfort, pain, limb tissue injuries, limited devic e usage, and potential rejection. Semi -passively controlled adjustable socket techno logies exist, but these depend upon the user’s perception to determine safe interfacial pressure levels. This paper presents a framework for automatic control of a n adjustable transtibial prosthetic socket that enables active adaptation of residuum -socket interfacial loading through localized actuators, based on soft tissue injury risk estimation. Method: Using finite element analysis, local interfacial pressure vs. compressive tissue strain relationships were estimated for thre e anatomical actuator locations, for tissue injury risk assessment within a control structure. Generalized Predictive Control o f multiple actuators was implemented to maintain interfacial pressure within estimated safe and functional limits. Results: Controller simulation predicted satisfactory dynamic performance in several scenarios, based on previous related studies. Actuation rates of 0.06 – 1.51kPa/s with 0.67% maximum overshoot, and 0.75 – 1.58kPa/s were estimated for continuous walking, and for a demonstrative loading sequence of ADL , respectively. Conclusion: The developed platform could be useful for extending recent efforts in adjustable lower limb prosthetic socket design, particularly for individuals with residuum sensory impairment . Keywords Adjustable prosthetic socket, Finite element analysis, Generalized Predictive Control, Interface pressure control, Transtibial 2 1. INTRODUCTION The socket is the fundamental interface between a person with an amputation (PWA) and her/his prosthetic, and hence the first element of the device that determines their perception of comfort. It is responsible for direct transfer of the ground reacti on force (GRF) to the musculoskeletal system during activities of daily living (ADL). The contact stresses at the interface between the prosthetic socket and the residuum skin, plus the strain of the underlying soft tissues greatly determine comfort and tissue injury risk. Poorly fitting sockets can cause discomfort and pain, and potentially limit prosthetic usage due to vascular occlusion, skin breakdown and tissue injuries such as degenerative stump ulcers, which in severe cases could lead to re -amputation or life threatening conditions [1]. Pressure -related tissue injury may initiate in the skin and advance to the underlying soft t issue layers, or begin in the internal tissues close to bony prominences and develop towards the skin surface [2], known as Deep Tissue Injury (DTI). Generally, prosthetic sockets are bespokely fitted by specialized clinicians, and require iterative replacement to accommodat e changes in residual limb volume and shape [3]. Standard transtibial socket designs present unmet challenges affecting wearer comfort. Some individuals experience pistoning [4], longitudinal movement between the prosthe tic socket and the residual limb during cyclic loading. Others report sensitivity to residuum volume and shape changes, with up to 8.5% volumetric fluctuation per hour during a typical day [5, 6] . A solution may be socket designs that allow user -operated [7] or automated socket fit adjustment [8–13] or have spatially variable socket wall impedance [14], for reduction of interfacial pr essure gradients that cause discomfort, and accommodation of diurnal and long -term residuum changes. The Infinite SocketTM (LIM Innovations, CA, USA), Socket -less SocketTM (MartinBionics, OK, USA), and RevoFitTM (Click Medical, CO, USA) are manually adjustable commercially available devices. Socket size adjustments are made to flexible socket frame struts using straps, laces and clamps, or to moveable cabled panels introduced to a conventional socket. They offer benefits of easy within -day comfort -based adjustments by the user. The socket biomechanical functional outcomes and the impact of adjustments on sub -dermal tissues are, however, unknown. Also, the literature reports powered user -controlled [7], and automatically ad justable interventions aiming at reducing interfacial stresses [8, 10, 13] or compensating for limb volume fluctuations [9], or both [11, 12] . The adjustments are made using m ovable socket panels and motoriz ed cables [7], or actuatable intra-socket bladders and interface pressure sensors [8–13]. These socket designs might be desc ribed as passive and semi -passive, aiming to maintain singular pre -determined user comfort and fit levels, as opposed to adjusting throughout dynamic, cyclic loading. Furthermore, they do not consider the internal tissue strain arising from the interfacial loading, which is the established predictor of DTI [15, 16] . The safety of these designs may be further improved by active control based on interfacial sensor measurements and tissue injury indicators [17], to address the cumulative effect of longer -duration loads, and to avoid the risk of users over - tightening the socket and inadvertently causing large strains of th e residuum tissues beyond safe levels, especially where vascular pathologies may diminish sensation. Interface pressure is practically measur able but it does not necessarily correspond with high tissue strain [18], or directly indicate DTI risk [2]. The purpose of this study is to describe a framework for developing an adaptive socket system that incorporate s an actuatable residuum/socket interface to actively modulate interfacial pressure within estimated safe tissue strain levels. Fi nite element analysis (FEA) was used to predict the relationships between internal strain and socket -limb interfacial pressure at specific anatomical regions of the residual limb, at several instants during the gait cycle. These relationships were used as training data for tissue injury risk assessment to determine control targets for socke t interface actuation. Generaliz ed Predi ctive Control (GPC) was simulated in MATLAB (MathWorks®, USA), and optimized to minimiz e cumulative residuum tissue injury risk. 2. METHODS A. Finite Element Analysis A previously reported FE model [19] was adapted for this study ( Fig. 1), to evaluate the relationships between predicted internal tissue strain and interfacial pressure at three anatomical regions of interest (ROI), to provide training data for a ctuator control b ased on minimiz ing tissue damage risk. Briefly, the model was developed from MRI scans of a person with unilateral transtibial amputation wearing a gel liner, segmented and meshed in Scan -IP software (Scan -IP N-2018.03, Synopsys Inc., USA) to represent liner, bones, soft tissue (combining muscles, skin and subcutaneous fat), patella and quadriceps tendons, and intra -articular structures. A socket model was generated by replicating the liner external surface up to the participant’s normal socket brim -line, and applying a non -uniform 0 to 2% cross -sectional area scaling factor about the residual tibia’s axis, to represent a simplified Total Surface Bearing (TSB) [20] design. Quasi -static 2D sagittal plane loading was applied to the model with a proximal force ( Fz), an anterior force ( Fx) and an extension moment ( My) (Fig. 1), for approximation of typical prosthetic use during the stance phase of gait [21]. The load values were 3 extracted from studies of dynamic load -cell data for unilateral transtibial p rosthesis users walking at self -selected speed [22, 23] . The applied quasi -static loads represented the heel strike, foot flat, mid stance, heel off and toe off stages of gait. The loads were applied across a circular region of nodes at the base of the socket whilst the model was constrained at the proximal cut surf ace of the femur and the quadriceps tendon. Fig. 1. A sagittal section of the FE model illustrating geometry, loading configuration and boundary conditions, plus the regions of interest for actuation : the patella tendon (PT), central posterior calf (PC) and tibia distal tip (DT). Estimates of pressure at the residuum surface an d internal strain within the soft tissue at the ROI were extracted from the model. 95th percentile values were used to avoid any single -node concentrations that may occur as artefacts of loading. The minimum principal strain, ε3, and maximum shear strain, γmax, were inspected. The predicted interfacial pressure -compressive strain relationships were used to build surrogate models for tissue injury risk evaluation for actuator control. B. Interface Actuation Model Suitable techniques for functional interface ac tuation within an active socket system should have measurable, easily interpretable and controllable mechanical and/or electrical parameters. In this study, liquid bladder socket inserts were implemented, conn ected to a controllable ideal pressure source, capable of delivering and maintaining the desired pressure level. This actuation method was modelled in the Simulink environment (MATLAB R2016a, MathWorks®, USA) as a hydro -mechanical transducer system. It was estimated as an ideal transducer with incompre ssible fluid, and Pascal’s law was applied assuming small fluid displacements. The pressure applied on the residuum surface at any instant is directly measurable using an interf ace sensor, and considered to be equal to the pressure in the fluid insert. Liquid socket bladders typically contain water as the primary medium [5]. The relevant variables used to model this actuator were derived from the properties of water, taken at 35°C, close to the average residuum skin temperature (34.1°C) after 30 minutes of treadmil l walking with a prosthesis [24] (Table I). TABLE I REPRESENTATIVE INTERFACE ACTUATOR PROPERTY MODELLING VALUES FOR WATER AT 35°C Property Value Density, ρ (kg.m-3) 993.7 Kinematic viscosity, ν (m2.s-1) 7.45 x 10-7 Bulk/Volume modulus, K @ atmospheric pressure (Pa) 2.24 x 109 Thermal conductivity, k @ 1 bar (W/m.K) 621.6 x 10-3 C. GPC Implementation for Interface Actuation A suitable control scheme for the adaptive socket system described in this study requires particular characteristics in order to 4 meet operational requirements: accommodation of multiple variables, sensors and actuator s, capability for real -time, bounded control, capability to estimate unobservable states, and capacity for disturbance rejection for elements external to the syst em, such as gait information and prosthe tic alignment effects. Generaliz ed predictive control is a model -based control method [25], which is widely adopted in industry due to its capability to handle multivariable, high model order and unstable open loop systems, dead time, and maintaining good stability margins [26, 27] . This control approach computes current control inputs based on anticipated future input demands and predicted model behaviour over a finite horizon, ny, into the future. The predicted output is derived from a plant model (1) and is dependent on the current measured variable and input. Matrix methods are used to recursively derive the equations for n-steps ahead prediction . At each sampling instant, a new control output prediction, y→k+1 (2) is computed based on anticipated future control targets, and the control input is adjusted accordingly. Level of model fidelity directly affects t he allowable number of reliable control moves, nu, at each step for dynamic performance optimiz ation during transients [27]. A(z) yk = b(z) Δuk (1) y→k+ 1 = HΔu→k+ PΔu←k-1+ Qy←k (2) where A(z) = a(z)Δ(z) and Δ(z) = 1− z-1, k is the current sample step, Δu is the vector of control input increments, and H, P, Q are the prediction matrices. Control inputs a re determined by minimiz ing a cost function, J, (3), (4) such that control action (5) and closed -loop performance minimiz e overall interfacial pressure magnitudes and tissue injury risk. This minimiz ation tends towards stability for a give n horizon and allows for optimiz ation to achieve a balance between adequate system sens itivity and the aggressiv eness of control action. Optimiz ation also involves application of a weighting constant, λ, that expresses the relative significance of control inputs compared to the tracking errors [28]. Only the first element, E1, in the future control increments vector Δu→k (the optimum input trajectory) is applied at each sampling instant . J = ∑e→k+ 1T e→k+ 1ny k=1+ λ∑Δu→kT Δu→knu k=1 (3) e→k+ 1 = r→k+ 1−y→k+1 where r is the vector of control targets, the safe target pressures at the residuum interface for each actuator location , generated from a tissue injury risk evaluation protocol described below . e denotes the vector of tracking errors. min Δu→kJ ≡ grad J (Δu→k) = 0 (4) Δuk = E1T (HTH + λI)-1HT [r→k+ 1−PΔu←k-1− Qy←k] (5) The input waveforms applied for simulating the adaptive socket system in Simulink® were determined from interfacial pressures arising from corresponding loading regimes, estimated using FEA. Residuum tissue injury risk due to loading was estimated by applying the surrogate models generated from the FEA , and a dynamic saturation block mo del that incorporated the sigmoid strain - time threshold curve published by Gefen et al. [16]. The dynamic saturation block model bound ed the range of the input signal to upper and lower limits, with the strain injury thr eshold [16] applied as the upper bound . The predicted strain upon socket donning determined the lower bound , to represent maintaining the socket suspended upon the residuum . Furthermore, as an initial step, an input signal of 600 kPa, about twice the maximum interfacial pressure value predicted for standard gait (Fig. 2A), was applied to generate estimates of local interfacial pressure -time safety thresholds for all ROI. The endurance limits for early and delayed onset tissue damage due to large compressive s trains are defined as within 0 – 63±37 minutes and 176 – 285±55 minutes, respectively [16]. The actuator plant m odel was converted into CARIMA (Controlled Auto Regressive and Integrated Moving Average) model transfer function of the form outlined in (1) [25, 27]. The controller was initiated at the pressure expected upon socket donning at the selected ROI, and the output sampl ing time was 15 seconds. Optimiz ation was carried out to meet design goals of fast rise time 5 and no overshoot, by examining the infl uence of the control weighting constant, λ, for satisfactory performance without over - aggressive actuation. Desirable control action w as defined as that which minimiz es overall pressure magnitudes, actuation rates and pres sure changes in order to minimiz e tissue strain injury risk, reduce the overall power consumption of the system, and in case large, fast actuations may cause wearer discomfort. Additionally, suitable values of the control horizon nu and the feedforward horizon na were determined by experim ent through control performance evaluation. na allows for identification of key future control target changes not covered within the control horizon. In designing for tar get tracking and control optimiz ation with GPC, an increase in λ demands increase in nu that in -turn may require an increase in na and/or ny. Large values of ny and na result ed in increased output deviation from the target, whereas large values of nu result ed in finer control moves per step and faster actuation. It was expected that values of ny, nu and na should vary across the ROI , due to distinct interfacial pressure -strain relationships, and between different locomotive modes. Fig. 2. An illustration of the adaptive prosthetic socket system concept. (A) Input gait loading signal , representative of pressure sensing at the residuum/socket interface for one gait cycle , 0 – 1 second . (B) Sagittal section of a 3D FEA model illustrating loading configuration, boundary conditions and actuator locations. (C) Estimated press ure-time injury risk thresholds , for 0 – 300 minutes, corresponding to the sigmoid strain -time curve [16]. (B) and (C) represent the tissue injury risk evaluation protocol utilizing biomechanical FEA output predictions of localized interfacial pressure -strain relationships to determine control targets for interface actuation . (D) GPC system for maintaining safe tissue strain levels by adaptive actuation of intra-socket liquid bladder s. (E) Exemplar control output at the posterior calf location (0 – 300 minutes ). P - interfacial pressure, t - time. The feasibility and performance of the GPC formulation for the proposed interface actuator model was firstly assessed for a standard gait input waveform ( Fig. 2A) corresponding to the forces and moments across the socket -tibia-knee joint construct [29]. The durations of stance and swing phases during one gait cycle were determined as 0.72 and 0.48 seconds, respectively, as reported for persons with unilateral transtibial amputation [30]. The input sampling rate was 50 Hz, to preserve at least up to 99% of gait signal power (~15 Hz) [31]. The output prediction horizon ny was chosen as between 30 and 100 minutes, i.e. 120 – 400 sample steps (ss), corresponding to the short loading exposure period after which there is notable decrease in muscle tissue comp ressive strain endurance [16]. Preliminary work indicated variation of λ in increment steps of one order of magnitude from 10-2 to 102 across all ROI for optimiz ation. Also, close resemblance was noted in the estimated GPC safe target pressure profiles at the PC and PT actuator locations, with cyclic loading in timeframes unde r 2 hours. nu values of 10, 20, a nd 10 sample steps (i.e. 2.5 min, 5 min , and 2.5 min ) were selected for the PT, PC and DT actuator locations, respectively, whereas the na values were 20, 30, and 100 sample steps (i.e. 5 min, 7.5 min , and 25 min ). A seco nd assessment was carried out to examine the efficacy and performance of GPC for a demonstrative loading sequence of some typical ADL that might be performed by active prosthesis users. These included donning the prosthesis, 30 minutes sitting, 15 minutes standing, 45 minute s walking at a comfortable self -selected pace, and finally sitting again for 30 minutes. For the FEA to determine inputs for this loading scenario, the user was considered to be a person with unilateral transtibial amputation weighing approximately 90 kg [22]. The output prediction horizon ny was selected between 15 – 30 minutes. Preliminary analysis dictated variation of λ from minimum 0.1 to maxim um 10 across all ROI for optimiz ation. nu values of 20, 20, and 15 sample steps (i.e. 5 min, 5 min, and 3.75 min) were selected for the PT, PC and DT actuator locations, respectively, whereas the na values were 30, 25, a nd 50 samp le steps (i.e. 7.5 min, 6.25 min , and 12.5 min ). 6 3. RESULTS A. Finite Element Analysis For the three loading cases, the local interfacial pressure estimated at actuator locations ranged from 25.5 – 155.1 kPa, 54.9 – 112.1 kPa and 42.3 – 116.1 kPa, for the DT, P C and PT locations, respectively. Compressive strain in the soft tissues ranged between 40.7 – 81.2%, 56.3 – 85.3% and 47.4 – 72.2%, while the shear strain was between 6.1 – 15.1%, 7.7 – 17.1% and 4.6 – 9%, for the DT, PC and PT locations, respectively. Va riations in the pressure and strain estimates were consistent across the loading cases throughout the gait cycle. Fig. 3 shows the predicted distributions of compressive strain on a sagittal plane section view through the tibia, and interfacial pressure for the five gait instances, for one loading case. During h eel strike to mid stance, areas of high compressive strain were the lateral femoral epicondyle, fibula head, tibial tuberosity and anterior distal tibia. For heel off and toe off, the strain was concentrated at the patella tendon, the patella and the tibia distal tip. Areas of high interfacial pressure were the tibial tuberosity, anterior distal tibia, proximal posterior calf close to the popliteal fossa and the fibula head d uring heel strike to mid stance, and the patella, patella tendon, central posterior calf and fibula hea d during heel off and toe off. Regression analysis of predicted interfacial pressure -compressive strain relationships, showed a linear relationship (R2 = 0.9) at the PC location, but more complex relationships at the DT and PT locatio ns (Fig. 4), which were described with cubic splines. Moreover, at the DT location, predicted compressive and shear strains were highest around the load -acceptance and push -off gait stages, whereas at the PC and PT locations the strains increased from heel strike to toe off . Fig. 3. TOP: Sagittal plane section views through the tibia showing the internal residuum compressive strain and, BOTTOM: the full field residuum interface pressure estimates during five key stages of stance for one loading case [22]. B. GPC Performance Evaluation Estimated pressure safety limits to avoid early onset of tissue damage were 54.8 – 51.3 (± 10.8) kPa, 50.8 – 49.1 (± 4) kPa and 68.4 – 57.6 (± 4.1) kPa at the PC, PT and DT regions, respectively, corresponding to the sigmoid strain -time curve [16]. The longer term limits for delayed onset were 27.6 – 24.4 (± 12.5) kPa, 38.6 – 37.1 (± 5.9) kPa and 24.5 – 27.2 (± 7.8) kPa and, at the PC, DT and PT regions, respectively ( Fig. 5a, Fig. 6a, Fig. 7a). GPC output profiles and actuation control performance measures for a standard continuous gait waveform at the three ROI are presented in Fig. 5b, Fig. 6b, Fig. 7b, and Table II. Larger values of λ resulted in smaller, slower actuations, and increased control output deviation from the target. For timeframes below 2 hours, control acted to maintain interfacial pressures below the safety threshold at all ROIs. After this time, safe target tracking was maintained at the PC and PT locations, but overshoots of 0.67 – 4.15% were predicted at the DT location. For the simulations of GPC for a loading sequence of typical ADL, peak actuation magnitudes and rates were predicted where the largest changes in t arget pressure occurred, during transitions from sitting to standing and walking to sitting actions for the PC and PT locations, and during transitions from standing to walking and walking to sitting actions for the DT location ( Fig. 5c, Fig. 7 6c, Fig. 7c). Fig. 4. Interfac e pressure vs. residuum tissue strain relationships at the posterior calf, distal tibia and patella tendon locations, showing c ombined results for all the three loading cases applied. HS - Heel Strike, FF - Foot Flat, MS - Mid Stance, HO - Heel Off, TO - Toe Off 8 Fig. 5. TOP: (a) Estimated interface pressure safety threshold, and GPC safe target pressure plot s for a standard continuous ambulation waveform at the posterior calf location. BOTTOM: GPC performance for a liquid bladder actuator for different values of the control weighting constant, λ, for (b) a standard continuous ambulation waveform, and (c) a demonstrative loading sequence of typical ADL, δ = 6.25 minutes and denotes the minimum delay, na, that may be required between loading input measurements and controlled actuation in practical applicati on. ss - sample steps. TABLE II SUMMARY OF SIMULATED GPC OUTPUT PERFORMANCE FOR A LIQUID BLADDER ACTUATOR BY RESIDUUM LOCATION FOR A STANDARD CONTINUOUS GAIT WAVEFORM , AND A DEMONSTRATIVE LOADING SEQUENCE OF TYPICAL ADL. BLUE SHADI NG INDICATES RESULTS WITHIN PREFERRED ACTUATION RATE RANGE . Actuator location Peak Actuation Pressure Magnitude (kPa) Peak Actuation Rate (kPa/s) Continuous Gait λ 0.01 0.1 1 10 100 0.01 0.1 1 10 100 PC 14.29 12.16 5.12 0.95 0.40 0.95 0.81 0.34 0.06 0.03 PT 5.42 4.28 1.68 0.38 0.33 0.36 0.29 0.11 0.03 0.02 Rise time (seconds) DT 43.4 44.5 65.6 134.7 300.0 4.01 3.71 1.51 0.51 0.20 ADL Loadi ng Sequence λ 0.1 0.5 1 5 10 0.1 0.5 1 5 10 PC 21.19 14.48 11.21 5.57 4.02 1.41 0.97 0.75 0.37 0.27 PT 29.39 20.08 15.55 7.59 5.43 1.96 1.34 1.04 0.51 0.36 DT 34.76 23.74 18.38 8.95 6.39 2.32 1.58 1.23 0.60 0.43 Actuator location Maximum Error (%) Maximum Overshoot (%) Continuous Gait λ 0.01 0.1 1 10 100 0.01 0.1 1 10 100 PC - - - - - 0 0 0 0 0 PT - - - - - 0 0 0 0 0 DT - - - - - 0 0 0 0.67 4.15 ADL Loadi ng Sequence λ 0.1 0.5 1 5 10 0.1 0.5 1 5 10 PC 11 31 40 58 63 0 0 0 0 0 PT 20 54 71 101 109 0 0 0 0 0 DT 33 91 119 170 184 0 0 0 0 0 9 Fig. 6. TOP: (a) Estimated interface pressure safety threshold, and GPC safe target pressure plot s for a standard continuous ambulation waveform at the patella tendon location. BOTTOM: GPC performance for a liquid bladder actuator for different values of the control weighting constant, λ, for (b) a standard continuous ambulation waveform, and (c) a demonstrative loading sequenc e of typical ADL, δ = 7.5 minutes and denotes the minimum delay, na, that may be required between loading input measurements and controlled actuation in practical application. ss - sample steps. 4. DISCUSSION This study presents development of a framework for an adaptive transtibial prosthetic socket that enables active interface actuation to modulate tissue strain within estimated safe levels. Local interfacial pressure and compressive strain estimates through out the gait cycle were observed to be comparable to related studies [21]: the distal anterior and proximal posterior parts of the residual limb were predicted to be loaded around heel strike and unloaded around toe off, a s a result of socket flexion and extension moments. The opposite loading trend was predicted at the proximal anterior and distal posterior locations ( Fig. 3). Peak soft tissue compressive strains were estimated as 81.2%, 85.3% and 72.2% at the DT, PC and PT regions, respectively, consiste nt with maxima reported in similar FEA studies [32]. Furthermore, peak shear strain of 15.1% was predicted at the di stal tibia, comparable to other published predictions [33]. These results provide some corroboration to the model predictions, though there will of course be considerable inter -person variability in the se measures, as well as recogniz ed inconsistency in FEA predictions across studies attributed to differences in model structures and levels of sophistication, material properties, loading regimes, and the methods applied for evaluating model outputs [34]. Numerous previous studies have quantified prosthesis -limb normal interfacial pressures and shea r stresses in efforts to optimiz e lower limb p rosthetic socket design for user comfort and the quality of socket fit. An important finding of the current study is that relatively low interfacial pressures, 27 – 55 kPa, can result in large local internal compressive strains, above 50% ( Fig. 4) indicating theoretical DTI risk for weight -bearing periods longer than 1 hr [16]. This observation is particularly important for prosthetic socket fitting for users with peripheral neuro -deficiency due to vascular diseases, who may lack adequate sensorial alert to onset of tissue damage. Other studies have also shown that interfacial pressures alone are misleading for determining susceptibility t o DTI, owing to inter -person variability and distinct geometry of bones and soft tissue layers, and tissue properties [35], and high interfacial pressures may not necessarily correspond to high internal tissue strain. Portnoy et al. [18] reported 65 kPa pressure against 73% compressive strain for one participant, and 92 kPa against <35% strain for another. A different study investigating 10 impact of permanent wheelchair use reported peak pressure of 18 ± 3 kPa under the gluteus ischial tuberosity against peak strain of 74 ± 7% in the gluteus muscle [36]. Fig. 7. TOP: (a) Estimated interface pressure safety threshold, and GPC safe target pressure plot s for a standard continuous ambulation waveform at the distal tibia location. BOTTOM: GPC performance for a liquid bladder actuator for different values of the control weighting constant, λ, for (b) a standard continuous ambulation waveform, and (c) a demon strative loading sequence of typical ADL, δ = 12.5 minutes and denotes the minimum delay, na, that may be required between loading input measurements and controlled actuation in practical application. ss - sample steps. In the prese nt study, GPC co ntrol was simulated with a cost function optimization to minimiz e residuum tissue injury risk with a liquid bladder actuator. For the three actuator locations considered, interface actuation maintained pressure within the es timated safety t hresholds, and above the nominal levels predicted upon socket donning alone, which was used as prediction of ensuring prosthesis suspension during swing ( Fig. 5 – Fig. 7). According to related studies evaluating user outcomes for the elevated vacuum socket suspension system, over 72% of users reported preferred variations in vacuum of 3.4 – 6.8 kPa (≈1 – 2 inHg) during ambulation [37]. Consequently, in the current study, estimates of preferred actuation performance for continuous walking were indicated as up to 0.34 kPa/s, 0.36 kPa/s and 1.51 kPa/s for the PC, PT and DT locations, respectively, with a maximum oversh oot of 0.67% at DT, and similarly, 1.41 kPa/s, 1.34 kPa/s and 1.58 kPa/s with no overshoot, for the loading sequence of typical ADL (Table II). Additionally, during continuous walking, cyclic control action observed at the PC ( Fig. 5b) and PT locations ( Fig. 6b) for timeframes under 2 hours may be beneficial for enhancing blood flow to the residuum tissues [38]. This study provides local interfacial pressure -time safety threshold estimates for the three actuator locations, generated based on an existing strain injury threshold [16]. Though external validity of these interfacial pressure thresholds is limited owing to different input data and conditions between the two studies, they offer some novel representative approximati ons for assessing injury risk of residuum tissues as a result of in -socket loading. Some comparable studies on self -adjusting sockets involving actuatable magneto -rheological fluid socket inserts [12], an air -cuff liner [10], and intra -socket flu id bladders [13] reported improved performance compared to conventional sockets [39] with regards to measured peak interfacial pressure – 70 kPa, 57 kPa and 72 kPa versus 170 kPa, 83 kPa and 79 kPa, at the patella tendon, central posterior calf and distal residuum regions, respectivel y. The results of the current study indicate that although self -adjusting sockets may show reduced pressures compared to standard sockets, additional measures may be necessary to sufficiently eliminate the risk of DTI in residuum tissues under long -term lo ading (Fig. 5a, Fig. 6a, Fig. 7a). 11 For the sequence of typical ADL, the GPC formulation based on future targets enabled smooth transitions between actions, avoiding large instantaneous pressure changes. Control outputs were below estimated pressure thresholds and errors did not represent poor control action, but rather could be applied as criteria for select ing control parameters for multi -modal prosthetic device usage for transitioning between different locomotion modes. For real implementation, explicit programming of a minimum delay equivalent to na between current interfacial pressure measurements and controlled actuation would be essential to enable timely detection of imminent control target changes based on user movements ( Fig. 5c, Fig. 6c, Fig. 7c). This study indicates that GPC can be applied to give satisfactory interface a ctuation performance and minimiz e tissue damage risk for an adaptive prosthetic socket with multiple in -socket actuators, in several scenarios. Control parameters can be sele cted which would be predicted to meet operational requirements and avoid deviations into high tissue damage risk, for an exemplar liquid bladder actuator model. Limitations The present FEA study involved quasi -static loading at several gait stages, an analysis simplification justified by the slow walking cases of interest. Also, only a limited set of prosthetic loading cases were applied, taken from published literature . Further studies involving full dynamic analysis, additional prosthetic l oading scenarios and characteriz ation of effects of different walking speeds could generate more robust surrogate models for DTI risk evaluation, and ideally the load cases would match the indivi dual from whom the modelling geometry was obtained. Moreover, the study only considered three anatomical regions of the transtibial residuum for in -socket actuation. Additional actuator locations and combinations should be evaluated to assess possible requirement of a more complex control structure [40]. Furthermore, the FE analysis in the present study was based on a single model. In a proposed practical application of this study, conducting person -specific, image -based FEA for each candidate patient would be prohibitively expensive. Instead, such a control framework might be tuned using simpler models [41] based on linear ultrasound measurements [42] of soft tissue coverage thickness over bone at key residuum regions, ultrasound elastography [43] or indenter measurements of skeletal tissue compliance [44], and population -driven techniques assessing effects of different residuum morphologies and geometries on biomechanical measurements [19]. Extrapolation of the predictions obtained in the current study is further limited by several model simplifications and assumptions. The present mo del is somewhat simple . More advanced models might be compared, considering the effects of different tissue continuum material models, multi -layered models with distinct tissue layers or discrete muscle sets, residuum interface boundary conditions consider ing the influence of temperature and humidity, and personalised tissue structures and mechanical properties . This is of particular importance because the tissue injury prediction process considers strain [45], and s uch studies would be useful for defining more detailed pressure -strain data capturing individual variability in tissue biomechanical response to loading. The current study is a theoretical analysis of GPC feasibil ity, and practical implementation may be different. GPC applies unbiased predictions in the steady state, and to improve accuracy for a physical implementation low -pass filters may be required to adequately handle additional impact of prosthetic alignment and other biomechanical gait effects, and measurement noise. This may enhance disturbance rejection by reducing input signal sensitivity to high frequency noise, and improving output predicti on accuracy by eliminating bias due to past random changes [27]. Also, the control optimiz ation parameters and constraints applied here may differ for a practical implementation due to system losses and gait effects. The study demonstrates that interface a ctuation performance measures can be manipulated within the GPC formulation to achieve various control objectives, and trade -offs between them. Studies considering end -user feedback are required to assist in prioritiz ing actuation performance metrics based on comfort levels, and to perform multi -objective optimiz ation to identify minimal values for actuation rates and pres sure changes . Design validation entailing prototyping with embedded actuators, including electroactive polymers ( EAPs ) for example, and interface sensors is required to robustly test the described socket concept. Development studies could be extended to further evaluate GPC performance measures for variation of actuator sites, multi -modal capacity for transitioning between different locomotion modes, or within multi -level control strategies with gait recognition, for establish ing a pathway to clinical adoption. 5. CONCLUSION This study presents a framework for controlling a self -adjusting transtibial pr osthetic socket based on minimiz ing an estimated residuum soft tissue injury risk. The study establishes the use of FEA to generate socket adjustment control training data for DTI risk assessment. It further demonstrates the feasibility of the GPC formulation for adaptive int erface actuation control minimiz ing tissue injury risk in several scenarios, and the infl uenc e of a cost function optimiz ation on actuation performance of intra -socket actuators. The presented platform could be useful for extending recent efforts in adjustable lower limb prosthetic sockets . 12 ACKNOWLEDGEMENT S Funding: This work was supported by: FMM: the Commonwealth Scholarship Commission UK under Ref. No. CA -16-28. JWS: the University of Southampton’s EPSRC Doctoral Training Program under Ref. No. EP/M508147/1 . ASD: the Royal Academy of Engineering UK under Ref. No. RF/1 30. CONFLICT OF INTEREST AND ETHICAL APPROVAL None of the authors has any conflict of interest to declare. Ethics permission obtained through the University of Southampton secondary data ethics approval,