Shannon entropy is currently the most popular method for quantifying the disorder or information of a spatial data set such as a landscape pattern and a cartographic map. However, its drawback when applied to spatial data is also well documented; it is incapable of capturing configurational disorder. In addition, it has been recently criticized to be thermodynamically irrelevant. Therefore, Boltzmann entropy was revisited, and methods have been developed for its calculation with landscape patterns. The latest method was developed based on the Wasserstein metric. This method incorporates spatial repetitiveness, leading to a Wasserstein metric-based Boltzmann entropy that is capable of capturing the configurational disorder of a landscape mosaic. However, the numerical work required to calculate this entropy is beyond what can be practically achieved through hand calculation. This study developed a new software tool for conveniently calculating the Wasserstein metric-based Boltzmann entropy. The tool provides a user-friendly human–computer interface and many functions. These functions include multi-format data file import function, calculation function, and data clear or copy function. This study outlines several essential technical implementations of the tool and reports the evaluation of the software tool and a case study. Experimental results demonstrate that the software tool is both efficient and convenient.

Chronic neck pain (CNP) is a common and disabling musculoskeletal disorder in developing and developed countries. Previous studies have shown that tuina and traditional Chinese massage are effective treatments for patients with CNP. However, there is little evidence to support the use of one intervention over the other. The aim of this study is to compare the effects of tuina and traditional Chinese massage in the treatment of pain and disability in patients with CNP. This is a multicenter, assessor- and analyst-blinded, randomized controlled trial with two parallel arms: a tuina group and a traditional Chinese massage group. A total of 356 eligible CNP patients will be randomly assigned to the groups in a 1:1 ratio. The intervention in the tuina group includes both structural and relaxation massage, while the traditional Chinese massage group will receive relaxation massage only. The interventions for both groups will last for 15 min and will be carried out three times a week for a period of 4 weeks. The primary outcome will be changes in the Northwick Park Neck Pain Questionnaire. Secondary outcomes will be measured by a visual analogue scale (VAS), the Neck Disability Index (NDI), and the 36-item Short-Form Health Survey (SF-36). The data will be analyzed at the baseline, at the end of the intervention, and during the 3 months of follow-up by repeated measures analysis of variance. The significance level is 5%. The safety of tuina and traditional Chinese massage will be evaluated after each treatment session. The results of this trial will help clarify the value of tuina and traditional Chinese massage as treatments for CNP and will highlight any differences in the efficacy of the treatments. The purpose of this trial is to determine whether tuina is more effective than traditional Chinese massage in adults with CNP. This trial will, therefore, contribute to providing a solid foundation for clinical treatment of CNP, as well as future research in massage therapy. Chinese Clinical Trial Registry, ChiCTR-INR-17013763 . Registered 8 December 2017.

Background: Low back pain is a common reason for medical care and carries a heavy social burden. The efficacy of Tuina or health care education for low back pain has been evaluated in previous systematic reviews. However, there is no evidence to support the superiority of one form of treatment over another. The aim of this study is to compare the efficacy of Tuina with health care education in the management of low back pain. Methods/design: This study is a randomized controlled trial with parallel-group design including two groups: a Tuina group and a health care education group. A total of 160 eligible participants will be randomly assigned to the groups in a 1:1 ratio. The interventions of both groups will last for 20 min and be carried out twice each week for a period of 12 weeks. The primary outcome is the Oswestry Disability Index. The secondary outcomes include a visual analogue scale and the 36-item Short Form Health Survey. They will be assessed at baseline, at the end of the intervention every month, and during 6 months and 9 months of follow-up by repeated measures analysis of variance. The significance level is 5%. The safety of Tuina and health care education will be evaluated after each treatment session. This study will focus on the value of Tuina and health care education for low back pain and will highlight any differences in the efficacy of the treatments. Discussion: This study will evaluate the efficacy and safety of Tuina intervention for low back pain, which could provide reliable evidence for clinical decision making for patients with low back pain. Trial registration: Chinese Clinical Trial Registry, ChiCTR1900022656. Registered on 23 April 2019.

Background: The chronic pain of patients with knee osteoarthritis (KOA) seriously affects their quality of life and leads to heavy social and economic burden. As a nondrug therapy in Traditional Chinese Medicine (TCM), Tuina is generally recognised as safe and effective for reducing the chronic pain of KOA. However, the underlying central mechanisms of Tuina for improving the pain of KOA are not fully understood. Methods/design: This study will be a randomised controlled trial with a parallel-group design. A total of 60 eligible participants will be assigned to the Tuina group or healthcare education group (Education group) at 1:1 ratio using stratified randomisation with gender and age as factors. The interventions of both groups will last for 30 min per session and be conducted twice each week for 12 weeks. This study will primarily focus on pain evaluation assessed by detecting the changes in brain grey matter (GM) structure, white matter (WM) structure, and the cerebral functional connectivity (FC) elicited by Tuina treatment, e.g., thalamus, hippocampus, anterior cingulate gyrus, S1, insula, and periaqueductal grey subregions (PAG). The two groups of patients will be evaluated by clinical assessments and multimodal magnetic resonance imaging (MRI) to observe the alterations in the GM, WM, and FC of participants at the baseline and the end of 6 and 12 weeks’ treatment and still be evaluated by clinical assessments but not MRI for 48 weeks of follow-up. The visual analogue scale of current pain is the primary outcome. The Short-Form McGill Pain Questionnaire, Western Ontario and McMaster Universities Osteoarthritis Index, 36-Item Short Form Health Survey, Hamilton Depression Scale, and Hamilton Anxiety Scale will be used to evaluate the pain intensity, pain feeling, pain emotion, clinical symptoms, and quality of life, respectively. MRI assessments, clinical data evaluators, data managers, and statisticians will be blinded to the group allocation in the outcome evaluation procedure and data analysis to reduce the risk of bias. The repeated measures analysis of variance (2 groups × 6 time points ANOVA) will be used to analyse numerical variables of the clinical and neuroimaging data obtained in the study. P<0.05 will be the statistical significance level. Discussion: The results of this randomised controlled trial with clinical assessments and multimodal MRI will help reveal the influence of Tuina treatment on the potential morphological changes in cortical and subcortical brain structures, the white matter integrity, and the functional activities and connectivity of brain regions of patients with KOA, which may provide scientific evidence for the clinical application of Tuina in the management of KOA. Trial registration: Chinese Clinical Trial Registry ChiCTR2000037966. Registered on Sep. 8, 2020. Dissemination: The results will be published in peer-reviewed journals and disseminated through the study’s website, and conferences.

Shannon entropy is the most popular method for quantifying information in a system. However, Shannon entropy is considered incapable of quantifying spatial data, such as raster data, hence it has not been applied to such datasets. Recently, a method for calculating the Boltzmann entropy of numerical raster data was proposed, but it is not efficient as it involves a series of numerical processes. We aimed to improve the computational efficiency of this method by borrowing the idea of head and tail breaks. This paper relaxed the condition of head and tail breaks and classified data with a heavy-tailed distribution. The average of the data values in a given class was regarded as its representative value, and this was substituted into a linear function to obtain the full expression of the relationship between classification level and Boltzmann entropy. The function was used to estimate the absolute Boltzmann entropy of the data. Our experimental results show that the proposed method is both practical and efficient; computation time was reduced to about 1% of the original method when dealing with eight $600\times 600$ pixel digital elevation models.