Coronary artery bypass grafting hemodynamics and anastomosis design: a biomedical engineering review

10.1186/1475-925X-12-129BioMedical Engineering Online121Article number 129, 28 page

Functorial Semantics for the Advancement of the Science of Cognition

Cognition involves physical stimulation, neural coding, mental conception, and conscious perception. Beyond the neural coding of physical stimuli, it is not clear how exactly these component processes constitute cognition. Within mathematical sciences, category theory provides tools such as category, functor, and adjointness, which are indispensable in the explication of the mathematical calculations involved in acquiring mathematical knowledge. More specically, functorial semantics, in showing that theories and models can be construed as categories and functors, respectively, and in establishing the adjointness between abstraction (of theories) and interpretation (to obtain models), mathematically accounts for knowing-within-mathematics. Here we show that mathematical knowing recapitulates--in an elementary form--ordinary cognition. The process of going from particulars (physical stimuli) to their concrete models (conscious percepts) via abstract theories (mental concepts) and measured properties (neural coding) is common to both mathematical knowing and ordinary cognition. Our investigation of the similarity between knowing-within-mathematics and knowing-in-general leads us to make a case for the development of the basic science of cognition in terms of the functorial semantics of mathematical knowing

Biomechanics of bone-fracture fixation by stiffness-graded plates in comparison with stainless-steel plates

BACKGROUND: In the internal fixation of fractured bone by means of bone-plates fastened to the bone on its tensile surface, an on-going concern has been the excessive stress-shielding of the bone by the excessively-stiff stainless-steel plate. The compressive stress-shielding at the fracture-interface immediately after fracture-fixation delays callus formation and bone healing. Likewise, the tensile stress-shielding of the layer of the bone underneath the plate can cause osteoporosis and decrease in tensile strength of this layer. METHOD: In order to address this problem, we propose to use stiffness-graded plates. Accordingly, we have computed (by finite-element analysis) the stress distribution in the fractured bone fixed by composite plates, whose stiffness is graded both longitudinally and transversely. RESULTS: It can be seen that the stiffness-graded composite-plates cause less stress-shielding (as an example: at 50% of the healing stage, stress at the fracture interface is compressive in nature i.e. 0.002 GPa for stainless steel plate whereas stiffness graded plates provides tensile stress of 0.002 GPa. This means that stiffness graded plate is allowing the 50% healed bone to participate in loadings). Stiffness-graded plates are more flexible, and hence permit more bending of the fractured bone. This results in higher compressive stresses induced at the fractured faces accelerate bone-healing. On the other hand, away from the fracture interface the reduced stiffness and elastic modulus of the plate causes the neutral axis of the composite structure to be lowered into the bone resulting in the higher tensile stress in the bone-layer underneath the plate, wherein is conducive to the bone preserving its tensile strength. CONCLUSION: Stiffness graded plates (with in-built variable stiffness) are deemed to offer less stress-shielding to the bone, providing higher compressive stress at the fractured interface (to induce accelerated healing) as well as higher tensile stress in the intact portion of the bone (to prevent bone remodeling and osteoporosis)

Passive and active ventricular elastances of the left ventricle

BACKGROUND: Description of the heart as a pump has been dominated by models based on elastance and compliance. Here, we are presenting a somewhat new concept of time-varying passive and active elastance. The mathematical basis of time-varying elastance of the ventricle is presented. We have defined elastance in terms of the relationship between ventricular pressure and volume, as: dP = EdV + VdE, where E includes passive (E(p)) and active (E(a)) elastance. By incorporating this concept in left ventricular (LV) models to simulate filling and systolic phases, we have obtained the time-varying expression for E(a )and the LV-volume dependent expression for E(p). METHODS AND RESULTS: Using the patient's catheterization-ventriculogram data, the values of passive and active elastance are computed. E(a )is expressed as: [Image: see text]; E(p)is represented as: [Image: see text]. E(a )is deemed to represent a measure of LV contractility. Hence, Peak dP/dt and ejection fraction (EF) are computed from the monitored data and used as the traditional measures of LV contractility. When our computed peak active elastance (E(a,max)) is compared against these traditional indices by linear regression, a high degree of correlation is obtained. As regards E(p), it constitutes a volume-dependent stiffness property of the LV, and is deemed to represent resistance-to-filling. CONCLUSIONS: Passive and active ventricular elastance formulae can be evaluated from a single-beat P-V data by means of a simple-to-apply LV model. The active elastance (E(a)) can be used to characterize the ventricle's contractile state, while passive elastance (E(p)) can represent a measure of resistance-to-filling