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**Objectives:**
** **
We investigated pharmacokinetic tissue distributions of Levofloxacin to explain adverse tendon incidents. **Methods:**
** **
The pharmacokinetic profiles of single and multiple dosing of 500
mg Levofloxacin following oral and IV infusion administration were simulated. Monte Carlo simulation was used to simulate the drug concentration profiles in plasma and tissue after seven dosing regimens while varying the drug’s elimination and distribution rates to analyze the effects of changing those rates on Levofloxacin accumulation in tissue. **Results:**
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Simulated data following oral and IV administration reflect well the reported data (mean simulated plasma Cmax
=
6.59
μg/mL and 5.19
μg/mL for IV and oral versus 6.4
μg/mL and 5.2
μg/mL for observed clinical IV and oral route, respectively). Simulations of seven repetitive doses are also in agreement with reported values. Low elimination rates affect the drug concentration in plasma and tissue significantly with the concentration in plasma rising to 35
μg/mL at day 7. Normal elimination rates together with escalation of distribution rates from plasma to tissue increase tissue concentration after 7 doses to 9.5
μg/mL, a value is more than twice that of normal. **Conclusions:**
** **
Simulation can be used to evaluate drug concentration in different tissues. The unexpectedly high concentrations in some cases may explain the reason for tendinopathy in clinical settings.

Tendinitis and tendon rupture have emerged with the popular use ofLevofloxacin [1-5]. Tendinopathy accounted for 4.1% of the cases and the compound could cause Achilles tendon rupture in 1% of subjects, a rate higher than previously thought [6,7]. The risk factors of Fluoroquinolones-induced tendinopathy include older age, concomitant corticosteroid therapy and renal dysfunction. Caution has been raised when prescribing a combination therapy of steroids and Levofloxacin to patients, particularly to those with known risk factors [

It has been shown that Levofloxacin levels were achievable in all tissue samples after a single intravenous dose despite high variability in its pharmacokinetics (PK) [_{max} (T_{max}) values in adipose (60 min) and muscle tissue (80 min) were shorter than that in lung tissue (90 min) yielding a shorter elimination half-life of Levofloxacin in the lung compared to muscle and adipose tissue [_{max} of the drug. In addition, stromatous tissue such as adipose tissue, articular capsule, trachea cartilage and tendon achieved similar concentrations of quinolones when subjected to a single dose of Fluoroquinolones intravenously in an experimental canine model albeit fat and the three latter kinds of tissues have significant discrepancy in structural constitution and distributive vasculatures [

The accumulation of Levofloxacin/Fluoroquinolones in tendon may be the reason for tendon incidents, however there is no confirmed mechanism or relationship between plasma concentrations to tendonitis and Achilles tendon rupture or whether additional unknown reasons cause increased drug accumulation in tendon tissue leading to complications. Therefore, a simple process useful to determine drug distribution rate to tendon tissue and to predict the biological outcomes in order to provide early warning for Levofloxacin toxicity in daily practice is warranted. Monte Carlo simulation was used in this study to assess the usefulness of pharmacokinetic prediction in relation to Levofloxacin tissue accumulation and tendinopathy. The objective was to elucidate possible factors that will delineate the potential relationships between Levofloxacin accumulation in tendon tissue (such as Levofloxacin tissue concentration, and distribution processes) and tendinopathy incidents that will lead to further studies that will refine the understanding of the Mechanism that cause tendinopathy so that prevention of the events can be better predicted.

A two-compartment open model with first-order absorption and elimination process was used to describe Levo-

floxacin plasma concentration time profile. The model is described by the following system of ordinary differential equations. Equation 1:. Equation (2):. Equation (3):. With X_{a}, X_{1}, X_{2} are the milligram amounts of drug in the gut, the central (plasma) and the peripheral compartments, respectively. K_{a} (hr^{−1}) and K_{0} (mg/h) are the absorption rate constant and the intravenous (IV) infusion rate of Levofloxacin, respectively. K_{el} (h^{−1}) is the elimination rate constant from the central compartment. K_{12}, K_{21} are the between-compartment transfer rate constants (all in hr^{−1}).

The other pharmacokinetic parameters are the volume of distribution (V). Equation (4):. Equation (5):. With C_{1}, C_{2} are Levofloxacin concentration in μg/mL in the central compartment and the peripheral compartments, respectively. V_{1}, V_{2} represent volume of distribution in the central and peripheral compartments in mL, respectively. F is the fraction of dose absorbed. In extravascular models, the fraction of dose absorbed cannot be estimated separately. Therefore, V_{1}/F was estimated together in PK modeling. Dpo is the administered dose orally. Pharmacokinetic parameter values (

Recall the ordinary differential Equations (2) and (3) above:

where: is the unit function

and T is the duration time of infusion.

Using the Laplace transform, we have the following

equation in the s domain:

where: are the initial conditions of.

At t = 0:

Linear equation and solution are as follows:

where:

and α, β are defined by:

, then:

Moreover,

where:

Now, by the inverse Laplace transform, we have the solution for in the time domain:

Then,

For a simulation of a 7 days treatment duration and 1 dose was administered a day, was replaced by in the above differential equations (Equations (6) and (7)). And as a result, was replaced by

in its representation in the s domain. Therefore, we had a similar solution for as follows:

And, see Equations (8) and (9).

Descriptive statistics of all levofloxacin PK parameters in healthy subjects and patients (mean, standard deviation, coefficient of variation) were obtained from literature. Pharmacokinetic simulation was then used to reveal the effect of input variables. A direct comparison of the experimental data (mean ± sd) obtained from simulation was involved. Comparison between the experimental and observed data from various studies reported in literature was conducted using a student t-test. Mean and standard deviations of PK parameters were determined to assess how well the model described the clinical data. The best PK model and log-normal distribution (mean and variance) of all the transfer rates were then used as input in the Monte Carlo simulation process to generate plasma and tissue concentrations.

A 2-compartment open model without a lag time was used to generate each concentration-time profile, where drug distribution rates (K_{12}, K_{21}) or drug elimination rate (K_{el}) were random variables associated with their distribution information. Their distributions were considered lognormal distributions. The mean concentration-time profile was generated by using mean values of PK parameters.

Investigation of varying the effect of elimination and distribution rates was performed using various values of those parameters. Monte Carlo simulation of 5000 drug concentration profiles was performed by importing elimination/distribution rates randomly into pharmacokinetic model and according gain blocks as in

Random function (rand) was used to randomly select pharmacokinetic parameter values which were associated to their distribution. The bounds for each PK parameter were set in accordance with the pharmacokinetic parameter values obtained. Simulink (Matlab, Natick, Massachusetts, USA) was used to simulate signals and determine how these concentrations vary over time using a system of 2 differential equations to describe plasma concentrations in compartment 1 and tendon concentration were in compartment 2.

The block Plasma (X_{1}) and Tissue(X_{2}) were two integrators. They took the integration of the inputs dX1/dt, dX2/dt and returned the outputs X_{1} and X_{2}. The block Pulse Generator 1 was to reset the integrator plasma compartment each 24 time steps (corresponding to 24 hours per day). The block Pulse Generator was to describe multiple doses: One dose oral or infusion calculated as amount over the time of infusion or duration of absorption (1 time step) dose per 24 hours (24 time steps). Other blocks including gain blocks (K_{12}, K_{21}, K_{el}, 1/V_{1}, 1/V_{2}) and sum blocks were to implement the left hand side of each of two differential equations. Concentration time profiles in two compartments were obtained in two scope blocks by running this simulation.

Plasma and well-perfused organs such as lung, skin, and

spongiosa etc. were grouped in compartment 1. Tissues characterized by poor blood flow such as tendon tissue (including Achilles tendon) along with adipose and cartilage were grouped in compartment 2. Tendon was anticipated to have very low redistribution rate compared to other sites, and was grouped in compartment 2 where the distribution rate is comparable to those of cortical bone and adipose tissue [9,11,13].

In addition, simulated data also show that after a single dose, drug concentration values in tissue achieved at Cmax of 3.08 μg/mL and 3.28 μg/mL, and Tmax of 3.25 hrs and 3.11 hr, and AUC0-24 of 42.05 μg∙hr/mL and 42.91 μg∙hr/mL for 500 mg oral dose and IV infusion, respectively.