BME 595

Spring 2003

HW #4.E

1. Write the model equations for the following two models.

1b. Assume that the Plasma input, P(t), is the same in both models. (What does it mean to make this assumption – one sentence.) Now rearrange the model for (II) to solve for P. Then substitute the expression for P into the model for (I). What have we accomplished (one sentence)?

2. Write a Matlab program to perform a Logan plot.

Program will need to

a. load in 2 text files: plasma curve (2 columns: [time concentration]), and PET curve (3 columns: [start_time stop_time radioactivity]) (these times are in sec!!!)

b. calculate the frame time midpoint

c. decay correct the PET curve (plasma already corrected) using the appropriate decay constant for ¹¹C-raclopride.

d. calculate the running integrals needed for the Logan plot to assemble the ‘Y’ and ‘X’ variables.

e. calculate the slope

Now lets test the program:

3. Apply the program to the 11 data files on the class web-site. The same plasma curve can be used for all tissue curves.

4. Calculate the DV for files #1-11.

5. Assume that file #11 is the cerebellum. Calculate the DV ratio for files #1-10. Why? What assumptions are at work here?

6. Plot the estimated DV vs. noise level for files #1-10.

7. What’s going on here (two sentences)?

8. What parameter are we really interested in? How is it related to DV.

Data files #1-5

K₁ = 0.0918 ml/min/g

k₂ = 0.4484 min^-1

k_on = 0.0282 (pmol/ml)^-1/min

k_off =0.1363 min^-1

B’_max = 44.0 pmol/ml

snr = [ 10 20 40 60 noiseless]

Data files #6-10

K₁ = 0.0918 ml/min/g

k₂ = 0.4484 min^-1

k_on = 0.0282 (pmol/ml)^-1/min

k_off =0.1363 min^-1

B’_max = 5.0 pmol/ml

snr = [10 20 40 60 noiseless]

Data file #11

K₁ = 0.0918 ml/min/g

k₂ = 0.4484 min^-1

B’_max = 0 pmol/ml

snr = 0