The yield coefficient and the specific growth rate used to develop three types of microbial growth kinetic relationships; Monod, first order,and zero order kinetics. Ecuacion De Monod 1 2 on WN Network delivers the latest Videos and Editable pages for News & Events, including Entertainment, Music, Sports, Science and. Original Title. Evaluacion de los parametros cineticos de la ecuacion de Monod. Primary Subject. BIOMASS FUELS (S09). Record Type. Journal article. Journal.
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We present an analysis of the corneal oxygen consumption Q c from non-linear models, using data of oxygen partial pressure or tension p O 2 obtained from in vivo estimation previously reported by other authors. Assuming that the ve is a single homogeneous layer, the oxygen permeability through the cornea will be the same regardless of the type of lens that is available on it.
The obtention of the real value of the maximum oxygen consumption rate Q c ,max is very important because this parameter is directly related with the gradient pressure profile into the cornea and moreover, ve real corneal oxygen consumption is influenced by both anterior and posterior oxygen fluxes. Our calculations give different values for the maximum oxygen consumption rate Q c ,maxwhen different oxygen pressure values high and ecuackon p O 2 are considered at the interface cornea-tears ecuzcion.
Present results are relevant for the calculation on the partial pressure of oxygen, available at different depths into the corneal tissue ecuaciin contact lenses of different oxygen transmissibility. The rate exuacion oxygen consumption in the cornea is an important parameter to guarantee its physiology, and it may be influenced by the use of contact lenses over the cornea.
Estimation of tear oxygen pressure or tension p c behind hydrogel lenses in humans, using a time-domain phosphorescence measurement system, allowed to obtain the oxygen consumption from established oxygen diffusion models.
Such authors make use of the nonlinear Monod kinetics model to describe the local oxygen-consumption rate. Nevertheless, although the consumption of oxygen is a result of corneal cell metabolism that depends on a great number of factors, Chhabra et al.
Here Q c ,max is the maximum corneal oxygen-consumption rate, k c is the corneal oxygen solubility, fcuacion D c is the corneal oxygen diffusion coefficient. K m is the methabolic or Monod dissociation equilibrium constant, and is a parameter in the Monod kinetic model, which determines the shape of the Q c vs.
The appropriate relationship ecuacino oxygen consumption and p c into the cornea should be continuous, yielding a value of zero mmonod when p c is zero. Moreover, oxygen consumption should increase with increasing p c until the saturation level is reached. Considering this, we proceeded with the analysis of the oxygen consumption using non-linear models, and also using data from in vivo estimations of partial oxygen pressure at the interface cornea-lens, provided by Bonanno personal communication.
This work aims to present a single mathematical one-dimensional model of monld oxygen diffusion through the cornea. The experimental data provided by Bonanno et al. For this purpose, similar to Chhabra et al. In our calculations ecuaccion oxygen permeability through the corneal tissue is considered constant, independent of the lens material situated onto the cornea, and the maximum oxygen consumption rate is also independent of the soft contact lens weared.
From the values obtained for the parameter Q c ,maxthe oxygen pressure profile into the cornea has been calculated for the open eye and closed eye conditions. Finally, we have established a comparison with the oxygen tension profiles given by Chhabra et al. The non-steady state diffusion equation that gives oxygen tension as a mono of time and position, for homogeneous slab of oxygen-consuming tissue assuming a one-dimensional model for the corneais given by:.
In steady-state conditions, Eq. As we have mentioned, the aerobic metabolism is quantified by the Monod kinetics model, also known as Michaelis—Menton model, 5,8 which relates the oxygen consumption with the oxygen tension by mean of the expression. By mean of the non-linear Monod kinetics model, Chhabra et al. This value is 2. Furthermore, Chhabra et al. Parameters optimized ecuaion Chhabra et al. Nevertheless, the Chhabra’s value for K m tends to be an estimated average value, and in this way it may be perfectly acceptable.
Anyway, our greater ecuwcion to the results given by Chhabra et al. This is clear evidence that the values obtained by Chhabra et al. These values are in disagreement with the value of the cornea oxygen permeability used by the researchers during the last 30 years, which are of For this reason, the values of the parameters ecuacoon Monod kinetic model should be revisited and new fits should be obtained. The analysis of the experimental transitory, in combination whith Eq.
In this paper, following a similar procedure to that of Chhabra et al. The noninvasive in vivo experimental data provided by Bonanno et al. Values of Q c ,max obtained fitting the curves showed in Figs. Red color is the fit to Bonanno data proposed by Chhabra et al.
Evaluation of the kinetic parameters of the Monod equation|INIS
Symbols are from Bonanno et al. A closer inspection of Fig. Table 1 to fit the experimental data of postlens tear-film oxygen tension as a function of time at the interface corneal lens red lineon wearing Balafilcon lens from Bonanno et al. This is clearly related to the value of oxygen corneal oxygen permeability considered by Chhabra et al. However, in the case of cornea-Polymacon1 lens and cornea-Polymacon2 lens systems, the behavior nonod our calculated curve is arguably similar than Chhabra’s curve, as can be seen in Figs.
On the other hand, Fig. As can be seen, the metabolic model Michaelis—Menton modelwith our parameters successfully reproduces experimental results for transient oxygen tension during closed-eyes contact lens wear and steady state oxygen tension over several eduacion transmissibilities. The values of our parameters, while fitting the data by Bonanno, provides good results, and the best fits are obtained for Monod dissociation equilibrium constant K mand corneal oxygen permeability constant for all systems analyzed.
Thus, for a given lens on the cornea, our results reproduce individual experiments in an acceptable manner, maintaining constant the values of the parameters K m and Dk c. However, the maximum oxygen consumption rate diminishes when the oxygen tension at the interface cornea-lens diminish, contrary to what was expected see Table 2. As occurs in other models, these results may be subject to certain limitations, like the uncertainties in experimental data, especially at high oxygen tensions and this could constitute as an intrinsic limitation of the model itself.
Considering the limitations of the model to explain the rate of change of the experimental data, which does not correspond to the tendency of the value reported by Bonanno et al. This kinetics transition can be understood as a consequence of the existence of other effects into the cornea than those eucacion in the metabolic reactions that occur in the Krebs cycle.
Bear in mind that, in the range from low to moderate other phenomena such as corneal swelling can occur.
It should be mnood that, when it has many parameters in an analysis of experimental data the physical meaning of the values obtained must be taken into account with caution. Dde, in Chhabra et al. In this paper we present a procedure for solving the non-linear partial differential equation for the position and time depending pressure p c xtfor the oxygen diffusion model of the human cornea, which is an alternative solution respect to Chhabra’s work.
In this sense, the novelty of the results obtained here, consists in provide, previous to the solution of the model, the values of diffusion coeffcient D c and solubility k c. Therefore, the only fitted value is the corneal oxygen-consumption rate Q c ,max.
Despite this limitation the present work shows a revision of the procedure described before by Chhabra et al. As can be seen, the metabolic model Michaelis—Menton modelwith our parameters, successfully reproduces experimental results for transient oxygen tension during closed-eyes contact lens wear and steady state oxygen tension over several lens transmissibilities.
Our results reproduce individual experiments in an acceptable manner, maintaining constant the values of the parameters K m and Dk c.
Moreover our main finding is that the maximum oxygen consumption rate is not a constant, but diminishes when the oxygen tension at the interface cornea-lens diminish. The general equation describing oxygen transport through the lens-corneal system, in one dimension, is Fick’s second law with a reaction term. The second term on the right-hand side in Eq. A is the oxygen consumption as a function of the partial pressure, which is absent in the contact lens region and follows a Monod kinetics form in the corneal system:.
Athe solubility k and diffusion coefficient D are considered function of the position, taking constant values across each of the ecjacion regions contact lens and cornea in the system. Using the above approach we could obtain the complete pressure profile, provided the continuity of the pressure is satisfied in the lens—cornea interface. This is automatically satisfied within our numerical scheme.
As for the initial condition, in order minod reproduce the evolution of the pressure profile from the closed eye condition, we need to feed the stationary pressure profile in Eq. This stationary closed eye profile can be obtained by solving the steady-state equation:.
Aby removing the temporal evolution. D is subject to the boundary conditions:. We then use the solution to Eqs. D and E to define:. The system of Eqs.
Table 1 shows the different values for the parameters used in the numerical solution of the equations. D and E are solved numerically, and the resulting profile is used as initial condition for Eqs. An iterative procedure was used due to the nonlinear nature of the transport Eqs.
We checked ecuavion, grid size and time step parameters, so that further decrease in size did not result in any improvement. All the computations were performed in a personal computer with an Intel Core iK under Debian Linux.
We used this optimization procedure to determine optimized values of the Q c monov and K m parameters, for a predefined set of the remaining parameters in the model. National Center for Biotechnology InformationU.
Journal List J Optom v. Published online Jul Del Castilloa Ana R. Ferreira da Silvac Saul I. Author information Article notes Copyright and License information Disclaimer. Received Jan 13; Accepted Jun 3. Abstract Purpose We present an analysis of the eciacion oxygen consumption Q c from non-linear models, using data of oxygen partial pressure or tension p O 2 obtained from in vivo estimation previously reported by other authors.
Methods Assuming that the cornea is a single homogeneous layer, the oxygen permeability through the cornea will be the same regardless of the type of lens that is available on it. Results Our calculations give different values for the maximum oxygen consumption rate Q c ,maxwhen different oxygen pressure values high and low p O 2 are considered at the interface cornea-tears film.
Conclusion Present results are ecuaacion for the calculation on the partial pressure of oxygen, available at different depths into the corneal tissue behind contact lenses of different oxygen transmissibility. Corneal oxygen consumption, Corneal oxygen permeability, Monod kinetics model, Corneal oxygen pressure. Introduction The rate of oxygen consumption in the cornea is an important parameter to guarantee its physiology, and it may be influenced by the use of contact lenses over the cornea.
Methods The non-steady state diffusion equation that gives oxygen tension as a function of time and position, for homogeneous slab of oxygen-consuming tissue assuming a one-dimensional model for the corneais given by: Table 1 Parameters optimized by Chhabra et al. Open in a separate window. Results The noninvasive in vivo experimental data provided by Bonanno et al. Table 2 Values of Q c ,max obtained fitting the curves showed in Figs. In this work we have only optimized of Q c ,max parameter.
The rest or parameters have been taken from literature, as we point out through the text.