RESUMO
The thermodynamically constrained averaging theory (TCAT) is a comprehensive theory used to formulate hierarchies of multiphase, multiscale models that are closed based upon the second law of thermodynamics. The rate of entropy production is posed in terms of the product of fluxes and forces of dissipative processes. The attractive features of TCAT include consistency across disparate length scales; thermodynamic consistency across scales; the inclusion of interfaces and common curves as well as phases; the development of kinematic equations to provide closure relations for geometric extent measures; and a structured approach to model building. The elements of the TCAT approach are shown; the ways in which each of these attractive features emerge from the TCAT approach are illustrated; and a review of the hierarchies of models that have been formulated is provided. Because the TCAT approach is mathematically involved, we illustrate how this approach can be applied by leveraging existing components of the theory that can be applied to a wide range of applications. This can result in a substantial reduction in formulation effort compared to a complete derivation while yielding identical results. Lastly, we note the previous neglect of the deviation kinetic energy, which is not important in slow porous media flows, formulate the required equations to extend the theory, and comment on applications for which the new components would be especially useful. This work should serve to make TCAT more accessible for applications, thereby enabling higher fidelity models for applications such as turbulent multiphase flows.
RESUMO
OBJECTIVE: To investigate radiographic changes of the tibial tuberosity after tibial plateau leveling osteotomy (TPLO) surgery and identify clinical findings and risk factors associated with such changes. STUDY DESIGN: Retrospective study. SAMPLE POPULATION: Hundred and eighty-six client-owned dogs (219 stifles) that had TPLO surgery. METHODS: Patient data retrieved included radiographic changes of the tibial tuberosity during re-examination, age, body weight, whether unilateral or single-session bilateral surgery had been performed, location of the anti-rotational pin, approximate tibial tuberosity area, and approximate average tibial tuberosity width. RESULTS: Fracture with resulting caudal displacement of the proximal tibial tuberosity (1.4%; 3 of 219) occurred less frequently than non-displaced tibial tuberosity fractures (7.3%; 16 of 219). Age, weight, average tibial tuberosity width, location of the anti-rotational pin, and single session bilateral surgery were identified as risks factors for non-displaced fracture. Weight divided by the square of the average tibial tuberosity width may be a stronger risk factor than either weight or average tibial tuberosity width alone. CONCLUSIONS: Dogs undergoing single session bilateral TPLO surgery are at greater risk for developing non-displaced tibial tuberosity fractures. The non-displaced tibial tuberosity fracture does not appear to adversely affect outcome or lead to tibial tuberosity avulsion. Significant risk factors for fracture of the proximal tibial tuberosity with caudal displacement were not identified. CLINICAL RELEVANCE: Factors including age, weight, tibial tuberosity thickness, and conditions that may enhance strain on the tibial tuberosity, such as single-session bilateral procedures, may increase risk of fracture.
