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Convolution and deconvolution using matrices
s92
365 EFFECT OF ALTERED PROTEIN ON HEPATIC EFFLUX OF DICLOFENAC
367 CONCENTRATION DIAZEPAM AND
Selma Sahin’And Malcolm Rowland* ‘Faculty of Pharmacy, Hacettepe University, 06100-Ankara, Turkey; ‘School of Pharmacy and Pharmaceutical Sciences, University of Manchester, M13, 9PL, UK.
Convohdion oed docoevolutlon EJlw.t. Muwini
w&g
mahices
Ct. A&War& A. Pebini Ricetchc S.p,A.. Via Tit0 Spmi 10, Pumezin(Italy)
One of the advantageof using the Ldplaca tatsfuns in compartmental analysis ts due tu the fact that the convolution and the deconvolution become a multiphcation and I division respectively. Such operations, patticularly interesting in model building. can be appmximated IU follows: if y(t) = g(t) ??x(t) is the convolution of g(t) nnd x(t) and if n(t) it appmximated by the areas subtended by the cutvc in each equal interval of time 6, and g(t) is represented by the values of the timction at the comspondingtimeinnrvalsg,.gt.gr,.....then(I):
The degree of protein binding greatly affects the ability of molecules to permeate the hepatocellular membrane and may play an important role in determining the uptake process involved. Aspects of protein binding were investigated using “C-diazepam and “C-diclofenac under various albumin concentrations @-ISA,0.25-l%) in a single-pass dual hepatic artery and portal vein perfused in S&I rat liver preparation. Regardless of route of input, the shape of the eftlux profiles for “C-diszepam were dependent upon the albumin concentration: with a decrease in the albumin concentration from 1 to 0.25% the early sharp peak (about 12-18 set) disappeared and the outflow curves displayed a flatter unimodal characteristic and a later peak (about 60-70 set). On the other hand, regardless of both the protein concentration and route of input, the hepatic outflow profiles of “C-diclofenac were characterized by a sharp peak followed by a slowly eluting tail indicating that radial distribution of diclofenac within the liver is not instantaneous. Comparison of estimated effective surface area to blood flow ratio @PS/Q; e.g. 4.7 for diclofenac and 21 for diazepam for 0.25% HSA) indicates that hepatic uptake of diclofenac is governed by both permeability and flow, whereas two different uptake process seem to operate for diazepam- intermediate with 1% HSA and flow limited uptake with 0.25% HSA.
). Writing the functions x(t). g(t) and y(t) as lower triangular matrices X. G and Y rcspcctively and taking 6 51I. then the convolution CM bc written as Y = G’X (when * is the matrix multiplication) and the deconvulution as X = Y * inv(G) (where inv(G) is the inverse matrix of G). Note that the deconvolution nquircs that the matrix G is invertible and that for these matrices G*X = X’G. When qually spacedsampling of the functions g(t), y(t) or x(t) are not available. the data points cm be interpolated. using rplincs for sxamplc. to get fl...fn and to wry out the convolution or the dewnvolution numerically. In these cases the interpolating method and the lcnght of the step arc critical for the accuracy of the result. Morecwn, if the following equations are considend: E’ = -k E (PO ~1) and p’ = R _ k Q (Qu = 0) where k4 then it can be shown that: ClIpI) P ??R = Q and that the matrix P has elements pl=(l-k) pZ=(l. A solution can also be found for a system of similar equattonr. k?........... pn=(l-k)‘. 1. Se@‘e G., M~themstiul Models la Medtdnc. Worlukep. Mdnr 1976 M.rch, Ed. by J. Berger. W. Buhler, R. Rcpg*r.Sprtngw, BerSn (1976).
366
368
ORAL MUCOSITIS IN CHILDREN WITH CANCER DISEASES t. Skibi&ka4 M. Kaczmarek-Kanold Department of Physical Chemistry and Department of Pediatric Haematology and Oncology Insitute of Pediatrics, Karol Marcinkowski
ENHANCJBIENT OF HYPOGLYCEMIC ACTIVITY TOLRUTAMlDE WITH CYCLODEXTRlNS
University of Medical Sciences, &v&i&ego 6, Sh. 61-781 Poznati, Poland. Oral mucositis is a common side effect afkr high-dose methotrexate therapy (HD-MTX), usually in children. The incidences of mucositis are observed.in about 40% patients causing oral infection and sepsis. The monitoring of methobexate (MTX) is not father sufficient to predict oral toxicity because no significant differences in strum MTX concentrations were observed in patients with and without mucositis. We therefore investigated the correlation be$ween salivary MTX concentrations and the side effects after HD-MTX. Additionaly we estimated if salivary albumin and total protein levels may be useful as a predictor and indicator of the oral mucositis. The studies were performed in 25 children with acute lymphoblastic leukemia aged from 5 to 15 years who received 3gkn’ dose of MTX in continuous 24-hours intravenous infusion. The MTX concentration in saliva was measured by an enzymatic method and salivary albumin and total protein levels by Abbotts tests and Lowrys method, respectively. The peak saliva concentration in patients was observed between 6 and 12 hour alk the start of infusion and varied from 0.206 to 1.076 pmoy1. There were observed the significant correlations between the peak saliva concentration of MTX and salivary albumin (ti.751, p
This operation
can be nprwented
using mrtricw
function f(t) and 6 step 6, define the vector lower triangullr matrices: f,
0
F=fa f, f, f,
0
0 fl
0
.. 0 ,,. 0:
. ,.. f,
in the following
Fv= [f(8).
f, -f,
f,-fl E’=fi-f2
f(Z &....f(n 0
A-f0 f*-fi
way. Given
the
6)I and the square. 0
0 f,-fo
0
... ,,.
0 0
. .. f.-f,,, .,, “’ f, -f, f” f”., f,, Where fi=f(i6). Define also the matrix E when the first point is taken at time 0 ( f(o)
,
OF
F. Veiga*, A. Sousa* and P. Maincent** +Fac. de Farm&a. Universidade de Coimbra. Coimbra. Portugal ** Fat. des Sciences Phannaceutiques et Biologiques. Universite de Nancy I. Nancy. France Cyclodextrins are able to form inclusion complexes with several drugs. The inclusion process of poorly water soluble drugs results in the following advantages: to increase the solubility and the dissolution rate and to improve the bioavailability. The objective of the present study was to evaluate the intluence of the complexation on the bioavailability of tolbutamide a&r oral administration to rabbits of TBM/l3CD and TBM/HP-D-CD inclusion complexes when compared with pure dtug. WIthout cyclodextrins the hypoglycaemic effect of TBM was observed with a maximum of 31% at 5.6 h. The hypoglycaemic effect of TBM&CD and TBM/HP-&CD inclusion complexes are 34.1% (at 6.5 h) and 37.7% (5.1 h), respectively. The areas above glucose variation coefficient versus time (AA&,) of the pure drug and the inclusion complexes (TBM/IJ-CD and TBM/HP-B-CD) revealed statistically significant differences. The AAC,, of the inclusion complexes is 1.4 times larger than of the pure tolbutamide. In conclusion, the results of the present study demonstrated that the bioavailability of TBM improve when administered as an inclusion complexes with cyclodextrins. Consequently, the complexation with cyclodextrins, could be interesting in developing a solid dosage form with reduced dose requirements.
365 EFFECT OF ALTERED PROTEIN ON HEPATIC EFFLUX OF DICLOFENAC
367 CONCENTRATION DIAZEPAM AND
Selma Sahin’And Malcolm Rowland* ‘Faculty of Pharmacy, Hacettepe University, 06100-Ankara, Turkey; ‘School of Pharmacy and Pharmaceutical Sciences, University of Manchester, M13, 9PL, UK.
Convohdion oed docoevolutlon EJlw.t. Muwini
w&g
mahices
Ct. A&War& A. Pebini Ricetchc S.p,A.. Via Tit0 Spmi 10, Pumezin(Italy)
One of the advantageof using the Ldplaca tatsfuns in compartmental analysis ts due tu the fact that the convolution and the deconvolution become a multiphcation and I division respectively. Such operations, patticularly interesting in model building. can be appmximated IU follows: if y(t) = g(t) ??x(t) is the convolution of g(t) nnd x(t) and if n(t) it appmximated by the areas subtended by the cutvc in each equal interval of time 6, and g(t) is represented by the values of the timction at the comspondingtimeinnrvalsg,.gt.gr,.....then(I):
The degree of protein binding greatly affects the ability of molecules to permeate the hepatocellular membrane and may play an important role in determining the uptake process involved. Aspects of protein binding were investigated using “C-diazepam and “C-diclofenac under various albumin concentrations @-ISA,0.25-l%) in a single-pass dual hepatic artery and portal vein perfused in S&I rat liver preparation. Regardless of route of input, the shape of the eftlux profiles for “C-diszepam were dependent upon the albumin concentration: with a decrease in the albumin concentration from 1 to 0.25% the early sharp peak (about 12-18 set) disappeared and the outflow curves displayed a flatter unimodal characteristic and a later peak (about 60-70 set). On the other hand, regardless of both the protein concentration and route of input, the hepatic outflow profiles of “C-diclofenac were characterized by a sharp peak followed by a slowly eluting tail indicating that radial distribution of diclofenac within the liver is not instantaneous. Comparison of estimated effective surface area to blood flow ratio @PS/Q; e.g. 4.7 for diclofenac and 21 for diazepam for 0.25% HSA) indicates that hepatic uptake of diclofenac is governed by both permeability and flow, whereas two different uptake process seem to operate for diazepam- intermediate with 1% HSA and flow limited uptake with 0.25% HSA.
). Writing the functions x(t). g(t) and y(t) as lower triangular matrices X. G and Y rcspcctively and taking 6 51I. then the convolution CM bc written as Y = G’X (when * is the matrix multiplication) and the deconvulution as X = Y * inv(G) (where inv(G) is the inverse matrix of G). Note that the deconvolution nquircs that the matrix G is invertible and that for these matrices G*X = X’G. When qually spacedsampling of the functions g(t), y(t) or x(t) are not available. the data points cm be interpolated. using rplincs for sxamplc. to get fl...fn and to wry out the convolution or the dewnvolution numerically. In these cases the interpolating method and the lcnght of the step arc critical for the accuracy of the result. Morecwn, if the following equations are considend: E’ = -k E (PO ~1) and p’ = R _ k Q (Qu = 0) where k4 then it can be shown that: ClIpI) P ??R = Q and that the matrix P has elements pl=(l-k) pZ=(l. A solution can also be found for a system of similar equattonr. k?........... pn=(l-k)‘. 1. Se@‘e G., M~themstiul Models la Medtdnc. Worlukep. Mdnr 1976 M.rch, Ed. by J. Berger. W. Buhler, R. Rcpg*r.Sprtngw, BerSn (1976).
366
368
ORAL MUCOSITIS IN CHILDREN WITH CANCER DISEASES t. Skibi&ka4 M. Kaczmarek-Kanold Department of Physical Chemistry and Department of Pediatric Haematology and Oncology Insitute of Pediatrics, Karol Marcinkowski
ENHANCJBIENT OF HYPOGLYCEMIC ACTIVITY TOLRUTAMlDE WITH CYCLODEXTRlNS
University of Medical Sciences, &v&i&ego 6, Sh. 61-781 Poznati, Poland. Oral mucositis is a common side effect afkr high-dose methotrexate therapy (HD-MTX), usually in children. The incidences of mucositis are observed.in about 40% patients causing oral infection and sepsis. The monitoring of methobexate (MTX) is not father sufficient to predict oral toxicity because no significant differences in strum MTX concentrations were observed in patients with and without mucositis. We therefore investigated the correlation be$ween salivary MTX concentrations and the side effects after HD-MTX. Additionaly we estimated if salivary albumin and total protein levels may be useful as a predictor and indicator of the oral mucositis. The studies were performed in 25 children with acute lymphoblastic leukemia aged from 5 to 15 years who received 3gkn’ dose of MTX in continuous 24-hours intravenous infusion. The MTX concentration in saliva was measured by an enzymatic method and salivary albumin and total protein levels by Abbotts tests and Lowrys method, respectively. The peak saliva concentration in patients was observed between 6 and 12 hour alk the start of infusion and varied from 0.206 to 1.076 pmoy1. There were observed the significant correlations between the peak saliva concentration of MTX and salivary albumin (ti.751, p
This operation
can be nprwented
using mrtricw
function f(t) and 6 step 6, define the vector lower triangullr matrices: f,
0
F=fa f, f, f,
0
0 fl
0
.. 0 ,,. 0:
. ,.. f,
in the following
Fv= [f(8).
f, -f,
f,-fl E’=fi-f2
f(Z &....f(n 0
A-f0 f*-fi
way. Given
the
6)I and the square. 0
0 f,-fo
0
... ,,.
0 0
. .. f.-f,,, .,, “’ f, -f, f” f”., f,, Where fi=f(i6). Define also the matrix E when the first point is taken at time 0 ( f(o)
,
OF
F. Veiga*, A. Sousa* and P. Maincent** +Fac. de Farm&a. Universidade de Coimbra. Coimbra. Portugal ** Fat. des Sciences Phannaceutiques et Biologiques. Universite de Nancy I. Nancy. France Cyclodextrins are able to form inclusion complexes with several drugs. The inclusion process of poorly water soluble drugs results in the following advantages: to increase the solubility and the dissolution rate and to improve the bioavailability. The objective of the present study was to evaluate the intluence of the complexation on the bioavailability of tolbutamide a&r oral administration to rabbits of TBM/l3CD and TBM/HP-D-CD inclusion complexes when compared with pure dtug. WIthout cyclodextrins the hypoglycaemic effect of TBM was observed with a maximum of 31% at 5.6 h. The hypoglycaemic effect of TBM&CD and TBM/HP-&CD inclusion complexes are 34.1% (at 6.5 h) and 37.7% (5.1 h), respectively. The areas above glucose variation coefficient versus time (AA&,) of the pure drug and the inclusion complexes (TBM/IJ-CD and TBM/HP-B-CD) revealed statistically significant differences. The AAC,, of the inclusion complexes is 1.4 times larger than of the pure tolbutamide. In conclusion, the results of the present study demonstrated that the bioavailability of TBM improve when administered as an inclusion complexes with cyclodextrins. Consequently, the complexation with cyclodextrins, could be interesting in developing a solid dosage form with reduced dose requirements.