## 1 Introduction  
The high median-ulnar nerve injury paralyzes the _flexor digitorum profundus_ (FDP) muscle partially and the _flexor digitorum superficialis_ (FDS) muscle completely, resulting in a limited grasping function. One current surgical solution to restore flexion of the four fingers is a tendon transfer surgery where the four FDP tendons of insertion are rerouted and sutured to the single tendon of insertion of the donor _extensor carpi radialis longus_ (ECRL) muscle, a wrist extensor innervated by another nerve, namely, the radial nerve [1, 2, 3, 4, 5]. However, this procedure has a fundamental drawback: it couples the excursion of the previously independent FDP tendons to the single ECRL tendon. This locks the movement of all four fingers even if just one finger is unable to move after making contact with an object during grasping; therefore, not all fingers are able to make contact when grasping irregularly-shaped objects, and even simple tasks, such as holding an apple, become challenging [6].  
Prior work has documented the disappointing grasping function that arises from coupled finger movement when multiple tendons are sutured to one muscle [7,8]. Specifically, the coupled finger movement leads to (i) incomplete, weak, and unbalanced grasps [7]; (ii) greater muscle force required to create full multi-finger contact, because the tendons of the open fingers need to be stretched to close them once one finger makes contact; and (iii) uneven tendon tensioning. Additionally, challenges arise from anatomical differences between patients and a limited set of donor muscles. For example, even when the number of functioning muscles is highly limited, the standard of care will not assign more than one function (such as finger and thumb flexion) to the donor muscle due to the suture's coupling effect [7]. Unfortunately, the hand grip remains weak post-surgery, because the suture couples the fingers and the fingers do not adapt to an object's shape. This greatly reduces the patient's independence and ability to work.  
To improve post-operative quality of life, we have developed a passive device implantable between the FDP tendons and the donor ECRL muscle to construct a network of _differential mechanisms_. This network of differential mechanisms will enable the fingers to continue to flex even if the other finger or fingers is/are locked after having already made contact. These devices have been patented by Dr. [PERSON] and Dr. [PERSON] along with Dr. [PERSON] (per U.S. Patents 9,925,035 and 10,595,984 [9,10]). Our previous simulation and human cadaver studies showed that such a network of implants embodied as hierarchically-arranged pulleys improved grasping of irregular objects [11]. However, the pulleys are too bulky and a low-profile embodiment is desired to create similar differential action.  
In this work, we explore the efficacy of two low-profile implant embodiments (a rod embodiment and a U-shaped embodiment; see Figure 1, panels A1 and B1, respectively), with the goal of advancing these implants toward clinical adoption. These implants form a triangle with the bifurcation point of the FDP tendons from the ECRL acting as the triangle apex [6]. In terms of mechanical action, this triangle would translate as the muscle contracts. However, the triangle also introduces a rotational degree-of-freedom about the triangle apex. This enables passive differential action between the index and middle finger, even if they are driven by one muscle. The embodiment's efficacy will be measured in terms of the improved evenness/balance in the force distribution between the two fingers and compared with the force distribution seen in the current suture-based surgery.