Convergence analysis and validation of a discrete element model of the human lumbar spine

Degenerative diseases of the spine can lead to or hasten the onset of additional spinal problems that significantly reduce human mobility. The spine consists of vertebral bodies and intervertebral discs. The most degraded are intervertebral discs. The vertebral body consists of a shell (cortical bone tissue) and an internal content (cancellous bone tissue). The intervertebral disc is a complex structural element of the spine, consisting of the nucleus pulposus, annulus fibrosus, and cartilaginous plates. To develop numerical models for the vertebral body and intervertebral disc, first, it is necessary to verify and validate the models for the constituent elements of the lumbar spine. This paper, for the first time, presents discrete elements-based numerical models for the constituent parts of the lumbar spine, and their verification and validation. The models are validated using uniaxial compression experiments available in the literature. The model predictions are in good qualitative and quantitative agreement with the data of those experiments. The loading rate sensitivity analysis revealed that fluid-saturated porous materials are highly sensitive to loading rate: a 1000-fold increase in rate leads to the increase in effective stiffness of 130 % for the intervertebral disc, and a 250-fold increase in rate leads to the increase in effective stiffness of 50 % for the vertebral body. The developed model components can be used to create an L4-L5 segment model, which, in the future, will allow investigating the mechanical behavior of the spine under different types of loading.

Effect of the Progressive Increase of Organic Loading Rate in an Anaerobic Sequencing Batch Reactor for Biodiesel Wastewater Treatment

The wastewater from the biodiesel industry is an environmental problem, and from a sanitation resources perspective, the anaerobic sequencing batch reactor (ASBR) is an interesting alternative for wastewater treatment. A better understanding of ASBR operation behavior under the progressive increase of the organic loading rate (OLR) is crucial for upscaling. The objective of this study was to monitor an ASBR operating with an OLR ranging from 1.3 to 9.3 kgCOD m−3 d−1. The average chemical oxygen demand (COD) removal efficiencies of the ASBR were 52, 41, 47, and 11% for phases 1, 2, 3, and 4, respectively. The apparent kinetic coefficient, i.e., the rate of degradation of organic matter, was between 0.10 and 1.80 h−1, considering the kinetic model that considers the residual substrate concentration, which was the one that best fit the obtained data. The progressive increase in applied OLR modified the microbial biomass diversity, which in turn influenced the degradation kinetics of the organic matter. In addition, the values of the applied OLR of 5.1 kgCOD m−3 d−1 and a food to microorganism ratio (F/M) of 0.6 kgCOD kgVSS−1 d−1 were shown to be limiting values that promoted the overload of ASBR.

Dynamic simulation and optimization of anaerobic digestion processes using MATLAB

Time series-based modeling provides a fundamental understanding of process fluctuations in an anaerobic digestion process. However, such models are scarce in literature. In this work, a dynamic model was developed based on modified Hill’s model using MATLAB, which can predict the biomethane production with time series. This model can predict the biomethane production for both batch and continuous process, across substrates and at diverse conditions such as total solids, loading rate, and days of operation. The deviation between literature and the developed model was less than ±7.6%, which shows the accuracy and robustness of this model. Moreover, statistical analysis showed there was no significant difference between literature and simulation, verifying the null hypothesis. Finding a steady and optimized loading rate was necessary to an industrial perspective, which usually requires an extensive experimental data. With the developed model, a stable and optimal methane yield generating loading rate could be identified at minimal input.