Functional Dependence of IM and HV Angle in Hallux Valgus Deformity before and after Operative

Hallux valgus is a relatively common and multifaceted complex deformity of the front part of the foot. It is the result of multiple effects of innate (endogenous) and exogenous etiological factors with different degrees of influence. The degree of hallux valgus deformity is usually assessed by radiological values of hallux valgus (HV) and intermetatarsal (IM) angles. The aim of the paper is to justify the definition of hallux valgus deformity as a function of one angle, (HVA or IMA), and then to determine the functional connection and the most suitable function equalizing the values of the angles IMA and HVA. As hallux valgus is a double angulation deformity, the analytically determined connection between the HVA and IMA angles reduces the study of the deformity to the study of function with one argument, and makes the analysis of deformity changes before and after operative treatment simpler. For the determined connections between the angles, the values of linear proportionality coefficients and regression coefficients of corresponding linear functions of analytical equalization of the value of the IM angle and the degree of deformity for a given value of the HV angle were experimentally determined. The obtained results were checked on a sample of 396 operatively treated hallux valgus deformities. The presented analytical approach and the obtained functional links of IMA and HVA enable quantitative observation of the change in the degree of deformity based on the radiologically determined value of these angles, and the established nonlinear function will be useful for evaluating the expected value of the IM angle and the degree of deformity based only on the measured value of the HV angle. .

Relationship between single and bulk mechanical properties for zeolite ZSM5 spray-dried particles

In this work typical mechanical properties for a catalyst support material, ZSM5 （a spray-dried granular zeolite）, have been measured in order to relate the bulk behaviour of the powder material to the single particle mechanical properties. Particle shape and size distribution of the powders, determined by laser diffraction and scanning electron microscopy （SEM）, confirmed the spherical shape of the spray-dried particles. The excellent flowability of the material was assessed by typical methods such as the Hausner ratio and the Cart index, This was confirmed by bulk measurements of the particle-particle internal friction parameter and flow function using a Schulze shear cell, which also illustrated the low compressibility of the material. Single particle compression was used to characterize single particle mechanical properties such as reduced elastic modulus and strength from Hertz contact mechanics theory. Comparison with surface properties obtained from nanoindentation suggests heterogeneity, the surface being harder than the core. In order to evaluate the relationship between single particle mechanical properties and bulk compression behaviour, uniaxial confined compression was carried out. It was determined that the Adams model was suitable for describing the bulk compression and furthermore that the Adams model parameter, apparent strength of single particles, was in good agreement with the single particle strength determined from single particle compression test.