CellML 2.0.

We present here CellML 2.0, an XML-based language for describing and exchanging mathematical models of physiological systems. MathML embedded in CellML documents is used to define the underlying mathematics of models. Models consist of a network of reusable components, each with variables and equations giving relationships between those variables. Models may import other models to create systems of increasing complexity. CellML 2.0 is defined by the normative specification presented here, prescribing the CellML syntax and the rules by which it should be used. The normative specification is intended primarily for the developers of software tools which directly consume CellML syntax. Users of CellML models may prefer to browse the informative rendering of the specification (https://cellml.org/specifications/cellml_2.0/) which extends the normative specification with explanations of the rules combined with examples of their usage.

Reproducing the Hemoglobin Saturation Profile, a Marker of the Blood Oxygenation Level Dependent (BOLD) fMRI Effect, at the Microscopic Level.

The advent of functional MRI in the mid-1990s has catalyzed progress pertaining to scientific discoveries in neuroscience. With the prospect of elucidating the physiological aspect of the Blood Oxygenation Level Dependent (BOLD) effect we present a computational capillary-tissue system capable of mapping venous hemoglobin saturation- a marker of the BOLD hemodynamic response. Free and facilitated diffusion and convection for hemoglobin and oxygen are considered in the radial and axial directions. Hemoglobin reaction kinetics are governed by the oxyhemoglobin dissociation curve. Brain activation, mimicked by dynamic transitions in cerebral blood velocity (CBv) and oxidative metabolism (CMRO2), is simulated by normalized changes in m = (ΔCBv/CBv)/(ΔCMRO2/CMRO2) of values 2, 3 and 4. Venous hemoglobin saturation profiles and peak oxygenation results, for m = 2, based upon a 50% and a 25% increase in CBv and CMRO2, respectively, lie within physiological limits exhibiting excellent correlation with the BOLD signal, for short-duration stimuli. Our analysis suggests basal CBv and CMRO2 values of 0.6 mm/s and 200 µmol/100g/min. Coupled CBv and CMRO2 responses, for m = 3 and m = 4, overestimate peak hemoglobin saturation, confirming the system's responsiveness to changes in hematocrit, CBv and CMRO2. Finally, factoring in neurovascular effects, we show that no initial dip will be observed unless there is a time delay in the onset of increased CBv relative to CMRO2.

Inlet conditions for image-based CFD models of the carotid bifurcation: is it reasonable to assume fully developed flow?

BACKGROUND: Computational fluid dynamics tools are useful for their ability to model patient specific data relevant to the genesis and progression of atherosclerosis, but unavailable to measurement tools. The sensitivity of the physiologically relevant parameters of wall shear stress (WSS) and the oscillatory shear index (OSI) to secondary flow in the inlet velocity profiles was investigated in three realistic models of the carotid bifurcation. METHOD OF APPROACH: Secondary flow profiles were generated using sufficiently long entrance lengths, to which curvature and helical pitch were added. The differences observed were contextualized with respect to effect of the uncertainty of the models' geometry on the same parameters. RESULTS: The effects of secondary velocities in the inlet profile on WSS and OSI break down within a few diameters of the inlet. Overall, the effect of secondary inlet flow on these models was on average more than 3.5 times smaller than the effect of geometric variability, with 13% and 48% WSS variability induced by inlet secondary flow and geometric differences, respectively. CONCLUSIONS: The degree of variation is demonstrated to be within the range of the other computational assumptions, and we conclude that given a sufficient entrance length of realistic geometry, simplification to fully developed axial (i.e., Womersley) flow may be made without penalty. Thus, given a choice between measuring three components of inlet velocity or a greater geometric extent, we recommend effort be given to more accurate and detailed geometric reconstructions, as being of primary influence on physiologically significant indicators.