Characterizing stages of COVID-19 epidemics: a nonlinear physics perspective based on amplitude equations

The relevant dynamics underlying COVID-19 waves is described from an amplitude space perspective. To this end, the amplitude dynamics of infected populations is considered in different stages of epidemic waves. Eigenvectors and their corresponding amplitudes are derived analytically for low-dimensional models and by means of computational methods for high-dimensional models. It is shown that the amplitudes of all eigenvectors as functions of time can be tracked through the diverse stages of COVID-19 waves featuring jumps at the stage boundaries. In particular, it is shown that under certain circumstances the initial, outbreak stage and the final, subsiding stage of an epidemic wave are primarily determined by the unstable eigenvector of the initial stage and its corresponding remnant vector of the final stage. The corresponding amplitude captures most of the dynamics of the emerging and subsiding epidemics such that the problem at hand effectively becomes one dimensional leading to a dramatic reduction of the complexity of the problem at hand. Explicitly demonstrated for the first-wave COVID-19 epidemics of the year 2020 in the state of New York and Pakistan are given.

Comparison of Two Synthetic Bone Graft Products in a Rabbit Posterolateral Fusion Model

BACKGROUND

The drawbacks of iliac crest autograft as graft material for spine fusion are well reported. Despite continued modifications to improve bone healing capacity, the efficacy of synthetic graft materials as stand-alone replacements remains uncertain. The rabbit posterolateral fusion model is an established environment for testing of fusion concepts. It offers the opportunity to obtain radiographic, biomechanical and histological data on novel fusion materials. The objective of this study was to compare the spine fusion capability of two synthetic bone graft products in an established rabbit posterolateral spine fusion (PLF) model: Signafuse® Bioactive Bone Graft Putty and Actifuse® ABX.

METHODS

Bilateral intertransverse spine fusion was performed at the L5-L6 transverse processes (TPs) of New Zealand White rabbits using either Signafuse or Actifuse ABX as the bone graft material. Bone remodeling and spine fusion were assessed at 6 and 12 weeks using radiographic, biomechanical and histological endpoints.

RESULTS

Fusion rate by manual palpation at 6 weeks was greater for Signafuse (33%) compared to Actifuse ABX (0%), and equivalent in both groups at 12 weeks (50%). Biomechanical fusion rate based on flexion-extension data was 80% in Signafuse group and 44% for Actifuse ABX. Histology revealed a normal healing response in both groups. MicroCT and histomorphometric data at 6 weeks showed greater new bone formation in the Signafuse group compared to Actifuse ABX (p <0.05), with no differences detected at 12 weeks. Histological fusion scores were greater in the Signafuse group at 6 and 12 weeks, indicated by higher degree structural remodeling and tendency towards complete bridging of the fusion bed compared to the Actifuse ABX group.

CONCLUSION

Confirmed by several metrics, Signafuse outperformed Actifuse ABX as a standalone synthetic bone graft in an established PLF model, demonstrating greater rates of bone remodeling and spine fusion. The combination of 45S5 bioactive glass and biphasic HA/βTCP granules of Signafuse appear to provide greater bone healing capability in comparison to the 0.8% silicate-substituted hydroxyapatite material of Actifuse ABX.

Effect of aspirin on bone healing in a rabbit ulnar osteotomy model

BACKGROUND

Aspirin is frequently prescribed following orthopaedic surgery. Although there is substantial evidence that some nonsteroidal anti-inflammatory drugs (NSAIDs) are associated with delayed bone healing, there have been few studies of the effects of aspirin on bone healing and, to our knowledge, none on the effects of physiologic dosages.

METHODS

Following ulnar osteotomy, fifty-six rabbits were administered a placebo (nine rabbits), indomethacin (nine rabbits given 12.5 mg/kg daily), or aspirin at various doses and schedules (2.7 mg/kg daily for ten rabbits, 10 mg/kg daily for nine rabbits, 50 mg/kg twice daily for ten rabbits, and 100 mg/kg three times daily for nine rabbits). The aspirin doses were chosen to span the clinical dosing range. The indomethacin group served as a positive control and as a relative comparison with the effect of aspirin. Radiographs were obtained every two weeks and the animals were killed at eight weeks. Mechanical testing was performed on all rabbits except for six selected for histological evaluation.

RESULTS

Aspirin delayed bone healing, as demonstrated radiographically and with mechanical testing, in a dose-dependent fashion at salicylate levels equivalent to those resulting from typical human dosing (low-dose aspirin). Receiver operating characteristic analysis demonstrated a plasma salicylate threshold above 20.7 μg/mL predicting delayed bone healing. This approximates a single human dose of 325 mg. Salicylate levels above this threshold were associated with delayed bone healing similar to that caused by indomethacin. Aspirin dosing frequency did not affect bone healing. Mechanical testing was highly predictive of radiographic healing. The interobserver reliability of radiographic assessment of healing at six and eight weeks (kappa = 0.83 and 0.79, respectively) compared favorably with interobserver reliability in previous studies assessing cortical bridging.

CONCLUSIONS

In a rabbit ulnar osteotomy model, aspirin delayed bone healing with a threshold equivalent to a human dose of 325 mg.

Cervical laminoplasty construct stability: an experimental and finite element investigation

STUDY DESIGN

Experimental and finite element investigation of cervical laminoplasty.

OBJECTIVE

To determine the stability of the construct post cervical laminoplasty.

SUMMARY OF BACKGROUND DATA

Cervical laminoplasty is a widely used technique to widen the spinal canal dimensions without permanently removing the dorsal elements of the cervical spine. Although various laminoplasty procedures have been developed recently, the use of mini-plates to hold the lamina open and prevent restenosis of the spinal cord is a fairly new method and has not been thoroughly investigated.

METHODS

Biomechanical compression tests and finite element analyses were performed in this study. Sixteen cervical vertebrae (C3 - C6) were isolated from six cadaveric cervical spines (age at death 68 to 91 years; mean 85 years) and were used for compression tests. Out of the 16 vertebrae, four were without any surgical intervention and the remaining 12 were implanted with one of the two laminoplasty plates: open door (OD) graft. Each vertebra was randomly assigned to one of the three groups: OD plate (6), graft plate (6) or intact vertebrae (4). The intact and implanted vertebrae were potted and loaded to failure. Cross-head displacements and the corresponding reaction force throughout the test were recorded to determine the failure loads. A finite element model of the C5 cervical vertebra was created to accommodate the laminoplasty implants. Experimental loading and boundary conditions were simulated and the stress distribution in the lamina was predicted in response to the compressive loads.

RESULTS

A substantial increase in the sagittal canal diameter (27%-33%) and the spinal canal area (31.2%-47%) was observed at all levels. The strength of the implanted specimens was considerably decreased (by six to eight times) as compared to the intact specimens.

CONCLUSION

Experimentally obtained data can be combined with mathematical models, such as finite element models, to accurately predict the biomechanical behavior (stresses and strains) of implants and the posterior bone which may not be possible by the use of any other method.

Validation of a C2-C7 cervical spine finite element model using specimen-specific flexibility data

This study presents a specimen-specific C2-C7 cervical spine finite element model that was developed using multiblock meshing techniques. The model was validated using in-house experimental flexibility data obtained from the cadaveric specimen used for mesh development. The C2-C7 specimen was subjected to pure continuous moments up to +/-1.0 N m in flexion, extension, lateral bending, and axial rotation, and the motions at each level were obtained. Additionally, the specimen was divided into C2-C3, C4-C5, and C6-C7 functional spinal units (FSUs) which were tested in the intact state as well as after sequential removal of the interspinous, ligamentum flavum, and capsular ligaments. The finite element model was initially assigned baseline material properties based on the literature, but was calibrated using the experimental motion data which was obtained in-house, while utlizing the ranges of material property values as reported in the literature. The calibrated model provided good agreement with the nonlinear experimental loading curves, and can be used to further study the response of the cervical spine to various biomechanical investigations.

Effects of direct current electrical stimulation on gene expression of osteopromotive factors in a posterolateral spinal fusion model

STUDY DESIGN

An in vivo model was used to determine levels of mRNA expression in response to direct current (DC) electrical stimulation in a rabbit posterolateral fusion model.

OBJECTIVES

This study tested the possibility that DC stimulation at the surgery site would increase expression of genes related to bone formation relative to expression in autograft alone.

SUMMARY OF BACKGROUND DATA

DC electrical stimulation as an adjunct treatment in spinal surgery has shown increased fusion rates when compared with autograft alone, yet the biology of such treatment is not fully understood.

METHODS

Thirty New Zealand White rabbits were entered into the study. A posterolateral, intertransverse process fusion was performed bilaterally at L4-L5, with autogenous bone graft. An implantable DC stimulator was placed across the decorticated transverse processes before placement of autograft. Animals were killed at 3, 7, 14, 21, and 28 days. mRNA levels of BMP-2, 4, 6, 7, VEGF, FGF-2, TGF-beta, ALK-2, and ALK-3 were evaluated with real-time RT-PCR.

RESULTS

mRNA expression was significantly higher in the DC stimulated animals versus the control animals for several of the genes studied. In particular, levels of mRNA were elevated for BMP-2, BMP-6, and BMP-7.

CONCLUSIONS

This study shows for the first time that DC stimulation results in a sustained increase of multiple osteogenic genes, suggesting that the biologic mechanism for the DC-induced increase in the rate and extent of bone formation observed clinically may be mediated by the up-regulation of these osteoinductive factors.

Multidrug-resistant Salmonella Typhimurium infection from milk contaminated after pasteurization

An outbreak of multidrug-resistant Salmonellaenterica serotype Typhimurium infections occurred in Pennsylvania and New Jersey. A case-control study implicated pasteurized milk from a dairy, and an inspection indicated the potential for contamination after pasteurization. Dairy cattle are the likely reservoir, and milk may be an important vehicle of Salmonella transmission to humans.