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Published bySandy Aster Modified over 2 years ago

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by Andrew McGovern

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Introduction What the model is What it does How it was implemented The model in action Results

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Purpose of the model To describe the function of the kidney mathematically. To enable renal function to be measure from imaging. A number of attempts to do this with limited success. 1-3 Tofts’ model measures: renal filtration, renal blood volume and blood flow. 4,5

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C p art C p glom CdCd ABC Composition of the model A: B and C:

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Implementing the model Maths:Images:

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Implementing the model boolean step5() { double t = Global.flipangle * Math.PI/180; double r1; float ct[] = new float[Global.size]; Global.modsigEV = new float[Global.size]; Global.modsigIV = new float[Global.size]; Global.modkidneysig = new float[Global.size]; float s0 = (float)(Global.precontrenalsig*(1.000-Math.cos(t)*Math.exp(-0.001*Global.trms/Global.t10kidney))/((1.000-Math.exp(-0.001*Global.trms/Global.t10kidney))*Math.sin(t))); int i; for (i = 0; i < Global.size; i++) { ct[i] = (float)(Global.vb*( *Global.hctsmall)*Global.cpren[i]); r1 = 1/Global.t10kidney + Global.r1kidney*Global.vdcd[i]; Global.modsigEV[i] = (float)(s0*(1.00-Math.exp(-0.001*Global.trms*r1))*Math.sin(t)/(1-Math.exp(-0.001*Global.trms*r1)*Math.cos(t))); r1 = 1/Global.t10kidney + Global.r1kidney*ct[i]; Global.modsigIV[i] = (float)(s0*(1.00-Math.exp(-0.001*Global.trms*r1))*Math.sin(t)/(1-Math.exp(-0.001*Global.trms*r1)*Math.cos(t))); ct[i] += Global.vdcd[i]; r1 = 1/Global.t10kidney + Global.r1kidney*ct[i]; Global.modkidneysig[i] = (float)(s0*(1.00-Math.exp(-0.001*Global.trms*r1))*Math.sin(t)/(1-Math.exp(-0.001*Global.trms*r1)*Math.cos(t))); } return true; } /** Model input selection function */ boolean getToftsInputs() { boolean error; String GIRFoptions[] = {"Gaussian", "Delayed exponential"}; String effluxoptions[] = {"Off", "On"}; String input, effout = effluxoptions[0], girfout = " "; if(Global.effluxoptions) effout = effluxoptions[1]; switch(Global.girfoption) { case(1): girfout = GIRFoptions[0]; break; case(2): girfout = GIRFoptions[1]; break; } /** Creates an input dialog box */ do { GenericDialog d = new GenericDialog("Tofts' Model: Input box", IJ.getInstance()); d.addNumericField("End fit time (seconds after bolus arrives): ", Global.endfittime, 0, 6, "s"); d.addChoice("Inpulse response function", GIRFoptions, girfout); d.addChoice("Efflux: ", effluxoptions, effout);

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Results

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Filtration rateBlood volume

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The future A few mathematical discrepancies to fix Publish the program on the internet Test the model with diseased kidneys Use as a research tool Use in clinical practice

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References 1.David LB, Ala'a ES, Ching MC, Andrew PJ, Hari M, Philip AK. Measurement of single kidney function using dynamic contrast-enhanced MRI: Comparison of two models in human subjects. J Magn Reson Imaging. 2006;24(5): Miles KA, Leggett DA, Bennett GA. CT derived Patlak images of the human kidney. Br J Radiol Feb;72(854): Daghini E, Juillard L, Haas JA, Krier JD, Romero JC, Lerman LO. Comparison of mathematic models for assessment of glomerular filtration rate with electron-beam CT in pigs. Radiology Feb;242(2): Tofts PS, Cutajar M, Mendichovszky IA, Peters AM, Miles KA, Buckley DL, et al. Estimation of renal filtration and vascular parameters using a simple three- compartment model for dynamic contrast-enhanced MRI of the kidney. Unpublished Work: Brighton and Sussex Medical School Tofts PS, Cutajar M, Mendichovszky IA, Gordon I. Accurate and precise measurement of renal filtration and vascular parameters using DCE-MRI and a 3- compartment model. International Society for Magnetic Resonance in Medicine Conference. Stockholm 2010.

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