**1. Introduction**

Knowledge of the order of motor nerve branching from main nerve trunks into skeletal muscles is of clinical importance when evaluating motor and sensory deficits, treating nerve entrapment and predicting the timing of recovery after nerve injury [1]. Radial nerve entrapments, such as radial tunnel and posterior interosseous nerve syndromes, are common and result in reduced quality of life and ability to carry out activities of daily living [2].

Numerous sites of radial nerve entrapment have been identified in the literature—five for the posterior interosseous nerve alone—each resulting in a unique clinical presentation specific to the nerve's motor branching pattern [3]. It is imperative that clinicians have thorough knowledge of the radial nerve's course and branching in order to provide accurate and timely diagnosis.

Although some parametric studies of the radial nerve focused on the "order of innervation" in the forearm have been carried out, they have typically defined this term poorly and employed

dissimilar metrics to represent it, making it difficult to compare studies [4,5]. Specifically, some authors have identified the order of motor branching from the radial nerve when determining the "order of innervation," while others have identified the order with which each muscle exhibits a motor entry point (the point at which a motor nerve first enters the muscle). Only a single study, carried out by Linell in 1921, documented both the branching order and motor entry order for the entire course of the radial nerve in the forearm, with findings indicating that those two orders are not always in agreement [6]. Thus, the methodological discrepancies present in modern studies prevent accurate comparisons and render them individually unable to present a complete picture of the radial nerve's motor branching pattern.

Beyond the knowledge of an archetypal "pattern" of the radial nerve and its branches in the forearm, an understanding of common variations is of particular clinical utility vis à vis preventing the iatrogenic loss of function or initial misdiagnosis of a lesion in a patient whose presenting symptomatology or underlying anatomy may be aberrant. Some existing studies have identified cases of innervation of the brachialis muscle by the radial nerve [4,7,8], as well as motor innervation by the superficial branch of radial nerve, which is often considered purely sensory [4,5,8]. These findings have thus far not been incorporated into most anatomical texts and remain relatively unknown.

This mixed methods study aimed to provide qualitative and quantitative data of both educational and clinical significance on the branching pattern and motor distribution of the radial nerve. The primary objectives of this study were to: (1) determine the branching order of the radial nerve in the distal arm and forearm; (2) determine the order of innervation of the radial nerve in the distal arm and forearm based on the distance to motor entry points; and (3) to identify the muscular territories of each branch of the radial nerve and quantify any variation thereof. The comprehensive measurement of both branching points and motor entry points set forth here provides a more complete and specific set of data than is currently available, as these parameters had previously been used independently to describe the nerve's anatomy or "order of innervation" [4,5]. These data will not only clarify existing reports in the literature, but also set forth an understanding of where and how branches divide from the radial nerve and reach their target structures.

#### **2. Materials and Methods**

#### *2.1. Cadaveric Study Sample*

This study utilized a sample of 35 embalmed cadavers housed in the gross anatomy laboratory at Tufts University School of Medicine that were concurrently being dissected as part of the medical and dental gross anatomy courses. One upper extremity from each cadaver was included. The selection of the laterality of each dissection was based on the fact that students performed a deep dissection of only one upper extremity, leaving the other one grossly intact and thus available for research purposes. As such, there was an inclusion of both right and left upper extremities. Cadaveric research of this nature does not require the Institutional Review Board or ethics approval at Tufts University.

#### *2.2. Measurement of Radial Nerve*

The 35 upper extremities were dissected initially to reveal the superficial musculature and then further to distally expose the radial nerve from the level of the spiral groove of the humerus proximally to the arcade of Frohse (supinator arch). With the extremity in anatomical position, the medial and lateral humeral epicondyles were palpated and a line was drawn bisecting them (the transepicondylar line, TEL). A pin was placed through the radial nerve at the point where it crossed the TEL to both fix it in place and serve as a consistent marker for measurement. Each muscular branch of the nerve was identified and the distance from the TEL to the nerve's branch point from the radial nerve ("branch distance") was measured to the nearest one-hundredth of a millimeter (0.01 mm) using a digital caliper (Neiko Tools®, Taipei, Taiwan). The branch points proximal to the TEL were recorded as negative values and those distal were recorded as positive. The length of each branch (a straight line from its

exit from the radial nerve to its motor entry point—MEP—at the muscle) was then measured in the same fashion. The branch distance and branch length were then summed to determine the "MEP distance." This was first performed for brachialis (B; if innervated supinator (S). The supinator was then reflected to allow for the dissection of the nerves supplying extensor carpi ulnaris (ECU), extensor digitorum and digiti minimi (ED, EDM), abductor pollicis longus (APL), extensor pollicis longus and brevis (EPL, EPB) and extensor indicis (EI).

Previous studies have used differing and often poorly defined terminology when discussing the distal branches of the radial nerve. In this study the deep branch of the radial nerve (DBRN) was defined as the nerve that remains after the superficial branch of the radial nerve (SBRN) branches from the radial nerve, while the posterior interosseous nerve (PIN) was defined as the continuation of DBRN distal to the distal border of the supinator. This is consistent with the definition used by Moore et al. in *Clinically Oriented Anatomy* [9].

#### *2.3. Analysis of Radial Nerve Branches*

The most common source of innervation for each muscle was determined based on the frequency with which each named branch of the radial nerve supplied it. A "most common branching order" was determined based on the mean branch distance for each muscle across all specimens. A "most common MEP order" was then determined based on the mean distance to the first MEP for each muscle. For both of these variables a one-way analysis of variance (ANOVA) followed by a post-hoc Tukey's test was used to evaluate the differences between the muscles. Significance was set to *p* < 0.05. Studies since Linell's in 1921 have used either one or the other of these two variables when defining the "order of innervation"; this study notably investigates both as we believe they each contribute to the conceptualization of an overall order of innervation and serve unique purposes in different clinical contexts.

#### **3. Results**

#### *3.1. Branching Order of the Radial Nerve in the Forearm*

Thirty-five cadavers, 14 of which were female and 21 of which were male, with a mean age of 79.9 ± 11.5, were included in this study. The muscular nerve branching order was determined based on the mean distance from the TEL to the first branch exiting off the main trunk to serve each muscle (branch distance, Table 1). The branching order is presented as follows, with (\*) representing a significant difference in the mean branch distance (*p* ≤ 0.05): brachialis, \* brachioradialis, \* ECRL,\* ECRB, supinator,\* ED, ECU, APL, EDM,\* EPB,\* EPL, EI. The mean branch distance was not statistically significantly different between the ECRB and the supinator; the ED and ECU; any of the ECU, APL and EDM; or the EI and EPL. The ECRB's branch arose proximal to that of supinator in 27 specimens (77.1%); ED's was proximal to ECU's in 24 (68.6%); ECU's was proximal to APL's in 33 (94.3%); ECU's was proximal to EDM's in 28 (80.0%); and EDM's was proximal to APL's in 18 (51.4%). The branch to the EPL arose proximal to that to the EI in 10 (28.6%) and the two arose co-terminally in 22 (62.9%).

#### *3.2. Motor Entry Point Order*

The distance from the TEL to the most proximal entry point of a nerve into each muscle (MEP distance) is depicted in Table 2. That order is as follows, with (\*) representing a significant difference in the mean MEP distance (*p* ≤ 0.05): brachialis, \* brachioradialis, \* ECRL, \* supinator, ECRB,\* ED, ECU, EDM, APL,\* EPL, EPB,\* EI. The mean distance to the MEP was not statistically significant between the supinator and ECRB; ED and ECU; EDM and APL; or the EPL and EPB. The supinator's MEP was proximal to the ECRB's in 27 (77.1%); ED's was proximal to ECU's in 25 (71.4%); EDM's was proximal to APL's in 24 (68.6%); EPL's was proximal to EPB's in 20 (57.1%); EPB's was proximal to EI's in 23 (65.7%).


**Table 1.** Branching order, based on the mean distance in mm along the trunk from the transepicondylar line to the first branch to a muscle. *p* values are listed for the comparison of a mean to the one below it. *p* values comparing any muscle to another muscle not adjacent to it on this table were all <0.05, except for the extensor carpi ulnaris (ECU) and extensor digiti minimi (EDM) (*p* = 0.1281).

\* Indicates significant difference in mean branching distance between the listed muscle and the muscle below it (i.e., more distally) on the chart.

### *3.3. Motor Innervation Territories*

Descriptive statistics of muscular territories are shown in Table 3. Brachialis received a branch from the radial nerve proper in 21 specimens (60%). Brachioradialis and ECRL were always innervated by the radial nerve proper, although brachioradialis also received innervation by a much more substantial branch from the SBRN in one specimen (2.9%) (Figure 1); the ECRL was solely supplied by radial nerve in all specimens (100%). The ECRB received sole innervation from the radial nerve in nine specimens (25.7%), DBRN in 16 (45.7%) and the SBRN in eight (22.9%, Figure 2); it received dual innervation from the radial nerve and DBRN in one specimen (2.9%). Supinator was generally innervated by DBRN (89%), but occasionally was served more proximally by the radial nerve (11%). The ED was innervated by PIN in 30 specimens (85.7%), DBRN in four (11.4%) and by the two nerves together in one (2.9%) The following muscles were generally innervated by PIN: ECU (82.9%), EDM (97.1%), APL (91.4), EPB (97.1%); they were otherwise supplied by DBRN (17.1%, 2.9%, 8.6%, 2.9%, respectively). EPL and EI were both exclusively innervated by PIN in all 35 specimens (100%).
