## Archive pour 7 septembre 2009

### lyon – vascular tree – theory – blood

Extension of Murray’s law using a non-Newtonian model of blood flow

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Author(s): Revellin R (Revellin, Remi)1,2, Rousset F (Rousset, Francois)1,2, Baud D (Baud, David)3, Bonjour J (Bonjour, Jocelyn)1,2
Source: THEORETICAL BIOLOGY AND MEDICAL MODELLING    Volume: 6  Article Number: 7    Published: MAY 15 2009
Times Cited: 0     References: 33 Citation Map
Abstract: Background: So far, none of the existing methods on Murray’s law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate.Modeling: In the present paper, Murray’s law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murray’s law remains valid (i.e. Sigma R-c = cste with c = 3 is verified and is independent of n, the dimensionless index in the viscosity equation; R being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of c may be calculated depending on the value of n.

Results: We find that c varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to c = 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature.

Conclusion: It is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid.

### LYON – mitochondria mammals birds lizard – UCP

Reptilian uncoupling protein: functionality and expression in sub-zero temperatures

Author(s): Rey B (Rey, Benjamin)1, Sibille B (Sibille, Brigitte)1, Romestaing C (Romestaing, Caroline)1, Belouze M (Belouze, Maud)1, Letexier D (Letexier, Dominique)1, Servais S (Servais, Stephane)1, Barre H (Barre, Herve)1, Duchamp C (Duchamp, Claude)1, Voituron Y (Voituron, Yann)1,2
Source: JOURNAL OF EXPERIMENTAL BIOLOGY    Volume: 211    Issue: 9    Pages: 1456-1462    Published: MAY 1 2008
Times Cited: 1 References: 51 Citation Map
Abstract: Here we report the partial nucleotide sequence of a reptilian uncoupling protein (repUCP) gene from the European common lizard ( Lacerta vivipara). Overlapping sequence analysis reveals that the protein shows 55%, 72% and 77% sequence homology with rat UCP1, UCP2 and UCP3, respectively, and 73% with bird and fish UCPs. RepUCP gene expression was ubiquitously detected in 4 degrees C cold-acclimated lizard tissues and upregulated in muscle tissues by a 20 h exposure to sub-zero temperatures in a supercooling state or after thawing. In parallel, we show an increase in the co-activators, peroxisome proliferator-activated receptor gamma coactivator-1 alpha (PGC-1 alpha) and peroxisome proliferator-activated receptors ( PPAR), mRNA expression, suggesting that the mechanisms regulating UCP expression may be conserved between mammals (endotherms) and reptiles (ectotherms). Furthermore, mitochondria extracted from lizard skeletal muscle showed a guanosine diphosphate (GDP)-sensitive non phosphorylating respiration. This last result indicates an inhibition of extra proton leakage mediated by an uncoupling protein, providing arguments that repUCP is functional in lizard tissues. This result is associated with a remarkable GDP-dependent increase in mitochondrial endogenous H2O2 production. All together, these data support a physiological role of the repUCP in superoxide limitation by lizard mitochondria in situations of stressful oxidative reperfusion following a re-warming period in winter.

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