Residual limb volume changes in transfemoral amputees

This study constitute the rst attempt to systematically quantify residual limb volume changes in transfemoral amputees. The study was carried out on 24 amputees to investigate changes due to prosthesis dong, physical activity, and testing time. A proper experimental set-up was designed, including a 3D optical scanner, to improve precision and acceptability by amputees. The rst test session aimed at measuring residual limb volume at 7 time-points, with 10 minute intervals, after prosthesis dong. This allowed for evaluating the time required for volume stabilization after prosthesis removal, for each amputee. In subsequent sessions, 16 residual limb scans in a day for each amputee were captured to evaluate volume changes due to prosthesis removal and physical activity, in two times per day (morning and afternoon). These measurements were repeated in three different days, a week apart from each other, for a total of 48 scans for each amputee. Volume changes overtime after prosthesis dong showed a two-term decay exponential trend (R 2 = 0.97), with the highest change in the initial 10 minutes and an average stabilization time of 30 minutes. A statistically signicant increasing effect of both prosthesis removal and physical activity was veried. No differences were observed between measures collected in the morning and in the afternoon.


Introduction
DESPITE the advancements in the prosthetic design and the enhancements concerning wearable robotic platforms 1 , 2 , most amputees still complain about discomforts related to the prosthetic physical humanmachine interface (pHMI), i.e. the socket [3][4][5][6] . An optimal prosthetic socket must be comfortable for the user, while ensuring stable tting and proper load transmission, especially in lower limb prostheses. These requirements are conditioned by residual limb volume uctuations. In fact, residual limb volume changes can compromise the prosthesis tting which can, in turn, cause relative socket-residual limb movements, alter the stress distribution on tissues, involve dermatological problems (i.e., ulcers, irritations, vascular occlusions, dermatitis, blisters etc) and pain for the user 3 , 7 .
Such volume uctuations are particularly relevant during acute and post-acute operative recovery periods (i.e., 12-18 months after amputation) [8][9][10] , albeit they occur in stabilized amputees (i.e., + 18 months since amputation) as well 10 . Changes of the residual limb volume are mainly due to body weight increase and peripheral vascular diseases (e.g., increased blood pooling in venous compartment, excessive arterial vasodilatation and changes in interstitial uid volume) 10 . The prosthesis suspension system and the socket size can further exacerbate these phenomena. As matter of facts, earlier studies have documented an increased volume after prosthesis do ng when vacuum suspension systems are used; noticeably, the rate of variation depends on the applied vacuum pressure [10][11][12][13] . On the contrary, suspensions not based on vacuum, e.g., pin locking systems, seem to mainly cause volume reductions after prosthesis removal 14 . Moreover, physical activity, diet, weather conditions, comorbidities, and several other factors can impact these changes 15 . All in all, these factors involve a rate of variation in volume ranging from − 11% to + 7% in transtibial amputees 16 .
Despite the widely documented variation of residual limb volume in transtibial amputees, to the best of our knowledge, no reliable data pertaining to transfemoral amputees are available in literature (seeTABLE S1in supplementary material). The skewed distribution of studies toward the population of below-knee amputees can be ascribed to different reasons such as the more straightforward measurement set-up and the more compelling need to reduce pain in bony regions. Speci cally, an improper tting of the prosthetic socket may involve high stresses on soft tissues more frequently in transtibial amputees than in transfemoral ones, because of the wide bony prominences at the residual limb-socket interface 3 . On the other hand, the larger volume of soft tissues in transfemoral residual limbs can be subjected to even larger uctuations 17 , highly affecting comfort and tting of the prostheses. Accordingly, volume uctuations in the residual limb of transfemoral amputees deserve to be in depth analyzed to provide suitable reference values for the design of novel prosthetic sockets.
This work aims at lling this gap in the state-of-the-art and to quantify the volume uctuations occurring in the transfemoral amputee population. Volume changes due to prosthesis do ng and physical activity were investigated on 24 enrolled amputees, both in the morning and in the afternoon, resulting in 16 scans per day for each amputee. The protocol was repeated three times in three different days, a week apart from each other, resulting in 48 scans for each amputee. We envisage that the outcomes of this study will help in identifying the requirements for the design of smart adjustable sockets, similarly to what has been done for transtibial prostheses 18 .

A. Subjects
This study was approved by the ethical committee "Area Vasta Emilia Centro, Regione Emiglia-Romagna CE-AVEC" (protocol ID: P-PPRAI1/2 − 01, CE protocol reference number: 105/2018/OSS/AUSLBO, date of registration: 11/05/2018; ClinicalTrials.gov ID: NCT04709367, date of registration: 12/01/2021) and carried out at the INAIL Prosthetic Center (Bologna, Italy). All experiments were performed in accordance with the World Medical Association's Code of Ethics and the Declaration of Helsinki. All recruited subjects signed an informed consent.
The inclusion criteria determined the involvement of stabilized (i.e., time since amputation > 18 months) transfemoral amputees between 18 and 65 years old. Subjects with concurrent medical issues or unable to safely perform the physical tasks required in the experimental protocol were excluded.
To identify the target number of subjects needed to obtain a statistical power of 95%, a preliminary study was carried out on 6 transfemoral amputees, to measure residual limb volume uctuations due to physical activity. Results of this preliminary study are reported in 19 . Then, using these data, the following equation was applied for the sample size estimation (paired t-test) 20 :   1 where is the type II error probability (0.05) for the desired statistical power of 95% (power = 1 -), α the desired signi cance level (0.05), α and β the standard normal scores for con dence level α and respectively, the population standard deviation (0.051 dm 3 ), and the expected difference (0.040 dm 3 ), both found in 19 . Thus, the target subjects number, , resulted equal to 24.
B. Measurement systems for the assessment of residual limb volume Residual limb volumes can be measured through many techniques, as we widely described in 10 . In this section, we will brie y recapitulate them in order to clarify the rationale undergoing the methodological approach used in this study. The simplest measurement system for the assessment of residual limb volume consists in dipping the residual limb or its cast within a box lled with water, and measure the water displacement 21 . However, this technique is susceptible to errors due to subject's movements and surface tension at the limb-water interface, thus resulting in a low reliability 10 .
Anthropometric models can be reconstructed by importing anatomical landmarks distances, measured by tapes or calipers, but these models are not accurate enough to guarantee reliable results 22 , 23 . Furthermore, as all techniques involving contact with tissues, anthropometric measurements in uence the residual limb shape during the evaluation 10 .
Magnetic Resonance Imaging, ultrasound and spiral X-ray Computed Tomography can detect changes in volume and internal residual limb structures. Nevertheless, they are costly, invasive, and affected by errors due to subject's movements. In addition, they are time-consuming and not fast enough to allow for measurements of volume changes due to prosthesis do ng.
More recently, Sanders et al. [24][25][26][27][28] developed a bioimpedance device to measure the conductive tissue extracellular uid (ECF) volume of transtibial residual limbs while donning the prosthesis. As a drawback, only ECF volume can be acquired, without including the one of bone and adipose tissues.
Measurement strategies comprising the use of a portable 3D scanner are among the most e cient solutions, as demonstrated by de Boer-Wilzing et al. 29 . Thanks to the recent developments in 3D scanning, these systems are nowadays reliable, safe, fast and portable. All these features are fundamental for clinical applications 15 , 30 . Dickinson et al. 31 have evaluated the accuracy of three hand- held 3D scanners: high reliability and accuracy for the VIUScan marker-assisted laser scanner and the Go!SCAN 3D optical scanner were demonstrated (both metrology-grade scanners of Creaform Inc; Canada). Moreover, the Go!SCAN50 scanner allows for a speci c body-scanning option (namely semirigid positioning), consisting of an algorithm implementation within the acquisition software able to compensate small body tremors associated to the hand holding the scanner and to the scanned object.
Furthermore, marker dots are not needed to be applied on the object to be scanned, thanks to the system ability to capture the object natural features. Thus, a 3D scanner based approach including the Go!SCAN50 was selected for the assessment of the volume uctuations of transfemoral residual limbs in the framework of this study.

C. Experimental setup and Data acquisition
To yield the protocol reliable and acceptable for the enrolled amputees, a dedicated experimental set-up was developed (Fig. 1a). It included a mechanical support, adequately designed to help the enrolled amputees standing on the sound limb in a stable and comfortable way during scanning. A laser level and a laser meter were used to project two perpendicular lines on the anterior surface of the residual limb and a dot on the distal end, respectively. Such tools were positioned at the beginning of the protocol for each amputee and were kept in position until the end. The two lines and the dot, projected on the residual limb, were drawn before starting the tests, to identify the same limb orientation for all the scans. A mirror was placed in front of the amputee to allow for visual feedback, hence helping to maintain the same position.
Before starting, four dots were drawn on the residual limb as anatomical landmarks to uniquely identify a scan cutting plane; they were used afterwards in the post-processing of the 3D image data. One dot was drawn on the ischial tuberosity, one on the external surface of the greater trochanter, and the two remaining dots were drawn on a horizontal axis, about 1 cm distally with respect to the great trochanter, and located about 5 cm anteriorly and 5 cm posteriorly on the skin (see Video 1in supplementary material). All dots were drawn by an expert prosthetist which identi ed the bony prominences by palpation. These body regions were selected since usually featured by minimal volume changes because of the presence of bony structures with a few soft tissues 10 .
Scan les were acquired with the VXelements software (Creaform Inc; Canada), that allows for real-time visualization of the 3D image data (Fig. 1b, see Video 1 in supplementary material). Once the acquisition was completed, the mesh optimization was carried out (i.e., lling holes, eliminating bad frames, performing data clean-up, smart decimation). Then, the meshes were imported in the VXmodel software (Creaform Inc; Canada) for post-processing. Three different options can be chosen in the software for aligning scans: (i) Global registration, (ii) Surface Best-Fit alignment and (iii) N-Point alignment. To select the best tool, 3 consecutive scans of a lower limb were performed on 4 not-amputated subjects, resulting in a total of 12 scans. Based on these data, the Surface Best-Fit alignment was selected (Table 1) since it involves the smallest volumetric error, as averaged across subjects.
The Surface Best-Fit tool aligns the meshes using their common surface when they are not in the same referential by considering one mesh xed. Thanks to the Pre-align option of the tool, it was possible to select at least 3 points on the xed mesh, and then the same points on the mobile one (Fig. 1c). Thus, the dots drawn on the residual limb as anatomical landmarks -visible in the acquired scan textures -were used (see Video 1 in supplementary material). Once the common points were selected, the Surface Best-Fit alignment was completed (Fig. 1d). Since the software allows for cutting meshes along planes, the point drawn on the ischial tuberosity, and the other two about 1 cm distally with respect to the great trochanter, were used to de ne the scan cutting planes (Fig. 1e). The resulted holes were lled in a planar way and the volume was computed by the software (Fig. 1f). Results reported in 19 highlighted that each amputee is featured by a speci c time of stabilization in volume after do ng the prosthesis. Hence, the experimental protocol was constituted of four test days and de ned as follows.
1st session: during this test session ( Fig. 2 -Monday week 0), a resting period of 10 min was scheduled upon arriving in order to reach a homeostatic condition of the limb within the prosthesis. Then, the prosthesis was doffed, the amputee was helped to reach the mechanical support of the experimental setup and 7 scans were acquired at intervals of 10 min in a standing position. This session allowed for the characterization, over time, of the residual limb volume changes due to prosthesis removal and for the identi cation of the time required to stabilize the residual limb volume for each amputee. More in detail, volume change was calculated starting from minute 20 and until it was lower than the error evaluated for the 3D body scanning method (i.e., 0.313%; Table 1). By that time, volume was considered stabilized.
2nd session, 3rd session, 4th session: further three sessions of tests were performed in three different days, a week apart from each other (Fig. 2 -Tuesday week 0, Tuesday week 1, Tuesday week 2). Each session was featured by two testing times, one in the morning and one in the afternoon. During both (morning and afternoon), upon arrival, the amputee rested for 10 minutes with the prosthesis donned. Then, 2 consecutive scans were performed immediately after prosthesis do ng. Other 2 consecutive scans were carried out after the amputee's stabilization time (evaluated in the 1st session). Then, the amputee donned the prosthesis and 15 minutes of physical activity were performed (i.e., walking at a self-selected speed on a treadmill) and the same scanning sequence (i.e., 2 scans just after do ng the prosthesis and 2 scans after the residual limb volume stabilization) was repeated. This resulted in 48 scans for each amputee.

E. Statistical analyses
All statistical tests were carried out in IBM SPSS Statistics environment and the signi cance level was set equal to 0.05.
1st session: the normality of the volume data acquired in this test session was veri ed (Kolmogorov-Smirnov's test and Shapiro-Wilk's test), while the assumption of sphericity was violated (Mauchly's test) ( ). Accordingly, the 1-way ANOVA with repeated measures and the Greenhouse-Geisser correctional adjustment was used to investigate the effects of the factor time (7 levels; i.e., time points at 10 min interval) on the measured volume (H 0 : no difference among sample means at different timepoints). Then, Bonferroni post-hoc comparisons were carried out.
The mean and the standard deviation of the post-do ng volume changes over time were calculated, using the rst scan ( , Fig. 2 -Monday week 0) as the reference. Then, the curve trend of the measured data was tted in Matlab R2018a.
2nd session, 3rd session, 4th session: during each session, volumes were computed and averaged between the 2 consecutive scans resulting at each time-point (Fig. 2). This resulted in 8 volume values per day for each amputee. Afterward, these volume values were averaged over the three different test days, resulting in 8 values for each amputee at the speci c time-points of the day. The normality (Kolmogorov-Smirnov's test and Shapiro-Wilk's test) and the sphericity (Mauchly's test) of data distribution were preliminarily veri ed. Then, the 3-way ANOVA with repeated measures was performed to investigate the effects of factors: testing time (2 levels: morning vs afternoon), physical activity (2 levels: before vs after physical activity), prosthesis removal (2 levels: immediately after prosthesis do ng vs after the stabilization time), and their interactions on measured volume.

A. Subjects and baseline condition (1st session)
The general features of the enrolled amputees are summarized in Table 2. All subjects were traumatic amputees. Only one female took part in the study. The 20.8% of subjects reported a recent amputation (2)(3)(4)(5) year) and the 79.2% was chronic (> 5 year). The majority of enrolled subjects wore a quadrilateral socket (54.2%) and a suction suspension system based on a unidirectional valve (91.7% in total: 50% without a liner and 41.7% with a Seal-In liner). The mean self-selected speed during walking on the treadmill resulted equal to 0.6 ± 0.1 m/s.   material). Results revealed an increasing effect of the prosthesis do ng on the residual limb volume, with the highest change rate in the rst 10 minutes (Fig. 3). In particular, the amputees' residual limbs required, on average, 30 min to stabilize in volume (see t* in Table 2 and Fig. 3).  As found in literature for transtibial amputees 15 , 27,32,33 , the following two-term exponential decay function was found and used to curve-t mean volume changes versus time: Results showed a good t (R2 = 0.97) with and equal to 1.80% and 0.08 min-1, respectively.
Notably, the maximum measured volume change among all subjects was found equal to +5.92%.
B. Volume changes within a day: 2ndsession, 3rdsession, 4th session Among the 24 recruited amputees, 1 dropped out of the study after the 1st test day, resulting in 23 amputees. Results of the 3-way ANOVA with repeated measures showed no statistical differences for testing time ( ), and a signi cant effect of both prosthesis removal ) and physical activity ( ) (TABLE 4 and Fig. 4). Speci cally, after removing the prosthesis, and after the physical activity, the residual limb volume increased, on average, of 0.50% and 0.46%, respectively.
A signi cant effect was also observed for the interaction among all the three within-subjects factors (i.e., testing time * physical activity * prosthesis removal) (  , TABLE 4). Speci cally, results revealed that the residual limb volume increased during the day, in particular after physical activity and prosthesis removal. Notably, the maximum volume changes due to the prosthesis removal as a percentage of the value immediately after the prosthesis do ng, across all subjects, ranged between -4.18% and 2.65%. Noticeably, the maximum volume reductions were always veri ed for subject 12, which is the only recruited amputee with a pin locking suspension system (TABLE 2). Also, the volume change due to the physical activity was evaluated for each subject as a percentage of the value before activity, resulting in a total change range equals to -1.43% ÷ 3.19%.

Discussion
This study focused on the volume uctuations affecting the residual limbs of transfemoral amputees. At rst, the volume changes after the prosthesis do ng was characterized overtime. Then, the effect of the prosthesis removal and the physical activity was investigated within a day -comparing morning and afternoon results -and repeating the tests during three different sessions, one week apart from each other.
A speci c experimental set up was realized, including a portable metrology-grade 3D scanner, namely the Go!SCAN50, that was identi ed as the most suitable solution for the study. A mechanical support for amputees in standing position was designed to increase the protocol acceptability and improve the measurements precision. The nal volumetric error of the 3D body scanning method was found equal to 0.3%. This value ensures a high reliability of the obtained results if compared to other measurement approaches described in the literature. Indeed, the water displacement method showed a measurement error between 2.1% and 3.7% when directly applied on residual limbs 34 . The error is improved to 1% when residual limb casts are measured 35 but they cannot perfectly replicate the residual limb volume.
The study included 24 amputees, a number guaranteeing a statistical power of 95% with an α-value of 0.05 by using preliminary data 19 . However, only 22 subjects completed the required scans of the 1 st test session, while 1 subject dropped out the subsequent ones. This resulted in a statistical power of 93% and 94%, respectively (α = 0.05).
The homogeneous features of the recruited population (TABLE 2) can be easily attributed to the recruiting prosthetic center, that is a national rehabilitation facility for work-related disabilities (INAIL, Italian National Institute for Insurance against Accidents at Work). This prosthetic center mostly deals with traumatic amputations due to work-related accidents; thus, it introduced a bias in the recruitment, as also described for other clinical studies 44 , and may likewise have contributed to the predominance of male amputees. Indeed, only one female subject was enrolled and all subjects reported a traumatic amputation.
The protocol consisted of four test sessions in four different days for an overall duration of 3 weeks.
During the 1 st session, amputees' residual limb volume was measured 7 times at intervals of 10 minutes after the prosthesis removal. As reported in literature on transtibial amputees 15 , 27,32,33 , a two terms exponential decay function demonstrated to curve-t well the data (R 2 = 0.97). Generally, residual limbs increased in volume after do ng the prosthesis (maximum measured value across all subjects equals to +5.9%). The greatest volume change was found in the initial 10 minute (Fig. 3 and TABLE 3). Then, values stabilized after 30 minutes, on average. This could be due to the effect of the negative pressures applied on residual limb tissues by the prosthesis suspension system. Indeed, 22 among 24 enrolled amputees used a vacuum suspension (i.e., suction by unidirectional valve with or without a Seal-In liner). Negative pressures on tissues mainly draw in body uids, differently from the drawing out effect of positive pressures 27 . As a consequence, the residual limb increased in volume when the prosthesis was removed. In addition, the socket do ng probably caused a reduction in the interstitial uid pressure. Thus, an increment of the amount of uid from arterial vessels into the interstitial space may occur, as well as a reduction from the interstitial space into the venous vessels 28 .
The increment in volume due to the prosthesis do ng was also con rmed by the results obtained in the following three test days. In particular, during these sessions, the residual limb volume was measured immediately after the prosthesis do ng and after the amputee's stabilization time, before and after 15min of walking on a treadmill, both in the morning and in the afternoon. The adopted stabilization time resulted from the 1 st test day for each amputee. After averaging the corresponding volumes of the three test days, the data were analyzed by a repeated measured 3-way ANOVA test, featured by three withinsubjects factors with two levels: (1) testing time (morning vs afternoon), (2) physical activity (before vs after physical activity), (3) prosthesis removal (immediately after the prosthesis do ng and after the stabilization time). Signi cance differences were found for factors 2 and 3 and the interaction of all the three factors (TABLE 4). Both prosthesis removal and physical activity showed a mean increasing effect on the residual limb volume (Fig. 4). Also for physical activity, this could be due to the pressure distributions applied on the residual limb tissues by the prosthesis socket and suspension system. Indeed, it is known that cyclic changes of pressures at the prosthetic pHMI continuously occur during walking -negative pressures in the swing phase and positive pressures in the stance phase 21 . Furthermore, the application of vacuum due to the suspension system causes an increment of the negative pressures during the swing phase and a reduction of the positive pressures during the stance phase 7 . This in uences the blood circulation and the drawing in/ out body uids, suggesting an increment in volume.
In addition, volume changes within a day, albeit not statistically signi cant, were also observed, resulting in an overall range across subjects of -4.2% ÷ +2.6% due to the prosthesis removal and -1.4% ÷ +3.2% due to the physical activity. However, it needs to be stated that high volume reductions were veri ed only in subject 12, which used a pin locking suspension system for the prosthesis. Then, the positive pressures applied on the residual limb tissues might have caused a drawing out effect of the body uids, when do ng the prosthesis.
These data point out the critical need for an optimal pHMI interface for transfemoral prostheses, able to adapt comfortably and effectively to the residual limb. Indeed, these volume increments are enough to generate severe discomforts for amputees and, in the worst cases, impediments in donning the prosthesis 13 . On the other hand, the residual limb volume reductions can compromise the prosthesis tting and stability, increasing the risks of falling. Generally, altered stress distributions at the interface and relative movements between the limb and the socket can occur, thus causing dermatological problems and pain. To achieve the challenging objective of an optimal prosthetic interface, the socket system should be able to compensate for these changes in volume.
Overall, the results reported in this study advance the state-of-the-art concerning the volumetric changes of transfemoral residual limbs. Furthermore, they provide the required constraints -previously missing in the state-of-the-art -for the design of smart prosthetic socket solutions for transfemoral amputees.

Conclusion
This study aimed at investigating volume changes in the transfemoral amputee population due to the prosthesis do ng and physical activity, at different testing times (i.e., morning and afternoon). The results of these tests, demonstrated a signi cant increasing effect of both prosthesis removal and 15-min of walking. In addition, the interaction of the three factors -prosthesis removal, physical activity and testing time -was found statistically signi cant. A two terms decay exponential function showed excellent tting with the mean data of the post-do ng volume changes over a 60 minutes period, demonstrating the highest change rate in the initial 10 minutes after the socket removal and an average stabilization time of 30 minutes. Considering volume changes of each subject, the total range measured during this study was -4.2% ÷ +5.9%, with maximum volume reductions measured in subject 12, which is the only amputee with a prosthetic suspension system not based on vacuum. In addition, this great volume change range might have been impacted by several other factors depending on the speci c subject and test day, e.g., diet, weather condition, comorbidities etc., making di cult to derive statistical conclusions.
The reported results could be exploited, in the future, for the design of smart prosthetic sockets able to compensate the limb volume uctuations overtime, thus to maximize stability and comfort.