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Dynamics of tear fluid components transportation through contact lenses
Physica Medica (2007) 23, 80e84
available at www.sciencedirect.com
journal homepage: http://intl.elsevierhealth.com/journals/ejmp
TECHNICAL NOTE
Dynamics of tear fluid components transportation through contact lenses ´niak, Zdzis1aw B1aszczak Micha1 S. Kaczmarek*, Zenon Woz Faculty of Physics, Division of Optics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznan´, Poland Received 7 April 2006; received in revised form 26 March 2007; accepted 28 March 2007 Available online 25 May 2007
KEYWORDS Contact lenses; Permeability; Jamin interferometer
Abstract The interference optical method has been applied to monitor the transportation of Naþ and Cl in solution through new and used contact lenses. The phenomenon of passive transportation (simple diffusion), induced by differences in osmotic pressure on both sides of the contact lenses has been discussed. Permeability coefficient of contact lenses of different optical power: 2.75 D and 3.75 D has been calculated. ª 2007 Published by Elsevier Ltd on behalf of Associazione Italiana di Fisica Medica.
Introduction The majority of information needed for everyday life is perceived through eyesight. Long hours spent on the observation of objects at short distances from the eye cause along lasting accommodation tension, which may lead to an incorrect relation between the power of the optical system and its size, and contribute to the development of defects in sharp vision in the period of the organism growth. A large percent of young people are short-sighted as a result of the increasing time spent at computers or reading. In combination with an intense growth of the organism these factors can lead to an elongation of the eyeball inducing the so-called axial short sight [1]. Another common eyesight defect that appears after the age of 40 is the loss of the eye lens flexibility and
* Corresponding author. Fax: +48 (0) 61 825 7758. E-mail address: [email protected] (M.S. Kaczmarek).
thus its accommodation ability (presbyopia). The period of civilisation development is too short to pass genetically the features of good accommodation, which leads to increasing appearance of the eyesight defects: short-sightedness (myopia), long-sightedness (hypermetropia), astigmatism and presbyopia. The methods for correction of these defects are based on the application of additional lenses of negative or positive refractive power at myopia or hypermetropia, respectively. Astigmatism is corrected by lenses whose surface is a combination of the spherical and cylindrical shapes. Till recently the correcting lenses have been mainly set in the frames to make spectacles. They have advantages e the correction lenses are outside the eye but also disadvantages e may cause problems on sports or other physical activity. Their use is also problematic when the refraction defects are much different in the two eyes (refractive anisometropia) as then the correction by glasses may lead to the appearance of retina images of different size and hence to the loss of fusion in the binocular vision [2]. There
1120-1797/$ - see front matter ª 2007 Published by Elsevier Ltd on behalf of Associazione Italiana di Fisica Medica. doi:10.1016/j.ejmp.2007.03.004
Dynamics of tear fluid components is also a range of psychological problems related to acceptance of the appearance in the glasses. A solution proposed are the contact lenses to be worn directly on the eyeball. Till 1962 contact lenses have been made only of glass, however, glass is not the best choice for direct contact with the eye. Because of the rigidity and too large diameter the lenses made of glass exert too much pressure on the eye sclera, which means that they can be worn for a limited time. Moreover, glass lenses are brittle and susceptible to mechanical damage and dangerous if the damage is done on wearing. The search for new materials to be used for contact lenses, characterised by excellent transparency of visible light, flexibility, high resistance, perfect wettability, gas and tear fluid permeability, non-toxicity and immunity from the accumulation of deposits has brought about the development of new polymer substances. The comfort of the use of contact lenses depends significantly on the gas and tear fluid permeability of the lens material. Correct functioning of the cornea requires a constant inflow of oxygen and contact with the tear fluid. The function of the anterior surface layer of tear fluid plays to protect and clean the lens, while the posterior surface layer plays an optical role forming a tear lens. The tear fluid circulation supplies oxygen to the cornea and removes the products of metabolism under the lens, for correct functioning of the cornea the lens should be characterised by a highest possible permeability of gases (oxygen) and tear fluid components. In this study the permeability of contact lenses towards Naþ and Cl ions, being components of the tear fluid, is measured by a highly sensitive method of optical interference. This method has been successfully applied in the investigation of transportation of some substances through semi-permeable membranes [3,4].
Methods and apparatus The method is based on measurements of changes Dn in the refraction index of the light passing through a solution in which the concentration of ions studied varies. A lens studied L separates two chambers R and W of a measuring vessel (Fig. 1) of cylindrical shape made of
Figure 1 Measuring vessel with the lens L separating the chambers R and W.
81 polyamide, of the length l Z 50 mm and closed with microscopic slides on both sides. The volume V of each chamber is 8.9 ml. Chamber W contains distilled water, while chamber R e physiological fluid (0.9% NaCl solution) being the main component of the tear fluid. The Naþ and Cl ions move from the solution (chamber R) to distilled water (chamber W) which changes the optical density and refraction index of the solution. The time changes in these parameters are determined by analysis of the interference pattern. The measuring vessel was placed between two plane-parallel plates of a Jamin interferometer (Fig. 2). The analysing beam produced by a HeeNe laser LG 600 of 5 mW power, of a wavelength l Z 632.8 nm, is directed onto the first plate P1 of the interferometer at which it undergoes multiple reflections and diffraction, dividing into a number of beams of lower intensities. The beam reflected from the external surface of the plate (beam 1) and the first beam reflected from the internal surface of the plate (beam 2) having passed through chambers R and W were allowed to interfere on plate P2 of the interferometer. The result of the interference was a pattern of bright and dark lines moving in front of the slit D and behind the slit a photodiode recorded changes in the light intensity in the form of pulses of voltage changes. A computer equipped with an analogedigital converter recorded the pattern of voltage pulses whose number depends on the rate and duration of ion transportation through the lens. The measurements were performed for the transportation time of 6 h. For the optical path length l of the beams passing through the chambers R and W, the change in the refraction index of the solution Dn Z 1.05 105 corresponding to a single complete interference line. This value can be assumed as describing the uncertainty of the light refraction index measurements. The dependence of the molar concentration of the solution on the light refraction index c Z c(n) was obtained on the basis of the light refraction index measurements n (l Z 625 nm) (by a refractometer type LI-3 made by Carl Zeiss Jena) for a series of physiological fluid solutions of concentrations from pure solvent (H2O) to 0.9% NaCl. The parameters of the relation were obtained by fitting the theoretical dependence to the experimental results. On the basis of the number of the interference lines corresponding to a certain value of the refraction index of the solution from which the ions are transported it is possible to calculate the concentration of the solution in the chamber R from the equation c Z c(n). The method had been used earlier for measurements of transportation of physiological fluid through semi-permeable membranes used for dialysis [3]. The main modification of the system was related to the mounting of the contact lens so that it would separate the two solutions. The process of dialysis and tear fluid transportation takes place at a constant temperature corresponding to that of the human body, so the system permitted the regulation of temperature in the range 293 Ke310 K to the accuracy of 0.1 K. The whole experimental set was protected by an isothermal coating made of foamed polystyrene, which permitted the elimination of the temperature gradient between the measuring chamber and the environment. The solutions and the experimental set were stabilised prior
82
M.S. Kaczmarek et al.
Figure 2 A scheme of the measuring setup: P1, P2 e Jamin interferometer plates; R, W e the chambers of the measuring vessel containing the physiological fluid and distilled water; and D e the slit.
to each measurement at a desired temperature for about 2 h. The temperature of the solutions in the chambers was controlled by digital thermometers to an accuracy of 0.1 K.
Theory of passive transportation
PS cII ðtÞZcII ð0Þexp t ; V
where cII(0) is the solvent concentration at time t Z 0, cII(t) is the solvent concentration after time t. Linearisation of Eq. (3) gives: ln
The transportation of the ions through the lens occurs as a result of the gradient of concentration. This type of transportation is known as direct diffusion. The dissolved substance is transported from higher to lower chemical potential in order to reach the state of equilibrium at the same concentrations of the solutions in both chambers. This process is described by the Fick law [5,6]: dN dc Z DS ; dt dx
ð1Þ
where dN=dt is the rate of diffusion expressed as the ratio of the number of the moles dN transmitted through the lens of the surface S to the time dt, and dc=dx is the gradient of concentration of a given substance in the solution. D is the coefficient of diffusion describing the number of molecules or ions diffusing in 1 s through the area S, if the concentration gradient is equal 1. The diffusion induced concentration changes in the regions of volume V separated by a lens of the area S can be described in equation [7]: dcII PS Z ðcI cII Þ; dt V
ð2Þ
where cI and cII are the concentrations in the regions on the two sides of the lens, PZD=dx is the lens permeability towards a given substance. If a stream of the dissolved substance flows into the region in which the concentration of this substance has been practically zero, then from Eq. (2) we have:
ð3Þ
cII ðtÞ PS Z t; cII ð0Þ V
ð4Þ
which permits the determination of the lens permeability P, as a result of the fit of experimental data to Eq. (4).
Results The study was performed on hydrogel lenses for day wearing throughout a period not longer than two-weeks, of the strength 2.75 D and 3.75 D, new and used. The parameters of the lenses are given in Table 1. Chamber R of the measuring vessel was filled with physiological fluid e NaCl solution of a concentration 0.9%. Transportation of Naþ and Cl ions through a given lens from chamber R to chamber W filled with distilled water was measured. The exemplary course of light intensity changes behind the slit, recorded by a computer is shown in Fig. 3. On the basis of the time dependence of the number of interference lines L the time changes of the light refraction index DnðtÞ were calculated. The dynamics of changes in
Table 1 studied
Selected parameters of the contact lenses
Optical power [D]
Radius of posterior surface of lens BC [mm]
Diameter DIA [mm]
Content of water [%]
2.75 3.75
8.7 8.3
14.0 14.0
66 58
Dynamics of tear fluid components
83
Figure 3 An exemplary pattern of interference lines observed on the monitor screen.
the molar concentration of the solution was illustrated by the plot of the light refraction index dependence on the molar concentration of NaCl in the concentration range studied. On the basis of this dependence it was possible to obtain the time dependence of molar concentration of NaCl in chamber R (Fig. 4 and Fig. 5). The permeability of the lenses studied was calculated from Eq. (4) and the results are collected in Table 2.
Concluding remarks The interference method applied permits investigation of the dynamics of transportation of Naþ and Cl being components of the tear fluid, through contact lenses. In this method the interference pattern dependent on the
Figure 5 Molar concentration of the physiological fluid c Z c(t) in R chamber versus the time of transportation for two 3.75 D lenses: a new one and a used one.
concentration of the medium studied is recorded and changes of the number of the interference lines in time are monitored. The latter dependence permits the determination of changes in the light refraction index versus the molar concentration of the NaCl solution which allows to calculate the permeability P of contact lenses. The results have shown that the lenses that had been used for some time are characterised by clearly lower permeability than the new ones. This change can be explained taking into regard the fact that during the hydrogel lenses use some proteins deposit on their surface, which significantly alters their surface properties. The results indicate the need of everyday cleaning and disinfection of contact lenses to prevent accommodation of micro-organisms and deposits on their surface. The type of disinfection and type of agents used for the lens cleaning significantly affect the permeability of the lenses. The results have shown that the method applied in the study is suitable for the assessment of effectiveness of different disinfecting substances used for the lens conservation.
Acknowledgements The authors wish to thank very much Mr Jerzy Piasecki, a representative of the firm Baush & Lomb, for the material to be studied.
Table 2 The calculated values of permeabilities of the contact lenses studied
Figure 4 Molar concentration of the physiological fluid c Z c(t) in R chamber versus the time of transportation for two 2.75 D lenses: a new one and a used one.
Optical power [D]
Permeability of new lens P107[m/s]
Permeability of used lens P107[m/s]
2.75 3.75
7.55 0.02 6.92 0.02
5.55 0.02 6.28 0.02
84
References [1] Sato C. The causes of acquired myopia. Tokyo: Kanehara Shupan CO; 1957. [2] Hirsch MJ. Anisometropia: a preliminary report of the Ojai longitudinal study. Am J Optom 1967;44:581e5. [3] Surma M, Kaczmarek MS, Woz ´niak Z, Drzewiecka A. Interference optical method of recording physiological fluids flow through semipermeable membranes. Polish J Med Phys Eng 2002;8(1).
M.S. Kaczmarek et al. [4] Kaczmarek MS, Woz ´niak Z, B1aszczak Z, Surma M. Optical interference study of physiological fluids transportation through semipermeable membranes. J Mol Liq 2003;106(1):81e8. [5] Kotyk A, Jana ´cek K. Membrane transport. Academia-Praha 1977;183e205. [6] Wilkinson DS. Mass transport in solid and fluids. United Kingdom: Cambridge University Press; 2000. [7] Wallach FW, Winzler RJ. Evolving strategies and tactics in membrane research. Berlin, Heidelberg, New York: SpringerVerlag; 1974. p. 72e7.
available at www.sciencedirect.com
journal homepage: http://intl.elsevierhealth.com/journals/ejmp
TECHNICAL NOTE
Dynamics of tear fluid components transportation through contact lenses ´niak, Zdzis1aw B1aszczak Micha1 S. Kaczmarek*, Zenon Woz Faculty of Physics, Division of Optics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznan´, Poland Received 7 April 2006; received in revised form 26 March 2007; accepted 28 March 2007 Available online 25 May 2007
KEYWORDS Contact lenses; Permeability; Jamin interferometer
Abstract The interference optical method has been applied to monitor the transportation of Naþ and Cl in solution through new and used contact lenses. The phenomenon of passive transportation (simple diffusion), induced by differences in osmotic pressure on both sides of the contact lenses has been discussed. Permeability coefficient of contact lenses of different optical power: 2.75 D and 3.75 D has been calculated. ª 2007 Published by Elsevier Ltd on behalf of Associazione Italiana di Fisica Medica.
Introduction The majority of information needed for everyday life is perceived through eyesight. Long hours spent on the observation of objects at short distances from the eye cause along lasting accommodation tension, which may lead to an incorrect relation between the power of the optical system and its size, and contribute to the development of defects in sharp vision in the period of the organism growth. A large percent of young people are short-sighted as a result of the increasing time spent at computers or reading. In combination with an intense growth of the organism these factors can lead to an elongation of the eyeball inducing the so-called axial short sight [1]. Another common eyesight defect that appears after the age of 40 is the loss of the eye lens flexibility and
* Corresponding author. Fax: +48 (0) 61 825 7758. E-mail address: [email protected] (M.S. Kaczmarek).
thus its accommodation ability (presbyopia). The period of civilisation development is too short to pass genetically the features of good accommodation, which leads to increasing appearance of the eyesight defects: short-sightedness (myopia), long-sightedness (hypermetropia), astigmatism and presbyopia. The methods for correction of these defects are based on the application of additional lenses of negative or positive refractive power at myopia or hypermetropia, respectively. Astigmatism is corrected by lenses whose surface is a combination of the spherical and cylindrical shapes. Till recently the correcting lenses have been mainly set in the frames to make spectacles. They have advantages e the correction lenses are outside the eye but also disadvantages e may cause problems on sports or other physical activity. Their use is also problematic when the refraction defects are much different in the two eyes (refractive anisometropia) as then the correction by glasses may lead to the appearance of retina images of different size and hence to the loss of fusion in the binocular vision [2]. There
1120-1797/$ - see front matter ª 2007 Published by Elsevier Ltd on behalf of Associazione Italiana di Fisica Medica. doi:10.1016/j.ejmp.2007.03.004
Dynamics of tear fluid components is also a range of psychological problems related to acceptance of the appearance in the glasses. A solution proposed are the contact lenses to be worn directly on the eyeball. Till 1962 contact lenses have been made only of glass, however, glass is not the best choice for direct contact with the eye. Because of the rigidity and too large diameter the lenses made of glass exert too much pressure on the eye sclera, which means that they can be worn for a limited time. Moreover, glass lenses are brittle and susceptible to mechanical damage and dangerous if the damage is done on wearing. The search for new materials to be used for contact lenses, characterised by excellent transparency of visible light, flexibility, high resistance, perfect wettability, gas and tear fluid permeability, non-toxicity and immunity from the accumulation of deposits has brought about the development of new polymer substances. The comfort of the use of contact lenses depends significantly on the gas and tear fluid permeability of the lens material. Correct functioning of the cornea requires a constant inflow of oxygen and contact with the tear fluid. The function of the anterior surface layer of tear fluid plays to protect and clean the lens, while the posterior surface layer plays an optical role forming a tear lens. The tear fluid circulation supplies oxygen to the cornea and removes the products of metabolism under the lens, for correct functioning of the cornea the lens should be characterised by a highest possible permeability of gases (oxygen) and tear fluid components. In this study the permeability of contact lenses towards Naþ and Cl ions, being components of the tear fluid, is measured by a highly sensitive method of optical interference. This method has been successfully applied in the investigation of transportation of some substances through semi-permeable membranes [3,4].
Methods and apparatus The method is based on measurements of changes Dn in the refraction index of the light passing through a solution in which the concentration of ions studied varies. A lens studied L separates two chambers R and W of a measuring vessel (Fig. 1) of cylindrical shape made of
Figure 1 Measuring vessel with the lens L separating the chambers R and W.
81 polyamide, of the length l Z 50 mm and closed with microscopic slides on both sides. The volume V of each chamber is 8.9 ml. Chamber W contains distilled water, while chamber R e physiological fluid (0.9% NaCl solution) being the main component of the tear fluid. The Naþ and Cl ions move from the solution (chamber R) to distilled water (chamber W) which changes the optical density and refraction index of the solution. The time changes in these parameters are determined by analysis of the interference pattern. The measuring vessel was placed between two plane-parallel plates of a Jamin interferometer (Fig. 2). The analysing beam produced by a HeeNe laser LG 600 of 5 mW power, of a wavelength l Z 632.8 nm, is directed onto the first plate P1 of the interferometer at which it undergoes multiple reflections and diffraction, dividing into a number of beams of lower intensities. The beam reflected from the external surface of the plate (beam 1) and the first beam reflected from the internal surface of the plate (beam 2) having passed through chambers R and W were allowed to interfere on plate P2 of the interferometer. The result of the interference was a pattern of bright and dark lines moving in front of the slit D and behind the slit a photodiode recorded changes in the light intensity in the form of pulses of voltage changes. A computer equipped with an analogedigital converter recorded the pattern of voltage pulses whose number depends on the rate and duration of ion transportation through the lens. The measurements were performed for the transportation time of 6 h. For the optical path length l of the beams passing through the chambers R and W, the change in the refraction index of the solution Dn Z 1.05 105 corresponding to a single complete interference line. This value can be assumed as describing the uncertainty of the light refraction index measurements. The dependence of the molar concentration of the solution on the light refraction index c Z c(n) was obtained on the basis of the light refraction index measurements n (l Z 625 nm) (by a refractometer type LI-3 made by Carl Zeiss Jena) for a series of physiological fluid solutions of concentrations from pure solvent (H2O) to 0.9% NaCl. The parameters of the relation were obtained by fitting the theoretical dependence to the experimental results. On the basis of the number of the interference lines corresponding to a certain value of the refraction index of the solution from which the ions are transported it is possible to calculate the concentration of the solution in the chamber R from the equation c Z c(n). The method had been used earlier for measurements of transportation of physiological fluid through semi-permeable membranes used for dialysis [3]. The main modification of the system was related to the mounting of the contact lens so that it would separate the two solutions. The process of dialysis and tear fluid transportation takes place at a constant temperature corresponding to that of the human body, so the system permitted the regulation of temperature in the range 293 Ke310 K to the accuracy of 0.1 K. The whole experimental set was protected by an isothermal coating made of foamed polystyrene, which permitted the elimination of the temperature gradient between the measuring chamber and the environment. The solutions and the experimental set were stabilised prior
82
M.S. Kaczmarek et al.
Figure 2 A scheme of the measuring setup: P1, P2 e Jamin interferometer plates; R, W e the chambers of the measuring vessel containing the physiological fluid and distilled water; and D e the slit.
to each measurement at a desired temperature for about 2 h. The temperature of the solutions in the chambers was controlled by digital thermometers to an accuracy of 0.1 K.
Theory of passive transportation
PS cII ðtÞZcII ð0Þexp t ; V
where cII(0) is the solvent concentration at time t Z 0, cII(t) is the solvent concentration after time t. Linearisation of Eq. (3) gives: ln
The transportation of the ions through the lens occurs as a result of the gradient of concentration. This type of transportation is known as direct diffusion. The dissolved substance is transported from higher to lower chemical potential in order to reach the state of equilibrium at the same concentrations of the solutions in both chambers. This process is described by the Fick law [5,6]: dN dc Z DS ; dt dx
ð1Þ
where dN=dt is the rate of diffusion expressed as the ratio of the number of the moles dN transmitted through the lens of the surface S to the time dt, and dc=dx is the gradient of concentration of a given substance in the solution. D is the coefficient of diffusion describing the number of molecules or ions diffusing in 1 s through the area S, if the concentration gradient is equal 1. The diffusion induced concentration changes in the regions of volume V separated by a lens of the area S can be described in equation [7]: dcII PS Z ðcI cII Þ; dt V
ð2Þ
where cI and cII are the concentrations in the regions on the two sides of the lens, PZD=dx is the lens permeability towards a given substance. If a stream of the dissolved substance flows into the region in which the concentration of this substance has been practically zero, then from Eq. (2) we have:
ð3Þ
cII ðtÞ PS Z t; cII ð0Þ V
ð4Þ
which permits the determination of the lens permeability P, as a result of the fit of experimental data to Eq. (4).
Results The study was performed on hydrogel lenses for day wearing throughout a period not longer than two-weeks, of the strength 2.75 D and 3.75 D, new and used. The parameters of the lenses are given in Table 1. Chamber R of the measuring vessel was filled with physiological fluid e NaCl solution of a concentration 0.9%. Transportation of Naþ and Cl ions through a given lens from chamber R to chamber W filled with distilled water was measured. The exemplary course of light intensity changes behind the slit, recorded by a computer is shown in Fig. 3. On the basis of the time dependence of the number of interference lines L the time changes of the light refraction index DnðtÞ were calculated. The dynamics of changes in
Table 1 studied
Selected parameters of the contact lenses
Optical power [D]
Radius of posterior surface of lens BC [mm]
Diameter DIA [mm]
Content of water [%]
2.75 3.75
8.7 8.3
14.0 14.0
66 58
Dynamics of tear fluid components
83
Figure 3 An exemplary pattern of interference lines observed on the monitor screen.
the molar concentration of the solution was illustrated by the plot of the light refraction index dependence on the molar concentration of NaCl in the concentration range studied. On the basis of this dependence it was possible to obtain the time dependence of molar concentration of NaCl in chamber R (Fig. 4 and Fig. 5). The permeability of the lenses studied was calculated from Eq. (4) and the results are collected in Table 2.
Concluding remarks The interference method applied permits investigation of the dynamics of transportation of Naþ and Cl being components of the tear fluid, through contact lenses. In this method the interference pattern dependent on the
Figure 5 Molar concentration of the physiological fluid c Z c(t) in R chamber versus the time of transportation for two 3.75 D lenses: a new one and a used one.
concentration of the medium studied is recorded and changes of the number of the interference lines in time are monitored. The latter dependence permits the determination of changes in the light refraction index versus the molar concentration of the NaCl solution which allows to calculate the permeability P of contact lenses. The results have shown that the lenses that had been used for some time are characterised by clearly lower permeability than the new ones. This change can be explained taking into regard the fact that during the hydrogel lenses use some proteins deposit on their surface, which significantly alters their surface properties. The results indicate the need of everyday cleaning and disinfection of contact lenses to prevent accommodation of micro-organisms and deposits on their surface. The type of disinfection and type of agents used for the lens cleaning significantly affect the permeability of the lenses. The results have shown that the method applied in the study is suitable for the assessment of effectiveness of different disinfecting substances used for the lens conservation.
Acknowledgements The authors wish to thank very much Mr Jerzy Piasecki, a representative of the firm Baush & Lomb, for the material to be studied.
Table 2 The calculated values of permeabilities of the contact lenses studied
Figure 4 Molar concentration of the physiological fluid c Z c(t) in R chamber versus the time of transportation for two 2.75 D lenses: a new one and a used one.
Optical power [D]
Permeability of new lens P107[m/s]
Permeability of used lens P107[m/s]
2.75 3.75
7.55 0.02 6.92 0.02
5.55 0.02 6.28 0.02
84
References [1] Sato C. The causes of acquired myopia. Tokyo: Kanehara Shupan CO; 1957. [2] Hirsch MJ. Anisometropia: a preliminary report of the Ojai longitudinal study. Am J Optom 1967;44:581e5. [3] Surma M, Kaczmarek MS, Woz ´niak Z, Drzewiecka A. Interference optical method of recording physiological fluids flow through semipermeable membranes. Polish J Med Phys Eng 2002;8(1).
M.S. Kaczmarek et al. [4] Kaczmarek MS, Woz ´niak Z, B1aszczak Z, Surma M. Optical interference study of physiological fluids transportation through semipermeable membranes. J Mol Liq 2003;106(1):81e8. [5] Kotyk A, Jana ´cek K. Membrane transport. Academia-Praha 1977;183e205. [6] Wilkinson DS. Mass transport in solid and fluids. United Kingdom: Cambridge University Press; 2000. [7] Wallach FW, Winzler RJ. Evolving strategies and tactics in membrane research. Berlin, Heidelberg, New York: SpringerVerlag; 1974. p. 72e7.