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Flow rate models in renal obstruction

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Abstract

Background

In acute unilateral renal obstruction, calculated divided renal uptake following injection of tracer may be normal. Divided renal function as measured by uptake may be insensitive to fall in renal plasma flow (RPF) to the obstructed kidney. This study analyses afferent flow rate parameters of optimised models of renogram time activity curves (TAC). Afferent flow rate parameters may have differing sensitivity to altered RPF from divided renal tracer uptake and may be more sensitive to changes in cortical function in renal obstruction.

Method

Twenty-four background-corrected renogram TACs using 99mTc-labelled mercapto-acetyl-triglycine (MAG3) with a unilateral obstructive pattern and six normal control renograms TACs were studied. Optimised computed models of each curve were constructed using specialised software (ModelMaker, Cherwell Scientific) and using the Marquardt Least Squares method. Following optimisation to the TAC of each target renogram, the afferent flow rate parameters were calculated.

Results

Following optimisation of models, afferent flow rate parameters, expressed as arbitrary units, (mean 0.15, SD 0.06) in acutely obstructed kidneys, were typically reduced in comparison with those of normal kidneys (mean 0.44, SD 0.04). (Paired t test; P < 0.005). By contrast, this reduction in afferent flow rate parameter was greater than the reduction in differential tracer uptake for the obstructed kidney (divided renal function of the obstructed group; mean 0.3, SD 0.14 compared with the control group; mean 0.45, SD 0.05 (P < 0.05).

Conclusion

Optimised modelling of TACs of obstructed renograms is feasible and may provide a more sensitive index of parenchymal dysfunction in early obstruction than comparing divided renal tracer uptake.

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Authors and Affiliations

  1. Nuclear Medicine Department, Royal Preston Hospital, Lancashire Teaching Hospitals NHS Trust, Preston, PR2 9HT, UK

    J. P. Coffey

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Correspondence to J. P. Coffey.

Appendix

Appendix

The differential equations describing the model are indicated below, where B is the tracer concentration in the blood compartment, C is tracer concentration in the renal compartment. The afferent and efferent flow constants for the compartments are represented by ka and ke, respectively.

$$ {\frac{{{\text{d}}B}}{{{\text{d}}t}}} = - k_{a} B $$
(1)
$$ {\frac{{{\text{d}}C}}{{{\text{d}}t}}} = k_{e} B - k_{e} C $$
(2)

With resolution of these, renal input time function may be obtained as.

$$ C_{1} (t) = e^{{( - k_{e} t)}} {\frac{{\left( {k_{e} - k_{a} } \right)C_{1,0} - k_{a} B_{0} + \left( {k_{a} B_{0} } \right)e^{{\left( {k_{e} - k_{a} } \right)t}} }}{{\left( {k_{e} - k_{a} } \right)}}} $$
(3)

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Coffey, J.P. Flow rate models in renal obstruction. World J Urol 29, 109–114 (2011). https://doi.org/10.1007/s00345-010-0569-8

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  • DOI: https://doi.org/10.1007/s00345-010-0569-8

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