Appendix C -MATHCAD Definitions and Subordinates

DOE-HDBK-1184-2004

APPENDIX C MATHCAD DEFINITIONS AND SUBROUTINES

As an alternative to calculating each total removal rate constant individually, one may use the

function total, which sums the rate constants in each row and assigns the sum to the diagonal

element of the rate matrix. The function is defined in the next appendix.

k = total( k, λ)

The eigenvalues and coefficients for each compartment are calculated. Note that the content of

each compartment at time t is defined in the function q(t,comp) by a sum of 39 exponential

terms.

( T)

e = eigenvals k

C = coeff (k, q0)

cols( k)

(

)

∑

⋅exp  e ⋅t

q(t , comp ) =



comp , i

i=1

The content of all compartments at time t=0 calculated with the function qall should equal the

sum of what was deposited in the body.

cols( k)

∑

qall(t) =

q(t , j)

j=1

In other words, if everything goes OK, what goes into the system

urine

∑

q0 = 0.81957

i = AI1

should equal the material that is in the system at t=0 days for a radioactive material(or any other

time for insoluble material).

qall(0) = 0.81957

The function Decays is used to calculate the number of decays that occur in each compartment

of the biokinetic model.

Decays(x) =

s←0

for j ∈ AI1 .. urine

( ( j)

(

))

x, j

s←s-

⋅ exp e ⋅0 - exp e ⋅50⋅365

x, j

Decays ← s ⋅24⋅3600