Search

Suhyun Jang,1,* Boram Lee,2,* Eunji Lee,1 Jungbin Kim,1 Jong In Lee,3 Jae-Young Lim,4,5 Ji Hye Hwang,6 Sunmee Jang1 1College of Pharmacy and Gachon Institute of Pharmaceutical Sciences, Gachon University, Incheon, Republic of Korea; 2Graduate School of Public Health, Seoul National University, Seoul, Republic of Korea; 3Department of Rehabilitation Medicine, Seoul St. Mary’s Hospital, College of Medicine, The Catholic University of Korea, Seoul, Republic of Korea; 4Department of Rehabilitation Medicine, Seoul National University Bundang Hospital, Seongnam-si, Republic of Korea; 5Department of Rehabilitation Medicine, Seoul National University College of Medicine, Seoul, Republic of Korea; 6Department of Physical and Rehabilitation Medicine, Samsung Medical Center, Sungkyunkwan University School of Medicine, Seoul, Republic of Korea*These authors contributed equally to this workCorrespondence: Sunmee Jang, College of Pharmacy and Gachon Institute of Pharmaceutical Sciences, Gachon University, 191 Hambakmoe‑Ro, Yeonsu‑Gu, Incheon, 21936, Republic of Korea, Tel +82 32 820 4941, Email smjang@gachon.ac.kr Ji Hye Hwang, Department of Physical and Rehabilitation Medicine, Samsung Medical Center, Sungkyunkwan University School of Medicine, #81 Irwon-Ro, Gangnam-Gu, Seoul, 06351, Republic of Korea, Tel +82 10 9933 2816, Email hwanglee@skku.eduAbstract: Rehabilitation using digital healthcare (DHC) has the potential to enhance the effectiveness of treatment for musculoskeletal disorders (MSDs) and associated pain by improving patient outcomes, while being cost-effective, safe, and measurable. This systematic review and meta-analysis aimed to evaluate the effectiveness of musculoskeletal rehabilitation using DHC. We searched PubMed, Ovid-Embase, Cochrane Library, and PEDro Physiotherapy Evidence Database from inception to October 28, 2022 for controlled clinical trials comparing DHC to conventional rehabilitation. We used a random-effects model for the meta-analysis, pooling the effects of DHC on pain and quality of life (QoL) by calculating standardized mean differences (SMDs) with 95% confidence intervals (CIs) between DHC rehabilitation and conventional rehabilitation (control). Fifty-four studies with 6240 participants met the inclusion criteria. The sample size ranged from 26 to 461, and the average age of the participants ranged from 21.9 to 71.8 years. The majority of the included studies focused on knee or hip joint MSD (n = 23), and the most frequently utilized DHC interventions were mobile applications (n = 26) and virtual or augmented reality (n = 16). Our meta-analysis of pain (n = 45) revealed that pain reduction was greater in DHC rehabilitation than in conventional rehabilitation (SMD: − 0.55, 95% CI: − 0.74, − 0.36), indicating that rehabilitation using DHC has the potential to ameliorate MSD pain. Furthermore, DHC significantly improved health-related QoL and disease-specific QoL (SMD: 0.66, 95% CI: 0.29, 1.03; SMD: − 0.44, 95% CI: − 0.87, − 0.01) compared to conventional rehabilitation. Our findings suggest that DHC offers a practical and flexible rehabilitation alternative for both patients with MSD and healthcare professionals. Nevertheless, further researches are needed to elucidate the underlying mechanisms by which DHC affects patient-reported outcomes, which may vary depending on the type and design of the DHC intervention.Keywords: musculoskeletal disorder, rehabilitation, digital healthcare, pain, quality of life, patient-reported outcomes

Although Nesterov's accelerated gradient (NAG) methods have been studied from various perspectives, it remains unclear why the most popular forms of NAG must handle convex and strongly convex objective functions separately. Motivated by this inconsistency, we propose an NAG method that unifies the existing ones for the convex and strongly convex cases. We first design a Lagrangian function that continuously extends the first Bregman Lagrangian to the strongly convex setting. As a specific case of the Euler--Lagrange equation for this Lagrangian, we derive an ordinary differential equation (ODE) model, which we call the unified NAG ODE, that bridges the gap between the ODEs that model NAG for convex and strongly convex objective functions. We then design the unified NAG, a novel momentum method whereby the continuous-time limit corresponds to the unified ODE. The coefficients and the convergence rates of the unified NAG and unified ODE are continuous in the strong convexity parameter $\mu$ on $[0, +\infty)$. Unlike the existing popular algorithm and ODE for strongly convex objective functions, the unified NAG and the unified NAG ODE always have superior convergence guarantees compared to the known algorithms and ODEs for non-strongly convex objective functions. This property is beneficial in practical perspective when considering strongly convex objective functions with small $\mu$. Furthermore, we extend our unified dynamics and algorithms to the higher-order setting. Last but not least, we propose the unified NAG-G ODE, a novel ODE model for minimizing the gradient norm of strongly convex objective functions. Our unified Lagrangian framework is crucial in the process of constructing this ODE. Fascinatingly, using our novel tool, called the differential kernel, we observe that the unified NAG ODE and the unified NAG-G ODE have an anti-transpose relationship.

In this paper, we generalize the Nesterov accelerated gradient (NAG) method to solve Riemannian optimization problems in a computationally tractable manner. The iteration complexity of our algorithm matches that of the NAG method on the Euclidean space when the objective functions are geodesically convex or geodesically strongly convex. To the best of our knowledge, the proposed algorithm is the first fully accelerated method for geodesically convex optimization problems without requiring strong convexity. Our convergence rate analysis exploits novel metric distortion lemmas as well as carefully designed potential functions. We also identify a connection with the continuous-time dynamics for modeling Riemannian acceleration in Alimisis et al. [1] to understand the accelerated convergence of our scheme through the lens of continuous-time flows.