paracosh curve-fitting codes  (MathWorks Inc)

Journal: International Journal of Molecular Sciences

Article Title: Determination of Krogh Coefficient for Oxygen Consumption Measurement from Thin Slices of Rodent Cortical Tissue Using a Fick’s Law Model of Diffusion

doi: 10.3390/ijms24076450

Figure Lengend Snippet: Representative O 2 pressure profiles drawn from datasets v4 (first two columns) and v5 (third column). Profiles ( a , b , d , f ) show a gradient discontinuity at the lower boundary; profiles ( c , e ) do not. Negative/positive locations correspond to points lying above/below the x = 0 line of symmetry. Key: × = sample values; ⊗ = samples selected for 9-point in-tissue curve-fit (parabola or paracosh); dashed-green = extrapolation of parabola/paracosh curve into fluid layers above (left) and below (right) the tissue–fluid interface; dashed-red = tangent to curve at boundary with slope ( ∂ P / ∂ x ) | x = L [mmHg/ μ m]; solid-black linear segments identify linear pressure trends in proximal fluid layer; ‘Curv’ = 10 3 × curvature = 10 3 × ( 2 a ) [mmHg/ μ m 2 ]. Gradient ratios ‘slopeL/tang’, ‘slopeR/tang’ give estimates for above-slice, below-slice ( K t / K f ) Krogh ratios; ratios exceeding cutoff value 0.725 are rejected.

Article Snippet: The Matlab paracosh curve-fitting codes plus associated sample pO 2 depth profiles will be supplied on request to the corresponding author (D.A.S.-R.).

Techniques:

Journal: International Journal of Molecular Sciences

Article Title: Determination of Krogh Coefficient for Oxygen Consumption Measurement from Thin Slices of Rodent Cortical Tissue Using a Fick’s Law Model of Diffusion

doi: 10.3390/ijms24076450

Figure Lengend Snippet: Summary table for 47 pO 2 pressure profiles. ‘Ref’ = vnn where v = [3, 4, 5] identifies dataset, nn = profile index; ‘Flow’ = aCSF flow rate [mL/min]; ‘Flat’ = flag indicating paracosh (1) or parabolic (0) fit; ‘rmse’ = rms error for curve fit [mmHg]; ‘Curvature’ = 10 3 × ( 2 a ) [mmHg/ μ m 2 ]; P s = fitted surface pressure at x = L boundary [mmHg]; P min = fitted pressure at x = 0 [mmHg]; ‘Tangent’ = ( ∂ P / ∂ x ) | x = L [mmHg/ μ m]; ‘Ratio (top)’, ‘Ratio (bot)’ = Krogh ratio ( K t / K f ) at upper, lower interface. NB: Values in [brackets] are to be disregarded (existence of stationary layer is implausible).

Article Snippet: The Matlab paracosh curve-fitting codes plus associated sample pO 2 depth profiles will be supplied on request to the corresponding author (D.A.S.-R.).

Techniques:

Journal: International Journal of Molecular Sciences

Article Title: Determination of Krogh Coefficient for Oxygen Consumption Measurement from Thin Slices of Rodent Cortical Tissue Using a Fick’s Law Model of Diffusion

doi: 10.3390/ijms24076450

Figure Lengend Snippet: Distribution of Krogh ratios as a function of curvature of fitted parabolic/paracosh function. Results are clustered by dataset (three columns: v3/v4/v5) and interface (two rows: upper/lower). Dashed-red horizontal marks the selected cut-off between accepted (below red line) and rejected (above line) Krogh ratios. Scanning from left to right, lower aCSF flow rates are generally associated with reduced curvature values, implying increasingly constrained O 2 consumption. Linked pairs show repeated sampling at the same location. For v4, flow rate was set at 1 (open circles) or 2 mL/min (filled circles); for v5, flow rate was fixed at 0.5 mL/min. Outlier pairs 414/416 (v4) and 507/508 (v5) have very discrepant Krogh ratio estimates at the lower interface, possibly due to mechanical disturbance of the slice during withdrawal of O 2 probe prior to repeat sounding. See and .

Article Snippet: The Matlab paracosh curve-fitting codes plus associated sample pO 2 depth profiles will be supplied on request to the corresponding author (D.A.S.-R.).

Techniques: Sampling

Journal: International Journal of Molecular Sciences

Article Title: Determination of Krogh Coefficient for Oxygen Consumption Measurement from Thin Slices of Rodent Cortical Tissue Using a Fick’s Law Model of Diffusion

doi: 10.3390/ijms24076450

Figure Lengend Snippet: Flow rate clustering and curvature dependence aggregated across (lower interface) of d–f. ( a ) Aggregated scatterplot of candidate Krogh ratio ( K t / K f ) vs. curvature of fitted parabolic/paracosh function, clustered by flow rate [10, 2, 1, or 0.5] mL/min, as indicated by shaded convex-hull polygons (computed via Matlab function convhull). Qualitatively, the polygon centroids move to the left as flow rate decreases, implying that curvature decreases (profiles become flatter) as perfusion flow rate is reduced. This trend is made quantitative in ( b ) with a sigmoid fit to the curvature means (magenta asterisks) at each flow rate. The fitted curve is y = y max · x n / ( K n + x n ) with [ y max = 7.5 × 10 − 3 mmHg/ μ m 2 ; K = 0.75 mL/min; n = 0.75 ].

Article Snippet: The Matlab paracosh curve-fitting codes plus associated sample pO 2 depth profiles will be supplied on request to the corresponding author (D.A.S.-R.).

Techniques:

Journal: International Journal of Molecular Sciences

Article Title: Determination of Krogh Coefficient for Oxygen Consumption Measurement from Thin Slices of Rodent Cortical Tissue Using a Fick’s Law Model of Diffusion

doi: 10.3390/ijms24076450

Figure Lengend Snippet: Curvature histograms for each of the [v3, v4, v5] datasets illustrated in . As flow rate decreases from ( a ) 10 → ( b ) [1 or 2] → ( c ) 0.5 mL/min, average curvature decreases, meaning that the parabolic/paracosh curves become ‘flatter’ with shallower wings. For fixed K t , a flatter curvature implies reduced metabolism.

Article Snippet: The Matlab paracosh curve-fitting codes plus associated sample pO 2 depth profiles will be supplied on request to the corresponding author (D.A.S.-R.).

Techniques: