Codman's Paradox Research Articles

A robotic model for Codman's paradox simulation and interpretation

A robotic approach based on Denavit–Hartenberg parametrization is proposed for simulating and interpreting Codman's paradox. A 3-degree-of-freedom robot model of the glenohumeral joint, driving the arm reduced to its long humerus, is considered for simulating the two-step rotational sequence of Codman's paradox. We propose to use the classical distinction made in robotics between the joint space, i.e. the inner space of joint angles, and the operational space, i.e. the outer physical space, for interpreting this historical version of the paradox, as there is some kind of confusion between these two spaces to be considered for arm movement definition. In its extended form, developed by MacConnail, the three-step rotational sequence of Codman's paradox would highlight the motor redundancy of the shoulder joint, necessitating for its simulation, according to our robotic approach, a 4-axis model of the shoulder spheroid joint. Our model provides a general prediction of the conjunct rotation angle in full accordance with clinical observation for a two-step or three-step version of Codman's paradox. The relation of the paradox with a possible general law of motion is finally discussed.

Codman's paradox in adhesive capsulitis

Background: Even though, it is said that adhesive capsulitis is a self-limiting condition, many subjects remain with long-term sequelae. Codman's paradox is commonly used in manipulation under anesthesia technique for adhesive capsulitis of shoulder, which composes of a specific pattern of motion at the shoulder joint leading to an indirect humeral rotation without placing a rotational torque on the humerus. In this case study, Codman's paradox movement was modified and performed within pain tolerable range and without anesthesia in a subject with adhesive capsulitis. Aim and Objective: This case study analyses the effect of modified Codman's paradox movement in a 50-year-old male diagnosed with symptoms of adhesive capsulitis for more than 6 months. Materials and Methods: A single case study design was used. The study duration was 4 weeks. Baseline and posttest outcomes measures of shoulder range of motion (ROM) (flexion, extension, abduction, external rotation, and internal rotation) were measured using a universal goniometer and Shoulder Pain and Disability Index (SPADI) questionnaire. Results: Posttest measures of numerical pain rating scale, shoulder ROM and SPADI showed improvement, proving that modified Codman's paradox is effective in adhesive capsulitis. Conclusion: This study result concludes that modified Codman's paradox is effective in improving shoulder ROM among subjects with adhesive capsulitis.

Manipulation under anaesthetic for frozen shoulder using Codman's paradox: a safe and early return of function.

Although previously frozen shoulder was thought to resolve by two to three years, recent studies demonstrated the symptoms can remain for much longer. Manipulation under anaesthetic (MUA) has been shown to be successful in relieving pain and restoring function. Yet, concerns have been raised regarding its safety and the risks of complications. We utilise Codman's paradox to manipulate the shoulder, avoiding rotational torque on the humerus. The aim of our study was to asses shoulder function in the early post MUA period. Two hundred twelve consecutive patients (224 shoulders) (mean age 52.4years) underwent MUA using Codman's paradox for frozen shoulder as sole procedure between 2005 and 2013. All were evaluated clinically, preoperatively and postoperatively, at three weeks and three months, for Constant score (CS), pain, range of motion (ROM), patient satisfaction and subjective shoulder value (SSV). At three weeks and three months, a significant improvement was found in CS from 30.7 to 66 and 70 respectively. Forward elevation improved from 91° to 154° and 160 °, abduction from 69° to 150° and 156 °, internal rotation from 12° to 62° and 66 °, and external rotation from 10° to 46° and 50 °. Pain score improved from 4.4/15 to 9.6/15 and 10.4/15, SSV improved from 1.5/10 to 6.5/10 and 6.7/10. (p<0.001). Use of Codman's paradox provides a safe and efficient way to perform MUA for frozen shoulder. It results in dramatic early improvement in ROM, functional outcomes and high satisfaction, as early as three weeks post-operatively.

Closed Rotation Sequences

A finite sequence of rotations is closed if a sequential application of all the rotations from the sequence results in no net orientation change. A complete characterization of closed rotation sequences involving a given set of rotation axes is presented, and the set of such sequences is shown to be a smooth manifold under a nondegeneracy condition on the rotation axes. The characterization is used to derive several examples of closed rotation sequences, some of which are then shown to specialize to classical examples of such sequences provided by the Rodrigues---Hamilton theorem and the Donkin's theorem. Discrete versions of the Goodman---Robinson and Ishlinskii theorems are also derived and illustrated using the so-called Codman's paradox.

肩関節の回旋角度表示における問題点と解決法の一提案

Angles of the shoulder joint are usually defined in each of the sagittal, coronal, and horizontal planes passing through the center of the shoulder joint. One of the problems with this method is the difficulty of describing some positions of the shoulder joint such as the anterolaterally elevated position. In 2005, the International Society of Biomechanics proposed a recommendation on definitions of joint coordinate systems including the shoulder based on Euler/Cardan angles, which have often been used for the purpose of research on shoulder joint movement in daily activities. With this definition, however, it still remains impossible to define the angle of axial rotation in the hanging down position. Also, Codman's paradox, the phenomenon where the rotation angle of the shoulder changes after motions without axial rotation of the arm, remains unsolved. To solve these problems, a new method to define the angle of shoulder axial rotation, the non-singular method, has been proposed. This review describes the history and the problems of the methods used to define shoulder angles, and presents this new method of definition.

On the hypotheses that determine the definitions of glenohumeral joint motion: with resolution of Codman's pivotal paradox

Current terminology of shoulder motion does not fully explain several well-known paradoxes. We developed a model of glenohumeral joint motion that describes shoulder motion more accurately and provides the ability for computer modeling of shoulder motion. All glenohumeral joint motions can be defined by the model, as well as resolving the problem of well-known paradoxes of shoulder motion. The group model was also extended to infinitesimal rotations of the glenohumeral joint. This model then becomes a description known in physics as Eulerian angles, the description of rotations of a rigid body. By use of this model, computer modeling of shoulder motion is possible, whereas it is shown that it is not in the current terminology. Several clinical situations are discussed and analyzed by the new model of shoulder motion. Among these are Codman's pivotal paradox and a paradox of shoulder motion described by Rowe. Both of these can be resolved mathematically using the group model of shoulder motion. Discussion centers on how the new model may affect therapy models for these motions. We conclude that a symmetric group model of motion centered at the glenohumeral joint may allow computer modeling of shoulder motion, allow resolution of several important paradoxes concerning shoulder motion, and have importance in therapeutic rehabilitation of shoulder problems.

Manipulation of the Shoulder Using Codman’s Paradox

Codman's paradox provides a safe method of shoulder manipulation, reducing the occurrence of fractures about the humerns.

Simulation of Codman's paradox reveals a general law of motion

Codman's paradox refers to a specific pattern of motion at the shoulder joint. It asked how a mysterious axial rotation about the longitudinal axis of the arm occurred during two or three sequential arm rotations that did not involve rotation about the long-axis. The objective of this paper was to find how the mysterious axial rotation occurred in the Codman's paradox. First, Codman's paradox and Codman's rotation were defined in general situations that involved arm rotations about orthogonal axes starting from the neutral attitude as well as rotations about non-orthogonal axes and starting from non-neutral attitudes. Then a general law of motion was proposed to answer the question of the Codman's paradox, which is stated as when the long-axis of the arm performs a closed-loop motion by three sequential rotations defined as Codman's rotation, it produces an equivalent axial rotation angle about the long-axis. The equivalent axial rotation angle equals the angle of swing—the second rotation in the three sequential long-axis rotations. Validity of the proposed law of motion is demonstrated by computer simulation of various Codman's rotations. Clinical relevance of the proposed law of motion is also discussed in the paper.

A numerical solution to calculate internal–external rotation at the glenohumeral joint

Objective. To validate the approach of using angular velocity vectors to quantify internal–external rotation of the humerus. Design. An experimental approach was used to compare predictions of internal–external rotation of the humerus based on angular velocity vectors, and known measurements of internal–external rotation. Background. A primary concern associated with description of glenohumeral biomechanics is measurement of internal–external rotation of the humerus. Euler angles are often used, yet they do not address problems such as Codman's paradox and `gimbal lock'. Previous work has presented a technique that uses angular velocity vectors to quantify internal–external rotation instead of Euler angles. This approach is promising with regard to providing an independent measure of internal–external rotation of the humerus, and requires validation for subsequent use on humans. Methods. A gimbal with three axes of rotation that simulated the rotational d.o.f. of the humerus relative to the glenoid was developed and used to validate the use of angular velocity vectors to quantify internal–external rotation of the humeral shaft portion of the gimbal. Results. Correlations between calculated and measured rotation values revealed R 2 values of 0.99, slopes at diagonal (1.0), and y-intercepts near zero (−0.6°). Conclusions. The expression developed here is a valid and useful method for measuring motion of the humerus relative to the glenoid. Relevance Angular velocity vectors can be used to accurately determine internal–external rotation of the humerus relative to the glenoid, and this may be useful for the development of arthrometers to characterize the glenohumeral joint.

Codman's paradox of the arm rotations is not a paradox: mathematical validation

Movement of a straight arm centred at the shoulder joint in three successive 90° rotations, each around the respective orthogonal coordinate axis, leads to an apparently unrelated 90° rotation around the longitudinal arm axis. This empirical fact is known as Codman's paradox, after a Bostonian surgeon who first reported it in 1934. However, by means of homogeneous coordinates, it is herein demonstrated that the phenomenon is just a mechanical property mathematically described by the equivalence between the matricial product of three orthogonal rotation matrices applied to a position vector and the matricial product of a single rotation matrix applied to the same vector. The latter rotation matrix corresponds to the middle one in the former group of three. When polar coordinates are used, the demonstration is even simpler, for the total shift vector clearly shows a single net effect on the longitudinal axis rotation. Thus, Codman's paradox is not a paradox. This property improves the muscle dynamics arm knowledge and might find applications in robotics.