**Renography**

The pharmacon injected into the body is excreted by the kidney and taken to the urinary bladder together with the urine. There can be a few reasons of inappropriate excretion. Mentioning only a couple of them: bad kidney blood supply, malfunction of kidney’s excretion function, barrier of urine flow (e.g. kidney stone or other space narrowing procedure). The last two can be examined by renography. In the case of classical renography, stationary detectors are used. Recently, this method has dated next to the renography made by camera.

During recording time, patient sits in front of a vertical camera.

The procedure is disturbed by background activity, therefore areas outside the kidney and the bladder behaving as background respect to the procedure are marked as well.

CPS means the Count Per Second and CPM denotes the Count Per Minute.

A time-activity curve is created for the marked areas. It has two methods: based on the total activity on the ROIs and the average pixel activity. Both of them have benefits and disadvantages. In the first case, the ratio of how the two kidneys are participating in the excretion can be seen. According to this, a choice can be made whether the remaining kidney is able to provide the excretion alone after the removal of a seriously diseased kidney. However, if one of the kidneys is significantly smaller than the other, it is hard to judge whether the smaller one participates accordingly to its size. In the case of the curves based on pixel averages the situation is the opposite. The degree of the participation of kidneys cannot be seen well, but it is decidable whether the smaller kidney works properly or not.

It is usual to apply background subtraction on the curves. In the case of the curves made by the average pixel method, i.e. the subtraction by the background curve from the other curves and the replacement of the negative values with 0. If the curves are created based on the total activity then the area of ROIs should be taken account. If T signifies the ROI, T_{BG} is the area of background, G is the curve and G_{BG} is the value of background curve, than the background corrected curve is G_{C} = G - G_{BG} T / T_{BG}.

Quantitative parameters important to physicians:

T_{max}:l time belonged to maximal value of the curve

Index: Integral of the curve up to the maximum

T_{1/2}: halftime belonged to descending part of the curve. In order to obtaining this, an exponential fitting to the descending part taken at the kidney is needed.

#### Clearance

Clearance is the amount of liquid filtered out of the blood per unit time respect to unit plasma concentration. If U is the amount of liquid in 1 ml urine, P is the same in 1 ml plasma and V is the amount of urine filtered out per unit time, than C clearance is:

C = U V / P ml/min

The meaning of clearance is how fast the excretion of a certain substance (alcohol, narcotic drug …) is from the body. To evaluate this, activity measurements are needed with camera and at a hollow measuring station.

Since the measurements are taken at different times, applying decay correction on all of the measured results is necessary. The values received after decay correction are the same values that we would get from measurements all taken at t=0. If the activity at t = t_{1} moment is N_{1}, then according to the law of decayN_{1} = N_{0} 0,5^{t1 / T1/2}, where N_{0} is the activity that one would measure at t = 0. From this, N_{0} = N_{1} 0,5^{- t1 / T1/2} = N_{1} 2^{t1 / T1/2}. Hereinafter activity is used for the decay corrected activity.

The activity of the full syringe is measured: C_0, after that the half of the activity is squirted into a flask and the remaining activity is measured with camera: C_1. The activity in the flask is diluted to D ml and one ml of its activity is measured at the hollow measuring station.

An examination is carried out with the remaining activity, for instance renography.

After the examination, the activity of the empty syringe is measured.

Then one determines how much the Ba activity injected into the patient would be measured at the hollow measuring station. The total activity of the standard (St) is measured to St = D * S. Ba was measured with camera as (C_{1}-C_{2}) and St to (C_{0}-C_{1}). So (C_{1}-C_{2}) = St:(C_{0}-C_{1}) and Ba = D * S * (C_{1}-C_{2}) / (C_{0}-C_{1}).

The plasma concentration can be written as A_{0}e^{-k t} exponential function, but neither A_{0} nor k are known. For their evaluation blood is taken from the patient at t_{1} and t_{2} moments, than the A_{1} and A_{2} activity of 1 ml of its plasma is measured at the hollow measuring station. With the substitution with these values and computing the logarithm of the two equations we get:

ln(A_{1}) = ln(A_{1}) - kt_{1} and

ln(A_{2}) = ln(A_{1}) - kt_{2}

Using the difference between the two equation and rearranging it, we get:

k = A_{1}) - ln(A_{2}? / (t_{2} - t_{1}).

From k , A_{0} can be calculated: A_{0} = A_{1}e^{kt}.

The area where the injected activity is distributed (circulating plasma) is called distributional area. The volume of it is: V = Ba / A_{0} the clearance is : C = V * k ml.

If V is known (it can be from other measurements), then according to Ba = A_{0} * V equation the concentration of alcohol, drugs… in the blood at a certain time can be evaluated with the measurement of the plasma concentration of alcohol, drugs… in the plasma afterwards in two times.

Comment: As we saw, there is no need to perform renography in order to obtain the clearance, but since the radiopharmaceutical has already been injected, the examination does not mean additional patient irradiation. Nowadays, clearance estimation and determination is performed together with the renography image processing support, i.e. clearance calculation is included into the renography evaluation in order to obtain the complete pharmaceutic kinetic analysis of the kidney (see Figure 16. the result of ^{99m}TcMAG3 Bubeck method for both TER clearance and renography evaluation). [4]; [5]

^{99m}TcMAG3)