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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Mechanical neck disorder (MND) is one of the most common health issues and is characterized by restricted cervical mobility. However, traditional kinematic information often focuses on primary movement in the cardinal plane, which seems insufficient to fully determine the kinematics of the cervical spine because of the complexity of the anatomical structures involved. Therefore, the current investigation aimed to modify the concept of the three-dimensional workspace to propose an objective mathematical model to quantify the complicated kinematics of the cervical spine. In addition, the observation evaluated the characteristics of the cervical workspace in asymptomatic and MND groups. Seventeen healthy volunteers and twenty-five individuals with MND participated in the study and executed the motion of circumduction to establish the cervical workspace using an electromagnetic tracking system. The results produced a mathematical model to successfully quantify the cervical workspace. Moreover, MND groups demonstrated significant reduction in the normalization of the cervical workspace with respect to the length of the head-cervical complex. Accordingly, the current study provided a new concept for understanding the complicated kinematics of the cervical spine. The cervical workspace could be a useful index to evaluate the extent of impairment of the cervical spine and monitor the efficacy of rehabilitation programs for patients with MND.

Mechanical neck disorder (MND) is one of the most common health issues of the modern lifestyle. It is characterized by the symptoms of neck pain, restricted cervical range of motion (ROM), altered neuromuscular control, neck muscle weakness and neck-related functional disabilities [

In general, the cervical spine is a highly flexible section of the spine. Owing to the complexity of the anatomical structures of the cervical spine, the movements of the cervical spine are three-dimensional and critical to the execution of many daily living activities. In the clinical setting, knowledge of the kinematics of the cervical spine is essential to examine the extent of impairment and evaluate the efficacy of rehabilitation programs for patients with MND. One way to comprehend the kinematics of the cervical spine fully is to quantitatively measure the cervical ROM. According to the recommendation of “Guides to the Evaluation of Permanent Impairment” [

Inasmuch as there are no definitive conclusions to clearly distinguish differences in the complicated kinematics of the cervical spine between asymptomatic persons and those with MND, an alternative and feasible method is desperately needed to overcome this problem. Further, traditional methods of assessment for cervical spine attempt to quantify individual cervical ROM in three separate major anatomical planes. No previous studies utilize the concept of combining three major anatomical planes to explore the kinematics of the cervical spine. Recently, the workspace defined as the volume of joint movement in the three-dimensional space had been proposed for application to human joint kinematics [

To improve knowledge of the complicated kinematics of the cervical spine, the major purposes of the present investigation were to modify the concept of the three-dimensional workspace to propose an alternative and quantitative method for depicting the kinematics of the cervical spine and to find a mathematical relationship to quantify the cervical workspace from the length of the head-cervical complex in healthy subjects. Through the proposed mathematical determination, the ideal amount of cervical workspace would be easily predicted from a given known amount of the length of the head-neck complex. Finally, the observation also evaluated the characteristics of cervical circumduction between the symptomatic and mechanical neck disorder groups. The findings give new insight into the properties of motion of cervical circumduction and further provide an index to determine the extent of impairment for patients with MND.

Forty-two subjects were recruited for this investigation. Seventeen of these subjects were healthy controls and volunteered to establish the normal database of the maximum cervical workspace. None of the subjects had any history of cervical surgery, cervical trauma or cervical pain. The remaining twenty-five subjects were included in the MND group because they had neck pain.

All subjects with MND had been diagnosed by a physician and had sought medical treatment within the past six weeks. If they showed any circulatory or neurological disorders the subjects were excluded. In addition, participants were also excluded if they were diagnosed with spinal orthopedic problems, such as spinal vertebral fracture, abnormal spinal lordosis, spinal spondylosis or spinal osteoarthritis and so on. All subjects gave informed consent to the experimental procedures, which had been approved by the Human Institutional Ethics Committee prior to participating in the investigations. Additional demographic details were initially recorded for each participant. Thirteen of twenty-five subjects with MND (eight men, five women) completed the Neck Disability Index to evaluate the functional disability [

Three-dimensional kinematic data of the motion of cervical circumduction was recorded with a six-degrees-of-freedom electromagnetic tracking system (ETS) (LIBERTY^{™}, Polhemus Inc., Colchester, VT, USA). The ETS is a non-invasive measurement tool consisting of a standard range electromagnetic source that generates low-frequency electromagnetic fields detected by one or multiple receiver sensors. The ETS is capable of tracking consecutive positions (X, Y and Z Cartesian coordinates) and the orientations (azimuth, elevation, and roll) of the receiver sensors relative to the electromagnetic source. As a result, the ETS can not only provide dynamic and continuous information, but also simultaneously measure the three-dimensional joint ROM in three planes over the time period of the movement. According to manufacturer specifications, the static root mean square (RMS) accuracy is 0.0762 cm for X, Y or Z position and 0.15° for sensor orientation and the useful operation is in excess of 180 cm (LIBERTY^{™} User Manual, Revision F, 2008). The size of the electromagnetic source size is 5.6 cm × 5.6 cm × 5.8 cm (length × height × width) and the dimension of the receiver sensor is 2.26 cm × 1.27 cm× 1.14 cm (length × width × height). Our previous investigations also demonstrated ETS is appropriate and applicable in quantifying the three-dimensional measurement of cervical kinematics [

In this experiment, the three-dimensional positions of the receiver sensors relative to the electromagnetic source were tracked at a measurement frequency of 120 Hz. To obtain the movement trajectories of the motion of cervical circumduction, three electromagnetic receiver sensors were applied in the experiment; one of these two receiver sensors was placed on the vertex of the head, which was defined as the conjunction point between the bi-auricular and the medial sagittal line by means of an adjustable, plastic hat and the other was firmly attached over the processus spinosus of the seventh cervical spine body (C7). Moreover, another receiver sensor mounted on a palpation stylus, pen-shaped device was used to palpate bone landmarks to define the position of the joint center of C7. The electromagnetic source was positioned near the subject (

All measurements were performed by the same tester in a quiet room. At the beginning of each measurement, each subject was requested to sit straight on a wooden chair to keep his or her thoracic spine in contact with the backrest, relax the cervical spine and look straight ahead. The subject’s feet were flat on the floor, and their arms rested freely on their thighs. First, the position of the incisura jungularis was recorded utilizing palpation stylus and the position of the joint center of C7 was subsequently determined. Next, the subject was instructed to flex the cervical spine and this flexed position was defined as the starting position of the motion of cervical circumduction. Each subject was then asked to execute the actively maximum motion of cervical circumduction as far as possible at a normal velocity, and then return the cervical spine to the starting point.

The motion of cervical circumduction was defined as the movement pattern which was a consecutive combination of flexion, extension, lateral flexion, and slight rotation (

While performing the motion of cervical circumduction, the consecutive position _{0} was the position of the joint center of C7; P_{1} was the starting position of the vertex of the head and P_{i} denoted the position data of the top of the head at the

Data were analyzed using the Statistical Package for Social Sciences (SPSS 12.0, Chicago, IL, USA). Descriptive statistics (mean ± standard deviation) were calculated for demographic data and the measurements of the cervical workspace and the normalization of the cervical workspace with respect to the length of the head-cervical complex for each group. To clarify the effect of the length of the head-cervical complex upon the normal cervical workspace for healthy subjects, a simple linear regression analysis was applied to produce a mathematical equation describing the relationship between these two factors. Since the data from the current study was not normally distributed according to the Shapiro-Wilk test (

The contour of motion of cervical circumduction was successfully modeled by the alternative method proposed in the current study. In the proposed graphic display of the cervical workspace, the major motion including flexion, extension, right and left lateral flexion could be easily illustrated in

The mathematical determination demonstrated the mean value (±standard deviation (SD)) of the cervical workspace for healthy subjects was 5,726.33 (688.87) cm^{3}. Simple linear regression analysis showed the cervical workspace was significantly correlated with the length of the head-cervical complex (^{2}^{2}

In addition, because the results from linear regression analysis distinctly suggested the length of the head-cervical complex could influence the cervical workspace, the normalization of the cervical workspace with respect to the length of the head-cervical complex was used to further analysis. Expectedly, a significant decrease in the normalization of the cervical workspace (

In a clinical setting, the kinematics of the cervical spine are useful and essential for basic understanding of cervical biomechanics and the mechanisms of cervical dysfunction. Unfortunately, traditional angular parameters seem to be unable clarify the complicated kinematics of the cervical spine clearly and thoroughly due to the complexity of anatomical structures of the cervical spine. Therefore, the major aims of this investigation were to modify the concept of the three-dimensional workspace to find an alternative and quantitative method to describe the complicated kinematics of the cervical spine and attempt to identify the proportional relationship between the cervical workspace and the length of the head-cervical complex for healthy subjects. Next, the characteristics of cervical circumduction were used to compare between the asymptomatic and mechanical neck disorder groups. As expected, a mathematical model was obtained to successfully quantify the cervical workspace. The mathematical determination to assess the cervical workspace provided a feasible and alternative manner for characterizing the complicated kinematics of the cervical spine, and what's more, the results of this study supported our hypothesis that a proportional relationship existed between the cervical workspace and the length of the head-cervical complex for healthy subjects. It was tentatively concluded the simple linear regression equation obtained from our experimental data was able to predict the ideal amount of cervical workspace for a given known length of the head-cervical complex for healthy subjects. Another important issue was to characterize the properties of the cervical workspace between the asymptomatic and MND groups. Undoubtedly, the findings of this current investigation demonstrated the normalization of the cervical workspace with respect to the length of the head-cervical complex was significantly reduced in the MND group compared to the asymptomatic group.

Since mechanical neck pain is one of the common health issues in the general population, many previous studies have attempted to clarify the different aspects of the biomechanical properties of the cervical spine in the neck pain population [

According to the results, there was a proportional relationship between the cervical workspace and the length of the head-cervical complex for healthy subjects that could be established by simple linear regression analysis. The results of statistical analysis showed the coefficient of determination (R-square) of the regression model was 0.701, indicating 70.1% of the variance in the cervical workspace could be accounted for by the known variance in the length of the head-cervical complex. That is to say the ideal amount of cervical workspace could be easily predicted from a given known length of the head-cervical complex for healthy subjects. For instance, the length of the head-cervical complex is 30 (cm) for a subject. It therefore could be predicted the ideal cervical workspace would be 5,499.1 (cm^{3}). Comparisons between the ideal cervical workspace predicted from the simple linear regression equation and the actual cervical workspace obtained from the clinical setting could provide an important index to evaluate the extent of impairment of the cervical spine or monitor the efficacy of rehabilitation programs for patients with MND.

Recently, there had been increasing evidence suggesting altered motor control strategies in patients with MND [

Besides, the current study had certain potential limitations. First, although the current observation demonstrated that the proposed mathematical method would be a feasible and alternative way to quantify the complicated kinematics of the cervical spine and our previous finding suggested the apparatus was appropriate in assessing the three-dimensional mobility of cervical kinematics [

A feasible and alternative mathematical model to quantify the complicated kinematics of the cervical spine was obtained. Through this alternative and quantitative method, the ideal amount of cervical workspace could be predicted for a known length of the head-cervical complex. Especially, the cervical workspace combines the cervical movements of all the major anatomical planes in a three-dimensional space. The findings from the present study provided a new concept for understanding the kinematics of the cervical spine. Moreover, the current observation demonstrated differences in the properties of the motion of cervical circumduction between the MND and asymptomatic group. It is reasonable to expect the proposed approach is useful in providing an important index to evaluate the extent of impairment of the cervical spine and monitor the efficacy of rehabilitation programs for patients with MND.

This work is supported by National Health Research Institutes NHRI-EX100-9713EC and Nation Science Council NSC96-2815-C-037-013-B, Taiwan.

Experimental set-up to collect the movement trajectories of the motion of cervical circumduction: (

Measurement method for measuring the motion of cervical circumduction: the motion of cervical circumduction was a consecutive combination of flexion, extension, lateral flexion, and slight rotation.

Illustration of the calculation of the volume of the cervical workspace: (

Graphic display of the cervical workspace for one subject (unit: cm).

Scatter plot of the cervical workspace ^{3}) = 577.13 × (Length of the head-cervical complex) – 11,814.82 (cm) (^{2} = 0.701,

Demographic data of healthy and MND subjects.

Men | 9 | 14 | 0.845 ^{d} |

Women | 8 | 11 | |

Age (years) | 23.7 (4.0) | 25.7 (4.4) | 0.091 ^{e} |

Height (cm) | 166.2 (8.5) | 166.5 (8.5) | 0.908 ^{e} |

Weight (kg) | 62.4 (11.8) | 59.9 (9.2) | 0.581 ^{e} |

BMI^{a} |
22.5 (3.0) | 21.5 (2.3) | 0.337 ^{e} |

NDI^{b} |
20.3 (5.3)^{c} |

BMI: Body mass index;

NDI: Neck disability index;

eight men and five women with MND completed the Neck Disability Index;

Chi-square test was used to verify gender proportion between healthy and MND groups;

Mann-Whitney

Comparison of the normalization of the cervical workspace with respect to the length of the head-cervical complex and the length of the head-cervical complex between healthy subjects and patients with MND.

Normalization of the cervical workspace (cm^{2}) |
187.99 (17.83) | 165.22 (32.79) | 0.037 |

Length of the head-cervical complex (cm) | 30.39 (1.01) | 29.83 (1.14) | 0.056 |

A significant level at 0.05.