Traditionally, there has been a widely accepted notion that the transition from acute to chronic pain follows a linear trajectory, where an injury leads to acute episodes, subacute stages, and progresses to a chronic pain condition. However, it appears that pain progression is much more complicated and individualized than this original unsupported assumption. It is now becoming apparent that, while this linear progression may occur, it is not the only path that pain, specifically low-back pain, follows. It is clear there is a definite need to evaluate how low-back pain trajectories are classified and, subsequently, how we can more effectively intervene during these progression stages. In order to better understand and manage pain conditions, we must examine the different pain trajectories, and develop a standard by which to use these classifications, so that clinicians can better identify and predict patient-needs and customize treatments for maximum efficacy. The present article examines the most recent trajectory research, and highlights the importance of developing a broader model for patient evaluation.

In this paper, we use mathematical analysis to study the transition of dynamic behavior in a system of two synaptically coupled Hindmarsh-Rose (HR) neurons, based on its flow-induced Poincaré map. Numerical simulations have shown that the individual HR neuron has chaotic behavior, but neurons become regularized when coupled. Using a geometric method for dynamical systems, we begin with an investigation of the bifurcation structure of its fast subsystem. We show that the emergence of regular patterns out of chaos is due to a topological change in its underlying bifurcations. Then we focus on the transitional phase of coupling strength, where the bursting solutions need to pass near two homoclinic bifurcation points located on a branch of saddle points, and we study the flow-induced Poincaré maps. We observe that as the gap between the homoclinic points narrows, the image of the return map moves away from chaotic regions where winding numbers vary abruptly. That, along with Lyaponov exponent calculations, reveals the fine dynamics in the pathway across chaotic bursting behavior and regular bursting of coupled HR neurons as the synaptic coupling strength of the neurons increases. The main contribution of this paper is the mathematical description of the transition of synaptically coupled neurons from chaotic trajectories to regular burst phases using dynamical system tools such as Poincaré maps.

Background: Fat infiltration in skeletal muscle is related to declining muscle strength, whereas excess subcutaneous fat is implicated in the development of metabolic diseases. Methods: Using multi-slice axial T2-weighted (T2w) MR images, this retrospective study characterized muscle fat infiltration (MFI) and fat distribution in the lower extremity of 107 subjects (64M/43F, age 11–79 years) with diverse ethnicities (including White, Black, Latino, and Asian subjects). Results: MRI data analysis shows that MFI, evaluated by the relative intensities of the pixel histogram profile in the calf muscle, tends to increase with both age and BMI. However, statistical significance was found only for the age correlation in women (p < 0.002), and the BMI correlation in men (p = 0.04). Sex disparities were also seen in the fat distribution, which was assessed according to subcutaneous fat thickness (SFT) and the fibula bone marrow cross-sectional area (BMA). SFT tends to decrease with age in men (p < 0.01), whereas SFT tends to increase with BMI only in women (p < 0.01). In contrast, BMA tends to increase with age in women (p < 0.01) and with BMI in men (p = 0.04). Additionally, MFI is positively correlated with BMA but not with SFT, suggesting that compromised bone structure may contribute to fat infiltration in the surrounding skeletal muscle. Conclusions: The findings of this study highlight a sex factor affecting MFI and fat distribution, which may offer valuable insights into effective strategies to prevent and treat MFI in women versus men.