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In the wake of the COVID-19 pandemic, many districts sought digital learning solutions to recover from learning loss, improve equity, and prepare for future interruptions. With this paper, we aim to provide information to policymakers and legislators regarding the value of resources needed to successfully implement comprehensive digital learning programing. We focus on the policies and resource allocation decisions made in North Carolina, one of the first states to launch a statewide digital learning initiative. First, we demonstrate the effects of state policy on school practices, then we turn the focus of the paper to how districts and schools allocated resources to implement digital learning. We apply the ingredients method to examine the costs of digital learning during the 2018-2019 school year. We close with recommendations for future policy and resource allocation.

Summary: Osteoporosis is related to changes in vertebral bone marrow tissues, which can be detected by MRI. A novel MRI scoring method based on routine T1 and T2 sequences has been developed and demonstrated capabilities in detecting osteoporosis and discriminating vertebral fractures. The scoring method may provide an alternative tool other than BMD measurement for broad, opportunistic use in clinics. Purpose: As a routinely used radiation-free modality at the spine, magnetic resonance imaging (MRI) is promising to assess osteoporosis because it can detect age- or osteoporosis-related changes in bone marrow tissues. Here, we proposed a new MRI scoring method using the patient's low-back subcutaneous fat and cerebrospinal fluid as reference controls on routine T1 and T2 sequences, respectively, to indicate proton-rich changes in vertebrae for assessing osteoporosis and vertebral fractures. Methods: The study included 60 female patients (64.1 ± 15.9 years) who underwent both MRI and quantitative computed tomography (QCT) at spine. T1-based F-scoresc.fat and T2-based W-scorecs.fluid were defined as the median signal intensity (SI) from L1 to L5 over their reference controls. QCT-measured vertebral BMD was used for defining osteoporosis. Receiver operating characteristic (ROC) analysis was performed to evaluate the diagnostic performances of the new scores for osteoporosis and vertebral fractures, which were also compared with L1–L5 signal-to-noise ratio (SNRL1−L5) or SNR-based vertebral bone quality (VBQ) score. Results: The F-scoresc.fat and W-scorecs.fluid increased significantly by 25.3% and 22%, respectively, in patients with osteoporosis compared to non-osteoporosis. Age was also found to be significantly different between non-osteoporosis and osteoporosis (49.92 and 74.03 years, p <.001). ROC analysis indicated that F-scoresc.fat had a greater AUC value (0.85, p <.001) than VBQ score (0.77) and SNRL1−L5 (0.71) when being used to detect osteoporosis. For separating vertebral fractures from non-fractures, F-scoresc.fat resulted in the largest AUC value of 0.81 (p <.001), compared to W-scorecs.fluid (0.74), VBQ (0.72), and SNRL1−L5 (0.75). Conclusion: A new MRI scoring method based on routine T1 and T2 sequences has been developed and demonstrated improved abilities in detecting osteoporosis and discriminating vertebral fractures over VBQ and SNR. [ABSTRACT FROM AUTHOR]

Osteocytes, situated within the lacunocanalicular network (LCN) of the bone matrix, play crucial roles in sensing mechanical signals and orchestrating bone adaptive responses. Alterations in LCN structure could significantly modify the fluid dynamic microenvironment of osteocytes, thereby influencing bone mechanoresponses (BMRs). However, a comprehensive understanding of this tissue remains elusive. In this study, a multi-scale model of whole bone-LCN was developed to systematically investigate the effects of lacunocanalicular morphology (lacunar volume [Lc.V] and canalicular area [Ca.S]) and network architecture (lacunar density [Lc.ρ] and canalicular density [Ca.ρ]) on fluid shear stress (FSS) within the LCN and BMR predicted by fluid flow. Furthermore, the relationships between fluid flow within the LCN and BMRs were examined in two specific scenarios: aging and lactation. Results demonstrated that changes in lacunocanalicular morphology (Lc.V and Ca.S) primarily influenced the intensity of fluid flow, while alterations in the LCN (Lc.ρ and Ca.ρ) largely affected the distribution of fluid flow. Increases in Lc.V or decreases in Ca.S increased FSS, whereas decreases in Lc.ρ or increases in Ca.ρ reduced FSS. Compared with other structural parameters, alterations in Ca.ρ had the greatest effect on FSS, while BMR primarily depended on changes in Lc.V and Ca.S. In agreement with experimental observations, aging- or lactation-induced changes in LCN structure (and fluid dynamics) were associated with reduced (−50%) or increased (+20%) bone responses to mechanical loading, respectively. These findings suggest that modifications in lacunocanalicular morphology and network architecture can substantially impact the fluid dynamic microenvironment for mechanosensing osteocytes and, consequently, BMRs. [ABSTRACT FROM AUTHOR]

Study Design: A prospective study. Purpose: To assess fat–water-like tissue changes on the 1st sacral vertebra using novel magnetic resonance imaging (MRI) phantom-based F- and W-scores and evaluate their diagnostic performances in osteoporosis detection. Overview of Literature: Using an uncommonly advanced MRI technique, previous studies have found that fat–water changes were consistent with osteoporosis. The role of routine MRI sequences can be extended in this regard. The S1 vertebra is considered a crucial anatomical site in spine surgeries because it seldom suffers from fractures. Thus, S1 could indicate osteoporotic fat–water changes. Methods: Forty-two female volunteers (aged 62.3±6.3 years) underwent spine examination with both MRI (including a phantom) and dual-energy X-ray absorptiometry (DXA) following ethical approval. MRI phantom-based F- and W-scoreS1 were defined by normalizing S1 vertebral signal intensities (SIs) by coconut oil and water SIs of the phantom on T1- and T2-weighted imaging, respectively. Using receiver operating characteristic analysis, the diagnostic performances of the new scores for evaluating osteoporosis and vertebral fractures were investigated against standard areal bone mineral density measured with DXA (DXA-aBMD). Results: The F-scoreS1 and W-scoreS1 were greater (4.11 and 2.43, respectively) in patients with osteoporosis than those without osteoporosis (3.25 and 1.92, respectively) and achieved areas under the curve (AUCs) of 0.82 and 0.76 (p<0.05), respectively, for osteoporosis detection. Similarly, the mean F-scoreS1 and W-scoreS1 were higher (4.11 and 2.63, respectively) in patients with vertebral fractures than in those without fractures (3.30 and 1.82, respectively) and had greater AUCs (0.90 for W-scoreS1 and 0.74 for F-scoreS1) than DXA-aBMD (AUC, 0.26; p<0.03). In addition, the F- and W-scoreS1 demonstrated a strong correlation (r=0.65, p<0.001). Conclusions: The new S1 vertebral-based MRI scores were developed to detect osteoporotic changes and demonstrated improvements over DXA-aBMD in differentiating patients with vertebral fractures. [ABSTRACT FROM AUTHOR]

In this study, a novel dynamic model of a ball bearing based on rigid–elastic–liquid (REL) coupling structure considering external load excitation is established, and the dynamic response of its outer ring under external load excitation is examined. First, the differential equation of the journal motion (i.e. the outer ring) is derived based on Newton’s law, and the oil film force induced by the REL coupling structure is determined by using the central finite difference method, planar bending theory of thin ring, and Simpson’s rule. Further, the fourth and fifth-order variable step length Runge–Kutta method is used to solve the kinematic differential equation. Second, the dynamic characteristics of the outer ring of the bearing under different speeds and elastic support structural parameters are examined. Finally, the feasibility of the theoretical model is verified through experiments. The results show that compared with the traditional squeeze film damper (SFD) system, the ball bearing with REL coupling structure is more stable, and the vibration damping effect is better under higher bearing speed, lower squirrel cage stiffness, and smaller elastic ring flexibility coefficient. The above findings provide useful insights into the dynamic characteristics of REL coupled ball bearings under unbalanced excitation, which can serve as a reference for the optimization design of such ball bearings. [ABSTRACT FROM AUTHOR]