Retardant Polymer Research Articles

Design and statistical optimization of an effervescent floating drug delivery system of theophylline using response surface methodology.

The aim of this research was to formulate effervescent floating drug delivery systems of theophylline using different release retarding polymers such as ethyl cellulose, Eudragit® L100, xanthan gum and polyethylene oxide (PEO) N12K. Sodium bicarbonate was used as a gas generating agent. Direct compression was used to formulate floating tablets and the tablets were evaluated for their physicochemical and dissolution characteristics. PEO based formulations produced better drug release properties than other formulations. Hence, it was further optimized by central composite design. Further subjects of research were the effect of formulation variables on floating lag time and the percentage of drug released at the seventh hour (D7h). The optimum quantities of PEO and sodium bicarbonate, which had the highest desirability close to 1.0, were chosen as the statistically optimized formulation. No interaction was found between theophylline and PEO by Fourier Transformation Infrared spectroscopy (FTIR) and Differential Scanning Calorimetry (DSC) studies.

Formulation and Evaluation of Nateglinide Sustained Release Tablets

The objective of the present investigation was to design suitable sustained release tablet formulation of Nateglinide by using different polymers such as hydroxy propyl methyl cellulose K15M, xanthan gum, guar gum as release rate retarding polymers. The tablets were prepared by direct compression technique. Nateglinide is used as anti diabetic drug. The objective of the treatment is to achieve hypoglycemia, by using an ideal dosage regimen. The sustained release formulation provides extend duration of action in therapeutic range without reaching toxic levels as in the case of conventional dosage forms. The real formulation trails are carried from F1 to F9 in which Drug: Polymer ratio was set as 1:9 respectively. The prepared formulations F1 to F9 were evaluated for pre and post compression characteristics, along with the in vitro dissolution Studies. It was found that the release of drug from F1, F2, and F3 gave the better release than other formulations. In these three formulations F2 showing highest release following first order kinetics. From the Higuchi plot good correlation coefficient was observed showing diffusion mechanism. From the peppas plot it was observed that the release model was non fickian anomalous. The release rate was decreased as polymer concentration increased so it shows that increase in diffusion length of polymer decreases the release rate.

Novel core in cup (In-lay) tablets of lamotrigine for mucoadhesive drug delivery system

Lamotrigine a BCS class II drug used in treatment of epilepsy has several disadvantages when taken orally (first pass metabolism and increased Cmax). The aim of the study is to design core in cup (In lay) buccoadhesive tablets which aims for controlled, unidirectional release, increased patient compliance and decreased side effects. The present study involves the preparation of core in cup tablets containing release retarding polymers like sodium alginate, xanthan gum and HPMC E 15LV in core and HPMC K 15M in cup for mucoadhesion. L9 orthogonal array Taguchi design was constructed for the study. The dependent variable studied for L9 orthogonal array Taguchi runs include % drug release from which the formulation with highest S/N ratio was optimized. All the runs were evaluated for physical parameters, drug release, mucoadhesive studies and assay. L1, L2, L4 and L8 formulations showed controlled release for up-to 8 hours with good assay values. The model dependent kinetics showed zero order kinetics with super case II transport and Hixson Crowell mechanism which indicates unidirectional drug release.Srinija and Lakshmi, International Current Pharmaceutical Journal, January 2016, 5(2): 9-13

Modulation of drug release mechanism by Higuchi model: Estimation of percent deviation

The objective of this study was to develop Nicorandil floating tablets by melt granulation technique using combination of almond gum as swellable plus retarding polymer and cetosteryl alcohol as waxy plus retarding polymer. The drug release mechanism is analysed by both Higuchi model and Hixson-Crowell model based on their higher square of correlation coefficient (R2). The best formulation of MCS4 is selected based on the identical drug release profile with theoretical release data calculated from Robinson Erickson equation which follows Higuchi model for drug release from tablet core. Further, the drug release of best formulation which follow Higuchi model is checked for its deviation from an ideal Higuchi release profile. The release profiles of the best formulation is greatly deviate the ideal Higuchi release profile. In order to minimise the deviation, twotiered method is used and confirm the drug release at two phases as Hixson-Crowell model for first phase and Higuchi model for second phase.

Gastroretentive Sustained Release Floating and Swellable Cefadroxil Formulation: In vitro and in vivo Evaluation

A new Gastroretentive Sustained Release (GRSR) tablet of cefadroxil was developed with floating and swellable properties. Various release retarding polymers, swelling agent, gas generating agent and release modifying agents were evaluated. The optimized formulation was studied for various physical parameters, in vitro drug release profile and for in vitro floating properties. The formulation provided sustained drug release for about 14 h with the floating lag time of 30 s and floating duration of about 14 h. Owing to the promising in vitro floating property, the formulation was explored for in vivo floating performance in healthy human volunteers by radio-analytical technique. The developed formulation of Cefadroxil showed prolonged gastric retention in vivo for 7 h. The tablets also showed significant swelling property with excellent tablet integrity till 7 h. The developed formulation exhibited promising gastroretention in vivo. The radio-analytical technique used to evaluate the in vivo gastroretention was found to be simple, cost-effective and was precisely used for detecting floating time and tablet integrity throughout the study.

Assessment of extrusion-sonication process on flame retardant polypropylene by rheological characterization

In this work, the rheological behavior of flame retardant polypropylene composites produced by two methods: 1) twin-screw extrusion and 2) ultrasound application combined with a static mixer die single-screw extrusion is analyzed in detail; results are related to the morphology of the composites. The flame retardant polymer composites are composed of a polypropylene matrix, an intumescent flame retardant system and functionalized clay. Scanning electron microscopy revealed that the combination of the static mixer die and on-line sonication reduced particle size and improved the dispersion and distribution of the intumescent additives in the polypropylene matrix at the micrometric level. From linear viscoelastic properties, the Han, Cole-Cole and van Gurp-Palmen diagrams characterized the improved particle dispersion of the flame retardant additives. Two well-defined rheological behaviors were observed in these diagrams. These behaviors are independent on clay presence and concentration. In fact, the ultrasound device generates a 3D highly interconnected structure similar to a co-continuous pattern observed in polymer blends as evidenced by rheological measurements. This improvement in the dispersion and distribution of the additives is attributed to the combined effect of the static mixer die and on-line sonication that allowed reducing the additive content while achieving the optimum classification UL94-V0.

Sustained Release Matrix Tablets of Furosemide

Objective: The objective of the present study was to develop and evaluate once-daily sustained release matrix tablets of furosemide using hydroxypropylmethyl cellulose K4M, xanthan gum and sodium alginate as release retarding polymers. Methodology: The matrix tablet formulations were prepared by using different drug: polymer ratios (1:1, 1:2, 1:3, 1:4 and 1:5). The prepared matrix tablets were evaluated for pre-compression parameters like angle of repose, bulk density, tap density and post-compression parameters like hardness, thickness, weight variation, friability, percent drug content and in vitro drug release studies as per USP guidelines. Results: The in vitro drug release data of all the prepared tablet formulations of furosemide were subjected to goodness of fit test by linear regression analysis according to zeroorder and first-order kinetics. Conclusion: The formulation SF 2 containing drug: sodium alginate ratio of 1:2 offered the required in vitro drug release rate according to the official limits of drug release as per USP and selected as a promising formulation among the fifteen formulations which shows 85% drug release in 12 hrs.

Design and Evaluation of Sustained Release Matrix Tablets of Indomethacin by Employing Gelucires and Badam Gum

Sustained release matrix tablets of indomethacin (IM) were developed by employing a relatively less used hydrophilic polymer badam gum and gelucires. The dissolution rate of IM is first improved by dispersing the drug in hydrophilic gelucire (50/13) and the dispersion is then embedded in the matrix of badam gum and hydrophobic gelucire (43/01). Different ratios of IM and gelucire (50/13) were employed, and the solid dispersions were prepared by melting and solvent methods. The dispersion prepared by employing solvent method resulted in much higher dissolving product than was possible with the melting method. The differential scanning calorimetry and infrared spectroscopy (IR) studies revealed that there are no interactions between IM and gelucire and the XRD studies indicated that the drug IM existed in amorphous state in gelucire dispersion. Matrix tablets were prepared by direct compression employing different proportions of badam gum and gelucire (43/01). The prepared tablets were found to be of optimum hardness, uniform weight and acceptable friability. The drug release was found to be dependent on the ratio drug: Gelucire in the solid dispersion and also on the proportion of the release retarding polymer employed – gelucire (43/01) or badam gum. The drug release data suggested that the release of the drug is the first order and is diffusion controlled

Controlled Release Imatinib Mesylate Tablet Formulation: Using Hydrophilic Matrix System

Background: Imatinib mesylat as an oral anticancer agent need a controlled released formulation to get steady and stable plasma concentration. The aim of the present study was to develop controlled release matrix tablet formulations of Imatinib using hydroxy propyl methyl Cellulose as a hydrophilic release retardant polymer and to study the effects of different formulation features like polymer viscosity grade, ratio of the polymer, compression force, and release medium on the in vitro release properties. Methods: The in vitro release studies were performed using US Pharmacopoeia type I apparatus. The release kinetics was analyzed by Korsmeyer–Peppas model and were also analyzed using statistical method and f2 metric values. The release profiles look like Higuchi’s square root kinetics model irrespective of the viscosity grade and polymer proportion. Results: The results showed that the release rate of the drug is greatly affected by the drug/polymer ratio and viscosity grade. Also, the effect of release medium and compression force was showed to be significant on the release profiles. The release mechanism was found to be anomalous non-Fickian diffusion in all formulations. Conclusions: The formulations were found to be reproducible and stable. Controlled release formulations were developed with different release rates and profiles so that these formulations could be evaluated for more in vivo studies.

Characterization and Compatibility Studies of Different Rate Retardant Polymer Loaded Microspheres by Solvent Evaporation Technique: In Vitro-In Vivo Study of Vildagliptin as a Model Drug.

The present study has been performed to microencapsulate the antidiabetic drug of Vildagliptin to get sustained release of drug. The attempt of this study was to formulate and evaluate the Vildagliptin loaded microspheres by emulsion solvent evaporation technique using different polymers like Eudragit RL100, Eudragit RS100, Ethyl cellulose, and Methocel K100M. In vitro dissolution studies were carried out in 0.1 N HCl for 8 hours according to USP paddle method. The maximum and minimum drug release were observed as 92.5% and 68.5% from microspheres, respectively, after 8 hours. Release kinetics were studied in different mathematical release models to find out the linear relationship and release rate of drug. The SEM, DSC, and FTIR studies have been done to confirm good spheres and smooth surface as well as interaction along with drug and polymer. In this experiment, it is difficult to explain the exact mechanism of drug release. But the drug might be released by both diffusion and erosion as the correlation coefficient (R 2) best fitted with Korsmeyer model and release exponent (n) was 0.45–0.89. At last it can be concluded that all in vitro and in vivo experiments exhibited promising result to treat type II diabetes mellitus with Vildagliptin microspheres.

Raft forming Buoyant Ph Dependent Thixotropic Gelling Systems Incorporated with Gelucire 43/01 as a Potential Stomach Specific Drug Delivery System for Famotidine

Famotidine (FMT) is known as a histamine blocker (H2) that inhibits stomach acid production and it is commonly used in the treatment of peptic ulcer disease and gastric-esophageal reflux disease. It has a short half life (2.5-3.5 hours), low bioavailability (40-45%). It has excellent solubility in acidic pH just reverse in alkaline pH. Therefore an attempt has been made to develop raft buoyant gastro-retentive sustains release delivery system with in situ gelling property which is based on thixotropy behavior. Twelve formulations (Excluding two controlled formulations i.e. F and F*) were designed to contain 40 mg of FMT using Chitosan; CH (cationic polymer), Sodium Alginate; SA (anionic polymer), Gelucire 43/01; G 43/01 (lipid phase) as retardant and adhesive polymers. Emulgel was prepared and evaluated for their physicochemical properties like buoyancy and lag time, cumulative % drug release, drug release kinetics and drug excipient interaction studies by thermal studies and functional group characterization. All formulations showed that with the increase in concentration of the polymer, the gel strength increased, but the % drug release decreased F8>F12>F11>F6>F5>F10>F7>F9>F3>F4>F1>F2>F*>F. Formulations F9, F10, and F12 were found to be optimum. They followed the non-ficikian mechanism of drug release.

Development and in-vitro Evaluation of Once Daily Tablet Dosage Form of Loxoprofen Sodium

Purpose: To formulate and characterize once daily controlled release tablet of loxoprofen sodium. Methods : Eudragit RS-100, hydroxylpropyl methylcellulose (HPMC) and pectin were used as release retarding polymers. All the formulations were prepared by direct compression method. Various precompression studies were carried out to determine Hausner’s ratio, Carr’s index, angle of repose, bulk density and tapped density Differential scanning calorimetry (DSC) studies and also post-compression studies to evaluate hardness, friability, weight variation, drug content, in-vitro drug release were conducted on the tablets. The drug release data were subjected to kinetic models, including zero order, first order, Hixon Crowell, Higuchi and Korsmeyer-Peppas. Results : Compressibility index (7.6 ± 1.32 - 12.5 ± 1.43%), Hausner’s ratio (1.08 ± 0.04 - 1.14 ± 0.03), angle of repose (27.78 ± 0.47 - 30.49 ± 0.46°), hardness (6.25 ± 0.27 - 7.21±0.21 kg/cm2), friability (0.14 ± 0.06 - 0.28 ± 0.0 %), weight variation (249.5 ± 2.09 - 251.35 ± 2.41 mg) and drug content (97.30 ± 0.28 - 103.70 ± 0.31 %) were within generally accepted limits for the pre-and post-compression formulations, respectively. The tablets having the maximum amount of among the three polymers tested as matrix materials, HPMC, represented by F3 tablets, exerted better sustained release properties after 12 h. Release pattern was more of Fickian diffusion followed by Higuchi mechanism. Conclusion : The release of the loxoprofen sodium was optimized up to 12 h. Keywords : Loxoprofen, Sustained release, hydroxypropyl methylcelluose, Pectin, Eudragit, Matrix tablets

Development and in-vitro Evaluation of Once Daily Tablet Dosage Form of Loxoprofen Sodium

Purpose: To formulate and characterize once daily controlled release tablet of loxoprofen sodium.Methods: Eudragit RS-100, hydroxylpropyl methylcellulose (HPMC) and pectin were used as release retarding polymers. All the formulations were prepared by direct compression method. Various precompression studies were carried out to determine Hausner’s ratio, Carr’s index, angle of repose, bulk density and tapped density Differential scanning calorimetry (DSC) studies and also post-compression studies to evaluate hardness, friability, weight variation, drug content, in-vitro drug release were conducted on the tablets. The drug release data were subjected to kinetic models, including zero order, first order, Hixon Crowell, Higuchi and Korsmeyer-Peppas.Results: Compressibility index (7.6 ± 1.32 - 12.5 ± 1.43%), Hausner’s ratio (1.08 ± 0.04 - 1.14 ± 0.03), angle of repose (27.78 ± 0.47 - 30.49 ± 0.46°), hardness (6.25 ± 0.27 - 7.21±0.21 kg/cm2), friability (0.14 ± 0.06 - 0.28 ± 0.0 %), weight variation (249.5 ± 2.09 - 251.35 ± 2.41 mg) and drug content (97.30 ± 0.28 - 103.70 ± 0.31 %) were within generally accepted limits for the pre-and post-compression formulations, respectively. The tablets having the maximum amount of among the three polymers tested as matrix materials, HPMC, represented by F3 tablets, exerted better sustained release properties after 12 h. Release pattern was more of Fickian diffusion followed by Higuchi mechanism.Conclusion: The release of the loxoprofen sodium was optimized up to 12 h.Keywords: Loxoprofen, Sustained release, hydroxypropyl methylcelluose, Pectin, Eudragit, Matrix tablets

Formulation and in vitro Evaluation of Glimepiride Sustained Release Tablets: Comparison with Immediate Release Tablets

This work aims at the design of a sustained release formulation of glimepiride which is currently available in the treatment of type 2 diabetes mellitus and to investigate the effect of polymers on the release profile of glimepiride. Glimepiride sustained release tablets were prepared by direct compression method using different ratios of various release retarding polymers such as carbopol, ethyl cellulose, methocel K4 MCR, methocel K15 MCR, methocel K100 MCR and xanthum gum. These formulations were also compared with glimepiride immediate release tablets. The prepared tablets were subjected to various physical parameter tests including weight variation, friability, hardness, thickness, diameter, etc. In vitro dissolution studies of the formulations were done at pH 6.8 in phosphate buffer using USP apparatus 2 (paddle method) at 50 rpm. The percent releases of all the formulations (30) were 73.11%- 98.76% after 8 hours. The release pattern followed zero order kinetics and the release of the drug was hindered by the polymers used in the study. On the other hand, 100% drug was released within 1 hour from the immediate release tablet of glimepiride. The study reveals that the polymers used have the capacity to retard the release of the drug from the sustained release tablets and the more is the amount of the polymer in the formulation the less is the release of drug showing more retardation of drug release.Bangladesh Pharmaceutical Journal 18(2): 157-162, 2015

Catalyzing charring effect of solid acid boron phosphate on dipentaerythritol during the thermal degradation and combustion

The aim of this study was to investigate the acid catalysis of boron phosphate (BP) to model compound dipentaerythritol (DPER) which acted as char source during the thermal degradation and combustion. Various amounts of BP were added in DPER and then the thermal degradation and combustion behaviors were studied by means of thermogravimetric analysis (TGA) and microscale combustion calorimeter (MCC). Evolved Gases were evaluated using TGA-FTIR; solid residues were fully characterized by FTIR, X-ray photoelectron spectroscopy (XPS), Raman analysis and scanning electron microscopy (SEM). The results of TGA and MCC showed that the addition of BP leaded to the earlier thermal degradation of DPER and increased the amount of char residues, significantly decreased the peak heat release rate of DPER; the results of TGA-FTIR, XPS, Raman analysis and SEM revealed that the presence of BP accelerated the dehydration of DPER, kept more carbon and oxygen elements in condensed phases, promoted the formation of compact and stable char layer. This study indicated that Lewis acidic and Brønsted acidic sites in BP altered the single degradation pathway and catalyzed the crosslinking and char forming of DPER. BP maybe as a potential acid source applied in intumescent flame retardant polymers in future.

Flame retardant polymer composites

In this review article, different approaches of enhancing flame retardancy of polymeric composite material and their effect on different composite properties are analysed critically. The mechanisms of fire spreading on composite materials are also discussed. Flame retardancy of polymeric composite material can be enhanced either by enhancing the fire performance of constituents of composite i.e. matrices and reinforcing agents or by providing a protective flame retardant (FR) coating around the composite material. Fire performance of reinforcing material is improved by treating with FR-chemicals while the fire performance of polymer matrices can be improved by incorporating micro and nano FR-fillers or by introducing FR-compound into polymer backbone. The flammability of micro and nano filler added polymeric composites and newly developed polymer derivatives and their effect on composite properties like mechanical, thermal have been discussed. However, the development of flame retardant polymer composite is still at nascent stage and for further development, it is necessary to work on the development of non-health hazardous, environment friendly flame retarding agents which will be able to enhance the fire performance of composite materials at very low concentration levels.

Development and evaluation of natural gum-based extended release matrix tablets of two model drugs of different water solubilities by direct compression

The study was aimed at developing extended release matrix tablets of poorly water-soluble diclofenac sodium and highly water-soluble metformin hydrochloride by direct compression using cashew gum, xanthan gum and hydroxypropylmethylcellulose (HPMC) as release retardants. The suitability of light grade cashew gum as a direct compression excipient was studied using the SeDeM Diagram Expert System. Thirteen tablet formulations of diclofenac sodium (∼100mg) and metformin hydrochloride (∼200mg) were prepared with varying amounts of cashew gum, xanthan gum and HPMC by direct compression. The flow properties of blended powders and the uniformity of weight, crushing strength, friability, swelling index and drug content of compressed tablets were determined. In vitro drug release studies of the matrix tablets were conducted in phosphate buffer (diclofenac: pH 7.4; metformin: pH 6.8) and the kinetics of drug release was determined by fitting the release data to five kinetic models. Cashew gum was found to be suitable for direct compression, having a good compressibility index (ICG) value of 5.173. The diclofenac and metformin matrix tablets produced generally possessed fairly good physical properties. Tablet swelling and drug release in aqueous medium were dependent on the type and amount of release retarding polymer and the solubility of drug used. Extended release of diclofenac (∼24h) and metformin (∼8–12h) from the matrix tablets in aqueous medium was achieved using various blends of the polymers. Drug release from diclofenac tablets fitted zero order, first order or Higuchi model while release from metformin tablets followed Higuchi or Hixson-Crowell model. The mechanism of release of the two drugs was mostly through Fickian diffusion and anomalous non-Fickian diffusion. The study has demonstrated the potential of blended hydrophilic polymers in the design and optimization of extended release matrix tablets for soluble and poorly soluble drugs by direct compression.

Release Profile of Losartan Potassium from Formulated Sustained Release Matrix Tablet

The present study was undertaken to develop sustained release (SR) matrix tablets of Losartan potassium, an angiotensin-II antagonist for the treatment of hypertension. The tablets were prepared by direct compression method along with Kollidon SR and Methyl Cellulose as release retardant polymers. The evaluation involves two stages- the physical properties studies of tablets and in vitro release kinetics assessment. The USP paddle method was selected to perform the dissolution test and 900 ml phosphate buffer of pH 6.8 was used as dissolution medium at 50 rpm at 370C. The release kinetics were analyzed. All the formulations followed Higuchi release kinetics. When the release data was plotted into Korsmeyer-Peppas equation, then it was confirmed that F-1, F-2, F-3, F-4 and F-5 exhibited non-fickian type drug release whereas F-6 exhibited fickian type drug release from the tablet matrix. The in-vitro release studies revealed that the formulation F-2 can be taken as an ideal or optimized formulation of sustained release tablets for 24 hours release as it fulfills all the requirements for sustained release tablet. Furthermore, when the tablets were preheated at different temperature (300C, 450C, 600C) before dissolution they showed decrease in drug release compared with ambient temperature DOI: http://dx.doi.org/10.3329/bpj.v16i2.22301 Bangladesh Pharmaceutical Journal 16(2): 177-183, 2013

RAFT FORMING BUOYANT pH DEPENDENT THIXOTROPIC GELLING SYSTEMS INCORPORATED WITH GELUCIRE 43/01 AS A POTENTIAL STOMACH SPECIFIC DRUG DELIVERY SYSTEM FOR FAMOTIDINE

Famotidine (FMT) is known as a histamine blocker (H2) that inhibits stomach acid production and it is commonly used in the treatment of peptic ulcer disease and gastric-esophageal reflux disease. It has a short half life (2.5-3.5 hours), low bioavailability (40-45%). It has excellent solubility in acidic pH just reverse in alkaline pH. Therefore an attempt has been made to develop raft buoyant gastro-retentive sustains release delivery system with in situ gelling property which is based on thixotropy behavior. Twelve formulations (Excluding two controlled formulations i.e. F and F*) were designed to contain 40 mg of FMT using Chitosan; CH (cationic polymer), Sodium Alginate; SA (anionic polymer), Gelucire 43/01; G 43/01 (lipid phase) as retardant and adhesive polymers. Emulgel was prepared and evaluated for their physicochemical properties like buoyancy and lag time, cumulative % drug release, drug release kinetics and drug excipient interaction studies by thermal studies and functional group characterization.

Formulation and Evaluation of Cefixime Trihydrate Matrix Tablets Using HPMC, Sodium CMC, Ethyl Cellulose.

The objective of the present work is to design sustained release matrix tablets of cefixime trihydrate by incorporating drug in a matrix made up of release retardant polymers, which prolong drug release leading to minimization of the peak and valley effect in the plasma and provide patient convenience. The effect of combination of polymers on parameters like release pattern, release mechanism of the drug were studied. Total nine formulations each containing 200 mg of drug were prepared by direct compression method. The formulations F-1, F-2, F-3 were prepared with a 1:1 drug to polymer ratio using hydroxypropyl methylcellulose, carboxymethyl cellulose sodium and ethyl cellulose. F-4 was prepared with a 1:1 ratio of hydroxypropyl methylcellulose, carboxymethyl cellulose sodium, F-5 as prepared with a 1:1 ratio of hydroxypropyl methylcellulose and ethyl cellulose, F-6 was prepared with a 1:1 ratio of carboxymethyl cellulose sodium and ethyl cellulose, F-7, F-8, F-9 were prepared by using polymers hydroxypropyl methylcellulose, carboxymethyl cellulose sodium and ethyl cellulose in the ratios of 0.5:0.5:1, 0.5:1:0.5, and 1:0.5:0.5. Designed matrix tablets were evaluated for various pre-compression and post-compression parameters. Formulation F-5 showed 102.15 % release at the end of 12 h and it is selected as the best formulation. All Formulations followed zero order with non-Fickian diffusion method.