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Generalized conservation equation for multicompartmental systems
Author(s) -
Adler Ronald S.
Publication year - 1987
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.596135
Subject(s) - tracer , projection (relational algebra) , simple (philosophy) , operator (biology) , lambda , exponential function , flow (mathematics) , mathematics , physics , mathematical analysis , statistical physics , chemistry , algorithm , mechanics , quantum mechanics , philosophy , biochemistry , epistemology , repressor , transcription factor , gene
A projection operator technique is used to derive an equation for local tissue tracer content Q ( t ), assuming linear multicompartmental kinetics for tracer utilization. The resulting equation has the form ( d / dt ) Q ( t )= FC a ( t ) −Λ Q ( t ) −∫ 0 td τ [ξ(τ) C a ( t −τ)−ψ(τ) Q ( t −τ)], where F and C a ( t ) denote local blood flow and concentration of tracer, respectively. Tissue complexity is contained within the new parameters Λ, ξ( t ), and ψ( t ), where the time dependent coefficients are expressed as sums of exponentials. Two simple applications are considered: tissue heterogeneity and internal trapping of tracer. The relationship to effective single compartmental analysis, as is used for local cerebral blow flow determination, is evaluated.