NMD-22

GFR snapshot (plasma slope)

GFR ≈ [ln(C1/C2)/(t2−t1)] Vd. Two-sample plasma clearance.

Reading speed

ClearanceGates GFR

Governing equation

\mathrm{GFR}=\dfrac{\ln(C_1/C_2)}{t_2-t_1}\,V_d

$C_2 \in \left[0.2, 20\right]$

where

C_1: Concentration 1 (kBq/ml)
C_2: Concentration 2 (kBq/ml)
t_1: Time 1 (min)
t_2: Time 2 (min)
V_d: Distribution volume (ml)
GFR: Plasma clearance (ml/min)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\mathrm{GFR}=\dfrac{\ln(C_1/C_2)}{t_2-t_1}\,V_d

$C_2 \in \left[0.2, 20\right]$

$C_2 = 0.2$ $GFR = 461.1$

Along the curve

②

Domain of the variable — blue

C_2_{\min} = 0.2,\quad C_2_{\max} = 20

$C_2 \in \left[0.2, 20\right]$

$C_2 = 0.2$ $C_2 = 0.2$

Along the curve

③

Response curve — green

\mathrm{GFR}=\dfrac{\ln(C_1/C_2)}{t_2-t_1}\,V_d

$C_2 \in \left[0.2, 20\right]$

$C_2 = 0.2$ $GFR = 461.1$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}GFR}{\mathrm{d}C_2}

$C_2 \in \left[0.2, 20\right]$

$C_2 = 0.325$ $GFR^{\prime} = -405.9$

Along the curve

Lecture brief

Historical brief

MIRD schema, in-vivo decay, uptake fractions and PET coincidence turned unsealed sources into organ dose. The sheets compute activity, residence and well-counter geometry. This sheet (NMD-22 — GFR snapshot (plasma slope)) is the form associated with Gates GFR. Working symbols: $C_1$ , $C_2$ , $t_1$ , $t_2$ , $V_d$ $\rightarrow$ $GFR$ . 51Cr-EDTA or 99mTc-DTPA. A single-compartment slope after the distribution phase is the classical snapshot.

Purpose

Purpose: compute

GFR

from

C_1

C_2

t_1

t_2

V_d

in Nuclear medicine via

\mathrm{GFR}=\dfrac{\ln(C_1/C_2)}{t_2-t_1}\,V_d

GFR ≈ [ln(C1/C2)/(t2−t1)] Vd. Two-sample plasma clearance. Use it when a real nuclear medicine question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

C_1 = 8.000\,\mathrm{kBq/ml}

C_2 = 3.000\,\mathrm{kBq/ml}

t_1 = 120.000\,\mathrm{min}

t_2 = 240.000\,\mathrm{min}

V_d = 15000.000\,\mathrm{ml}

, the governing relation

\mathrm{GFR}=\dfrac{\ln(C_1/C_2)}{t_2-t_1}\,V_d

yields

GFR = 122.6\,\mathrm{ml/min}

. Two plasma points and a falling log-line. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Concentration 1 C_18 kBq/mlConcentration 2 C_23 kBq/mlTime 1 t_1120 minTime 2 t_2240 minDistribution volume V_d15000 ml

Outputs

Plasma clearance GFR122.6 ml/min

Reading speed

Watch on YouTube

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Narration of this film

Two plasma points and a falling log-line.

51Cr-EDTA or 99mTc-DTPA. A single-compartment slope after the distribution phase is the classical snapshot.

Reading speed

Watch on YouTube