(312a) Analytical Model of Local Distribution of Chemicals in Tissues with First Order Rate Metabolism Kinetics

Analytical
model of local distribution of chemicals in tissues with first order rate
metabolism kinetics.

Alexander
Golberg,

Department
of Mechanical Engineering, Etcheverry Hall,
6124, University of California at Berkeley, Berkeley, CA 94720 USA

Email:
agolberg@gmail.com

Tel:
+1 -510-2216557

Abstract

The profile of regional distribution of
chemicals in tissue is important for the fundamental analyses of metabolism,
morphogenetic growth control and the development of novel regional therapies. One
of the challenges in tissue and whole organ research is predicting local
chemical distribution. Here we introduce an analytical approach for the temporal
and spatial regional distribution mapping of chemicals in metabolically active,
perfused tissues. The new aspect of this model is in local chemical
concentration dependence on of tissue perfusion rate, in addition to diffusion
and metabolism rates. Using Duhamel theorem we performed dimensionless and
dimensional analysis for local chemical distribution and report on steady-state
and transient solutions for tissues with the first rate kinetic order of clearance
by perfusion and metabolism. The predictions of our model are in good
correlation with clinically observed data on percutanious ethanol ablation volumes
of liver. Our study shows the importance to incorporate tissue perfusion rate to
the fundamental  understanding of in vivo intercellular
signaling and treatment planning of regional therapies, which
include local drug injection, which include electrochemotherapy, percutanious
ethanol ablation and regional anesthesia.

Table
1. Model
inputs and values investigated in the parametric study.

Fig.1  Analyzed physical system.

Fig.2 Parametric study
results. a. Dimensionless drug penetration depth (X_t) 
as a function of minimum active concentration(ε). b. Drug
penetration depth as a function of a drug fraction in %. c. Dimensionless
steady state concentration as a function of dimensionless metabolic rate (W). 
d. Drug steady-state concentration (C_ss) for various
perfusion and absorption rates.

Fig.3  Parametric
study results. Transient dimensionless concentration as a function of
dimensionless perfusion rate (W) and time (F).

Fig.4  Parametric study
results. a. Transient dimensionless concentration as a function of
dimensionless time and location for dimensionless perfusion rate W=50
b. Transient concentration as a function of time and location for perfusion
rate w_p+k_b=5*10^-3 s^-1.

Fig.5  Parametric study
results. a. Dimensionless time to steady-state (F_ss) as a
function of dimensionless metabolic rate (W) b. Time to reach steady
state (t_ss) as function of perfusion (w_p) and metabolism
rates (k_b).

Fig.6  Practical
example. Ethanol concentration in a liver as a function of location and
time during percutaneous
ethanol injection therapy. The system parameters appear in Table
2. 98% ethanol was injected in the liver (Boundary condition).

Table
2. Diffusion
and metabolic parameters for percutaneous ethanol injection of liver
model.

Fig.7  Practical example. Calculated
distance
from the injection point at which ethanol causes liver tumor ablation by
necroses (points 1-4) and apoptosis (point 5) as described in Table 3:

Table
3. Toxic
ethanol concentration for various exposure durations.