Appendix C -MATHCAD Definitions and Subordinates cont'd

DOE-HDBK-1184-2004

Eckerman in "A Conversational Eigenanalysis Program for Solving Differential Equations," in

Computer Applications in Health Physics, Proceedings of the Seventeenth Midyear Topical

Symposium of the Health Physics Society, 1984 (Killough 1984). Excellent examples may be

found in "The Linear Algebra Problem Solver" by the Research and Education Association,

1980, gives excellent examples and discussion of the method (see problems 18-6 through 18-

11). Given the initial content of each compartment at t=0 and the rate matrix, the following

function calculates the coefficients for the retention functions:

coeff (k, q0) =

q0 ← submatrix(q0, 1, rows (k) , 1, 1)

( T)

V ← eigenvecs k

M ← lsolve(V, q0)

for j ∈ 1.. cols (k)

for i ∈ 1.. cols (k)

← V ⋅M

i, j

Deposition fractions for aerosol AMADs in the range of 0.001 to 10 microns are calculated by

interpolating from the respiratory tract deposition table given in the ICRP CD-ROM14. The

ICRP 66 respiratory tract model for occupational exposure (light work) was used to calculate the

values given in this table.

0.001

0.003

0.01

0.03

0.1

0.3

AI1

1.359E-04

6.714E-03

8.229E-02

1.525E-01

8.688E-02

4.458E-02

AI2

2.718E-04

1.343E-02

1.646E-01

3.051E-01

1.738E-01

8.916E-02

AI3

4.530E-05

2.238E-03

2.743E-02

5.085E-02

2.896E-02

1.486E-02

bbf

2.262E-02

8.770E-02

1.291E-01

7.188E-02

3.328E-02

1.523E-02

bbs

2.294E-02

8.895E-02

1.309E-01

7.290E-02

3.376E-02

1.544E-02

bbseq

3.212E-04

1.245E-03

1.833E-03

1.021E-03

4.726E-04

2.162E-04

BBf

3.117E-02

4.420E-02

2.685E-02

1.035E-02

4.746E-03

3.260E-03

BBs

3.161E-02

4.483E-02

2.723E-02

1.049E-02

4.813E-03

3.293E-03

BBseq

4.425E-04

6.276E-04

3.812E-04

1.469E-04

6.738E-05

4.619E-05

ET2

4.390E-01

3.494E-01

1.735E-01

6.994E-02

3.218E-02

5.820E-02

ETseq

2.196E-04

1.748E-04

8.680E-05

3.499E-05

1.610E-05

2.912E-05

ET1

4.433E-01

3.327E-01

1.539E-01

6.248E-02

3.071E-02

5.217E-02

The following function performs a linear interpolation of the values in the table to calculate the

deposition fractions in each compartment of the respiratory tract.

The ICRP Database of Dose Coefficients for Workers and Members of the General Public, Version 1.0

(Pergamon Press: New York) 1998 (ICRP 1998a).