## 1 Introduction  
This study proposes a technique that can be used by individuals with lower limb amputations for the management of their residual limb's volume variations, especially when using prosthetic socks. The focus of this study was to develop a low-complexity system such that it would be inexpensive, easy to install inside the user's prosthetic socket, less prone to failures, and easy to use from the end-user's perspective. These characteristics would increase the impact that this technology would have on the affected population by enhancing the adaptability of the developed system. Variations in the shape and volume of an individual's residual limb are common amongst individuals with amputations. Some of the causes of such variations are the residual limb's fluid volume changes, the user's weight variations, the limb's muscle activity, and muscle atrophy and edema in immature residual limbs--defined as less than a year post amputation [1; 2]. Even in mature residual limbs, both diurnal and long term fluctuations in the volume of the limb may occur. The amount of volume variations in mature residual limbs varies considerably amongst individuals depending on their activity level, socket fit, dietary habits, etc. [3; 4; 5]. Although volume changes occur in both upper and lower extremities, due to the weight bearing nature of lower residual limbs, such volume fluctuations are more considerable in individuals with lower extremity amputations, which accounted for more than 65% of all amputations in the United States in 2005 [6]. Variations in the size of the limb can negatively impact the quality of the prosthetic socket fit, leading to the user's discomfort and causing skin health problems, such as edema, dermatitis, and ulceration [7; 8; 9] which are common problems in individuals with amputations of the lower limb. A commonly prescribed volume management method to mitigate variations in the volume of the residual limb is to add or remove prosthetic sock plies worn on the limb [2; 4; 10]. Although prosthetic socks and other volume management methods are available and commonly used to compensate for volume fluctuations in the residual limb, management of sock plies remains an issue amongst users [3], especially those with cognitive issues and/or limited sensation in their residual limbs [11]. Various methods can be used to guide users in managing their volume adjustment systems to maintain a proper socket fit. Measurements of the volume of the limb can be used to provide feedback to assist users in maintaining a proper socket fit. The most practical volume measurement method for this application is bioimpedance that measures limb's volume by monitoring its resistance to electrical current which is then used to determine changes in fluid volume of the limb [12]. Although the bioimpedance method has shown promise for limb volume measurements within the socket, it requires electrodes to make proper contact with the skin through the use of hydrogel [13], which makes this method less favorable. Another approach to address the problem considered in this study is to focus on biomechanical analysis, e.g., through development of a numerical model of the limb based on which the assessment of the positions and the number of required sensors can be determined. Although such methods have been explored in various articles for different applications including the assessment of the residual limb-socket interface pressure [14; 15], a great amount of variability can be observed in the reported results and parameters used in such works. Due to such variability, results of these types of studies are often validated using experimental measurements [16; 17; 18]. In fact, one of the most common methods used to obtain experimental measurements of the interface pressure for validation of such biomechanical models is the use of force/pressure sensors [18; 19; 20].