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Calculation of pharmacokinetic parameters from hemodialysis or hemoperfusion data — a mathematical treatise

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Abstract

A method is outlined to estimate from hemodialysis or hemoperfusion data, respectively, the rate constants, the distribution volume in the beta-phase, and other pharmacokinetic parameters of toxic substances. All calculations are based on the assumption that the usual linear open two-compartment system is also the appropriate model in a particular intoxication. No prior knowledge of the time of application or of the dose of the toxic substance is needed. The pharmacokinetic parameters may be helpful to estimate the benefit of hemodialysis or hemoperfusion, respectively, in future intoxications.

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Abbreviations

\(A_c (\overline t _0 ), A_c (\overline t _0 ), A_c (\overline t ), A_c (\overline t _{late} ), A_c (\overline t _0 ), A_c (\overline t ),\),A c (t 0),A c (t):

amount of substance in the central compartment at times\(\hat t_0 ,\bar t,\bar t_{late} \),t 0, andt, respectively

A H :

amount of substance removed by HD/HP

\(A_p (\overline t _0 ), A_p (\overline t ), A_p (\overline t _{late} )\),A p (t 0),A p (t) :

amount of substance in the peripheral compartment at times\(\overline t _0 , \overline t , \overline t _{late} \),t 0, andt, respectively

\(A_{c\bar a} ,A_{c\bar \beta } ,A_{p\bar a} ,A_{p\bar \beta } ,A_{ca} ,A_{c\beta } ,A_{pa} ,A_{p\beta } \) :

time-invariant constants as defined for instance in equations 26 and 31

\(A(\overline t _0 )\),A(t 0):

total amount of substance in the body at\(\overline t _0 \) andt 0, respectively

A u :

amount of unchanged substance eliminated into the urine

A w (t 0):

total amount of substance in the body if no HD/HP has been performed

ā c ,ā p ,a c ,a p :

Laplace-transforms of\(A_c (\overline t ), A_p (\overline t )\),A c (t), andA p (t), respectively

C(¯t 0),C(¯t),C(t 0),C(t) :

concentrations in the central compartment at times\(\overline t _0 , \overline t \),t 0, andt, respectively

\(C_{out} (\overline t )\) :

concentration at the outlet of the HD/HP equipment

\(C_{\bar a} ,C_a ,C_{\bar \beta } ,C_\beta \) :

time-invariant constants as defined in equations 46a and 46b

\(\bar g_c , \bar g_p \),g c ,g p :

numerator matrices

\(\bar h\),h :

denominator matrices

\(\bar k\),k 10,k H ,k 12,k 21 :

micro-constants of compartments

\(\bar m\),m :

constants relating the central amount to the peripheral amount at the onset and offset, respectively, of the HD/HP phase

n :

running number of a sample pair

N :

final number of a sample pair

Q u ,Q h :

renal and HP clearance, respectively

s :

Laplace operator

\(\hat t_0 ,\hat t,\hat T\) :

onset time, running time, and offset time, respectively, of the pre-HD/HP period

\(\overline t _0 , \overline t , \bar T\) :

onset time, running time, and offset time, respectively, of the HD/HP period

t 0,t :

onset time and running time, respectively, of the post-HD/HP period

V c :

volume of the central compartment

\(V_{d\bar \beta } ,V_{d\beta } \) :

volume of distribution in theβ-phase of the HD/HP period and post-HD/HP period, respectively

\(\bar Z\) :

abbreviation for\(A_c (\overline t _0 )\) andA c (t 0 ), respectively

\(\hat a,\bar a,a;\hat \beta ,\bar \beta ,\beta :\),ā,α;\(\hat \beta \),\(\bar \beta \),β :

“distribution” coefficients and disposition coefficients in the pre-HD/HP phase (\(\hat t\)-domain), HD/HP phase (\(\bar t\)-domain) and post HD/HP phase (t-domain), respectively

ɛ(t) :

extraction ratio of HD/HP

Φ(¯t) :

flow during HD/HP

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Authors and Affiliations

  1. Department of Toxicology, Medizinische Hochschule Hannover, D-3000, Hannover, Federal Republic of Germany

    Hans H. Wellhöner

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  1. Hans H. Wellhöner
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Wellhöner, H.H. Calculation of pharmacokinetic parameters from hemodialysis or hemoperfusion data — a mathematical treatise. Arch Toxicol 53, 17–31 (1983). https://doi.org/10.1007/BF01459998

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  • DOI: https://doi.org/10.1007/BF01459998

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