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In vitro studies and modeling of a controlled-release device for root canal therapy
Journal of Controlled Release 67 (2000) 293–307 www.elsevier.com / locate / jconrel
In vitro studies and modeling of a controlled-release device for root canal therapy a a a a, b b J. Huang , H.-L. Wong , Y. Zhou , X.Y. Wu *, H. Grad , R. Komorowski , S. Friedman b a
Faculty of Pharmacy, University of Toronto, Toronto, Canada M5 S 2 S2 Faculty of Dentistry, University of Toronto, Toronto, Canada M5 S 2 S2
b
Received 21 October 1999; accepted 26 January 2000
Abstract Endodontic disease is caused primarily by bacteria that interact with periradicular host tissues. Therefore, treatment of endodontic disease aims at the exclusion of bacteria from the root canal system. This work focused on in vitro studies and modeling of a controlled-release device for delivering antimicrobial agents in root canals. A cylindrical, needle-shaped device was prepared consisting of a matrix core and a polymer coating, loaded with 30–45% chlorhexidine (CHX). The composition of the core, a blend of water-permeable polymers, and the thickness of the coating were tailored to impart various release rates. A relatively steady release rate for over 40 days after an initial burst was achieved using a formulation for long-term release, which is desirable for establishing and maintaining the necessary therapeutic levels. Mathematical models were developed for both in vitro and in vivo drug release into a liquid of limited volume, taking into account a moving boundary of the dispersed drug and a time-dependent boundary condition. A concentration-dependent effective diffusion coefficient was used to count increased porosity as the solid drug had dissolved. The finite element method and computer programs were applied to solve the differential equations and predict the in vitro and in vivo release kinetics. The model prediction agreed well with the in vitro experimental data and provided guidance for designing the device for in vivo release in root canals. The result of in vitro antimicrobial tests, performed using a bovine tooth model, suggested that the device was effective in reducing growth of microbes. 2000 Elsevier Science B.V. All rights reserved. Keywords: Controlled-release device; Dental root canal; Antimicrobial; Modeling; Finite element method; Moving boundary; In vitro and simulated in vivo
1. Introduction Endodontic disease, such as pulpitis or periradicular periodontitis, is caused by infection or inflamma*Corresponding author. 19 Russell Street, Toronto, Ontario, Canada M5S 2S2. Tel.: 11-416-978-5272; fax: 11-416-9788511. E-mail address: [email protected] (X.Y. Wu)
tion of the dental pulp tissue and the bone supporting the tooth, which are affected by oral microorganisms invading the tooth. It is a very common occurrence that affects 70% of the population in countries with well-developed dental care modes, and by estimate, over 95% of the population in other parts of the world; and it is one of the major causes of tooth loss in these populations. Endodontic disease is an all-inclusive term for a
0168-3659 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0168-3659( 00 )00225-X
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variety of clinical conditions that are forms of either pulpitis or periradicular periodontitis. Pulpitis is an inflammation of the dental pulp that can be induced by mechanical, physical or microbial stimuli. If the stimulus is not eliminated in the early stage of pulpitis, the disease process will escalate beyond potential repair, leading to pulpal necrosis. Frequently at this stage, oral microorganisms infect the necrotic pulp and the pulp space inside the tooth, i.e., the pulp chamber and root canals. The bacteria in the root canal can further cause the development of periradicular periodontitis, an infective disease in the bone supporting the tooth. Symptoms that may be encountered in the various stages of the disease process frequently lead to the loss of the affected tooth. Untreated or intractable root canal infection may also lead to tooth loss. Periradicular periodontitis can be treated by debridement of the infected pulp tissue and disinfection of the root canal by a combination of three modes: (a) debriding the pulpal tissue and enlarging the root canal; (b) flushing the canal to kill microorganisms using antimicrobial irrigating solutions, mainly sodium hypochlorite; and (c) killing surviving microorganisms by applying antimicrobial medicaments to the root canal between consecutive treatment sessions. Such treatment is effective and results in complete healing of the diseased sites in 46–93% of the cases [1], yet up to 54% treatment failures are observed attributable to residual root canal infection [2]. This is because root canal microorganisms can persist mainly by residing in root canal irregularities and dentinal tubules, where they may be inaccessible to the files, irrigants, and conventional medicaments [2,3]. Most available root canal medicaments, such as camphorated parachlorphenol or iodine potassium iodide, are bactericidal. However, they are effective for only a few hours. After they have expired, microorganisms can repopulate the root canal [4]. Another commonly used medicament, calcium hydroxide, though it remains bioactive for weeks [4], is not very effective against specific enteric bacteria [5] that are frequently associated with failures of root canal treatment [6]. Also the ability of calcium hydroxide to affect microorganisms harbored in the dentinal tubules is questionable [7–9]. In contrast,
chlorhexidine effectively eliminates oral microorganisms when it is applied to treat gum disease [10,11] and its antimicrobial efficacy equals that of the conventional root canal medicaments [12,13]. Unlike the other medicaments, chlorhexidine binds to the dentin and thus induces substantive antimicrobial activity of the dentin surface [14]. Such activity can be obtained by irrigating the root canal with chlorhexidine [15]. Nevertheless, to resist re-infection, the canal has to be exposed to chlorhexidine for longer times, preferably 1 week [16]. In addition, for patients who may miss a scheduled revisiting time, an even longer time period of drug exposure is required in order to protect the canal from reinfection. Hence, a major therapeutic goal is to develop a vehicle to deliver chlorhexidine to root canals for extended periods of time. Sustained-release devices have been developed by several groups for treatment of periodontal disease [17–22]. It has been demonstrated that a biodegradable device containing chlorhexidine is more effective than calcium hydroxide in disinfection of root canal dentine in bovine teeth [17–19]. However, these devices were prepared for periodontal application and thus may not be suitable for root canal application. Firstly, unlike periodontal pocket, the fluid present in root canals is minimal, which may be insufficient to cause drug release by degradation or diffusion. Secondly, in the case of a degradable polymer as the carrier, the device may not be completely degraded when it is time to permanently fill the root canal. The remaining fragments may interfere with permanent filling and sealing of the root canal, resulting in leakage and thus ingress of bacteria. Consequently, infection of the filled root canal, constituting treatment failure, may occur [9]. Thirdly, owing to the size and shape of root canals, the materials and formulations useful for periodontal application may not warrant mechanical strength of the needle-shaped device for insertion into root canals. In addition to the aforementioned concerns about root canal device, delivering chlorhexidine is another challenge. Because of a strong, positive charge of chlorhexidine and its consequent binding capability, polymers used for delivery other antimicrobial agents such as metronidazole become unsuitable for chlor-
J. Huang et al. / Journal of Controlled Release 67 (2000) 293 – 307
hexidine. For example, cellulose acetate phthalate, used for sustained release of metronidazole, strongly binds with chlorhexidine, resulting in undetectable release of chlorhexidine (X.Y. Wu, H. Grad, P.I. Lee, unpublished data). Besides, chlorhexidine is incompatible with many pharmaceutical excipients such as dibutyl phthalate, which are commonly used to plasticize the polymers. These characteristics of chlorhexidine make it difficult to formulate a delivery composition for chlorhexidine. Our group has developed a non-degradable and retrievable device for sustained release of therapeutic agents in dental root canals [23,24]. To design suitable formulations for delivering sufficient medicament in the small cavity of root canals for days or weeks, extensive experimental tests and sophisticated computer modeling are needed. In this work, fundamental properties of chlorhexidine were characterized, including its solubility, partition between the polymers and the media, and permeability through the polymers. In vitro release kinetics was studied in various media of different volumes. Shortterm test (about 1 day) was conducted in a larger volume of liquid with stirring, simulating the extreme of high release rate. Long-term test (.40 days) was carried out in small vials without mixing, where the release medium was changed daily. The long-term test was designed to mimick in vivo condition with possible drug loss by tissue binding, drug absorption, or leaking through the temporary sealing. The antimicrobial efficacy of the device was assessed using in vitro bovine tooth model [16], and compared with conventional disinfection solutions. Mathematical models were developed to describe the kinetics of drug release in vitro and in vivo taking into consideration a moving boundary of the dispersed drug in a liquid of limited volume and a time-dependent boundary condition. The kinetics of drug release in root canals was predicted by computer simulation using the finite element method.
2. Experimental section
2.1. Preparation of the device The devices, with dimensions suitable for insertion
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in dental root canals, e.g., 0.6–0.8 mm in diameter and 11–18 mm in length, were prepared using waterpermeable polymers such as ethyl cellulose and antibacterial agents such as chlorhexidine (CHX) and its salts [23,24]. In a typical preparation, chlorhexidine acetate (Wiler Fine Chemicals, Ontario, Canada) was dissolved or dispersed in a 10% ethyl cellulose (Dow Chemicals) solution in alcohol. Most of the solvent in the mixture was evaporated at room temperature in a fumehood, and the remaining gellike mixture was used to form the needle-like device. The device was then completely dried in a mold at room temperature. Four different formulations were prepared with different drug loading and drug release mechanisms. In formulation 1 (F1), the initial chlorhexidine concentration was 30%, no coating was applied. In formulation 2 (F2), the drug loading was |45%, and the device was coated with 10% ethyl cellulose solution. Formulation 3 (F3) was similar to F2 except for the addition of other components. Formulation 4 (F4) was also similar to F2 but with thicker coating. The thickness of the coating was evaluated based on mass balance before and after the coating, dimension of the device, and density of the polymer membrane.
2.2. Determination of solubility, partition coefficient and permeability Solubility of chlorhexidine in water or pH 7.4 buffer at 378C was determined using equilibrium solution method. Various amounts of solid drug were added to a known volume of liquid in different vials. The vials were incubated in a water bath at 378C for 2 days with stirring. After equilibration, i.e., no more drug could be dissolved, the drug concentration in the solution was assayed by UV-vis spectrophotometry following appropriate dilution. A known amount (e.g., 0.75 g) of polymer sheets was immersed in either water or pH 7.4 buffer (0.05 M) with different drug concentrations at 378C for at least 5 days. The remaining drug in the solution was then analyzed by spectrophotometry. The concentration of the drug in the polymer was calculated from mass balance and then plotted against drug concentration in the solution. The partition coeffi-
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cient of CHX between the polymer and the liquid was determined from the slope of the plot by linear regression. The permeability of CHX through the polymers was measured using side-by-side diffusion cells with a water jacket. The polymer membranes, prepared by casting polymer solutions in alcohol in glass rings, were mounted between the donor cell and the receptor cell. The concentration in the receptor cell was monitored by spectrophotometry. The permeability, P, defined as a product of partition coefficient, K, and diffusion coefficient, D, was evaluated from the slope of the plot of the amount of drug permeated versus time at the steady state.
2.3. In vitro release test 2.3.1. Short-term drug release test Each device was immersed into 3.0 ml of 0.05 M pH 7.4 buffer solution in a cuvette at 378C with vigorous stirring. The amount of drug released into the solution was continuously monitored with a diode array spectrophotometer (Hewlett-Packard 8452A) at 256 nm. The measurement lasted for more than 20 h, with a sampling interval of 10 min. 2.3.2. Long-term drug release test Each device was placed in 0.35 ml of deionized water at 378C without stirring in a small glass vial. At every 24 h, the drug concentration in the medium was determined by spectrophotometry after appropriate dilution. The device was immediately patted dry, and transferred into fresh water in a clean vial, followed by subsequent release test.
2.4. Antibacterial tests Haapasalo and Ørstavik’s method [7] was modified to prepare bovine tooth model for the antibacterial tests. The root segment was cut into 5-mm thick discs with a rotating diamond saw. Each disc had an external diameter of approximately 7 mm. The canals of the discs were enlarged with an ISO 033 round bur, to standardize the internal diameter. Absence of smear layer was confirmed by examination of a control disc with scanning electron microscopy. The discs were sterilized separately by autoclaving three times in test tubes containing brain heart infusion (BHI) broth for 30 min at 1218C. The discs were then coated with nail varnish on the outer surfaces, and mounted with sticky wax at the bottom of petri dishes. Two sets of tests were carried out to evaluate (1) conventional irrigation process in endodontic practice and (2) sustained exposure of various disinfectants.
2.5. Irrigation test Ten ml of testing solution were applied to the canal for 5 min and the excess amount of the solution was removed. A suspension of E. faecalis (ATCC 29212) in BHI broth was then introduced to the canal, and a fresh innoculum was added every other day.
2.6. Immersion test The discs were immersed in the testing solutions presented in Table 1 and thus the canals were filled by the solutions entirely. The discs were then left to stand for 7 days at 378C in air. At the end of the
Table 1 Conditions for irrigation and immersion tests using bovine root canal model Test
Irrigation
Group 1 Group 2
With sterile saline With 5.25% sodium hypochlorite With 0.2% chlorhexidine
Group 3
Immersion Group 4 Group 5
In 0.2% chlorhexidine In sterile saline
Group 6
In 5.25% sodium hypochlorite In water with insertion of the controlled-release device in the canal
Group 7
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testing time, sterile round burs, ISO sizes 035, 037, 040 and 042 were sequentially used to enlarge the canals of the discs. The dentine powder obtained with each bur was collected in separate test tubes containing 3 ml of sterile BHI broth, and incubated for 24 h at 378C in air. The optical density of the broth, proportional to the number of bacteria present, was then measured by a spectrophotometer at 540 nm. The mean optical density and the standard deviation were calculated for each group and statistically analyzed using Student’s t-test.
3. Theoretical section
3.1. General model The needle-shaped device, with a length to diameter ratio over 20, can be considered as a long cylinder where drug release from its two ends is negligible [25]. The device consists of a matrix core and a membrane coating. The drug is released from the device into a liquid of limited volume. The structure of the device and the definitions of various regions are schematically presented in Fig. 1a–c. Fig. 1a illustrates in vitro drug release into a wellstirred medium with a boundary layer resistance. In the figure, j is the moving boundary of the dispersed drug, R and R m are, respectively, the radius of the matrix core and that of the device; h m and h b denote the thickness of the membrane coating and that of the diffusion boundary layer, respectively; C1 , C2 , C3 , and C4 stand for the drug concentrations in four different regions, i.e., the matrix core, the membrane, the diffusion boundary layer, and the bulk liquid. The drug release is assumed to be diffusion controlled. Hence a diffusion model can be used with consideration of a moving boundary of the dispersed drug and a variable boundary condition owing to drug release into a finite liquid volume [25–28]. The governing equation of diffusion for an axisymmetrical, one-dimensional cylinder is given as follows [29],
S
≠C 1 ≠ ≠C ] 5 ] ] rD ] ≠t r ≠r ≠r
D
(1)
where r denotes the radial distance of the cylinder, D
Fig. 1. Schematic illustration of the structure of the device, a boundary layer, a moving boundary of a dispersed drug, and concentration profile of the drug. (a) In vitro release in a liquid of finite volume with mixing; (b) in vitro release in a liquid of finite volume without mixing; and (c) in vivo release in a root canal with drug removal.
and C are the diffusion coefficient (cm 2 / s) and solute concentration (g / cm 3 ), respectively. Eq. (1) and the following initial and boundary conditions are applicable to all three cases studied, i.e., in vitro release with mixing, in vitro release in a daily-changed medium with no stirring, and in vivo release.
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C1 5 C10
in the core, t 5 0
(2)
C2 5 C20
in the membrane, t 5 0
(3)
C30 5 C40 5 0 in the boundary layer and bulk liquid, t 5 0
(4)
≠C1 dj (C10 2 Cs )] 5 D1 ]] dt ≠r
(5)
C1 5 Cs
on j , 0 , t , t*
on j , 0 , t # t*
(6)
where C10 , C20 , C30 and C40 are the initial drug loading (g / cm 3 ) in the aforementioned four regions, respectively; Cs is the drug solubility in the polymer; D1 is the diffusion coefficient of the drug in the device; and t* is the time required for all the dispersed drug to dissolve. Furthermore, the drug concentration in the membrane and the liquid is linked by the following interfacial boundary conditions: ≠C2 ≠C3 D2 ]] 5 D3 ]] ≠r ≠r C2 5 KC3
on R m
t.0
t.0
on R m,
(7) (8)
where K is the partition coefficient of the drug between the polymer phase and the liquid. Because of the different external conditions in three different cases, additional boundary and / or initial conditions are needed, which are presented in the following section.
3.2. Additional initial and boundary conditions 3.2.1. In vitro release in a finite well-mixed liquid For in vitro release in a finite liquid volume with mixing, the whole system including the device and the liquid is a closed system. This means that there is no mass transport beyond the boundary, R s , ≠C ]]4 5 0 on R s ≠r
t$0
(9)
where Vb is the volume of the bulk liquid and S is the surface area of the cylinder at R b .
3.2.2. In vitro release with daily-changed medium The model for in vitro release in a non-mixed medium is portrayed in Fig. 1b, where the definitions of the parameters are the same as those in Fig. 1a. Please note that a boundary layer is absent in Fig. 1b since the entire liquid is assumed to be stagnant, though the boundary condition for the system remains: ≠C ]]3 5 0, on R s ≠r
t$0
(11)
When the release medium is replaced by a fresh, drug-free liquid after the release has proceeded for a time interval, t9 (e.g., 24 h), the initial condition for the medium is reapplied, C3 5 0, t 5 mt9, m 5 1, 2, 3, . . .
(12)
A non-uniform drug profile in the device is carried over from the previous release period and used as the initial condition for the device.
3.2.3. In vivo release in a root canal During in vivo release in a root canal, some of drug may be removed from the cavity due to tissue binding, drug absorption, or leaking from dentinal tubules or temporary sealing. Such an in vivo condition is taken into account by applying another layer outside the boundary, R s . Drug permeates through this layer with a permeability, P (P5DK), into the body fluid with a zero drug concentration and is then carried away by the fluid (see Fig. 1c). It is assumed that the drug permeation is governed by passive transport, i.e., diffusion. Hence, the diffusion equation such as Eq. (1) and corresponding initial and boundary conditions presented in Section 3.1 are applicable, yet a sink condition is added for the body fluid (see Fig. 1c), C 5 0, t $ 0
(13)
As depicted by Fig. 1a, drug concentration in the finite, well-mixed liquid is uniform and can be derived from mass conservation [28,29],
3.3. Treatment of moving boundary of the dispersed drug
≠C4 ≠C3 Vb ]] 5 2 SD3 ]] ≠t ≠r
To include the condition of moving boundary of the dispersed drug (Eqs. (5)–(6)) in the program, the
t.0
(10)
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entire polymer region was divided into many thin layers. The drug was allowed to diffuse out initially in the outermost thin layer, where the drug concentration was examined frequently using an iteration checking subroutine. Once the excess amount of solute, (C10 –Cs )d x, had been depleted, i.e., C1 5Cs in the current layer, the solute diffusion in the next thin layer was initiated. Such a procedure was repeated until all the dispersed drug dissolved. The finite element method was used to solve the diffusion equations with the initial and boundary conditions presented above. Computer programs and computational procedures from our previous work [25–28] were modified and used to obtain numerical solutions.
4. Results and discussion
4.1. Morphology of the device Fig. 2 is the microscopic photograph of a device (F2) before (a) and after (b) a long-term release in water at 378C for 40 days. It is seen that the device maintains the shape although it becomes more porous. This observation suggests that the device
299
unlikely disintegrates or ruptures during release, and it is mechanical stable. Such stability makes it possible to retrieve the device after its insertion in a canal for days or even weeks. Moreover, the obvious porous structure after CHX has been consumed (Fig. 2b) implies that the effective diffusion coefficient of CHX in the device may increase in the region where the solid drug has been exhausted.
4.2. Partition coefficient, diffusion coefficient, and solubility of CHX To ensure the incubation time for determination of CHX partition is sufficient to reach equilibrium, the reduction of CHX concentration in the solution was monitored by spectrophotometry. Fig. 3 shows the fraction of CHX remaining versus time reaches a plateau after about 3 days. Therefore, the polymer sheets were incubated with drug solutions for more than 5 days. To confirm that the reduction in CHX concentration is not due to drug adsorption onto the glass vials during incubation, the drug concentration in the solution in the absence of polymer was assayed after incubation for the same time periods. The change in drug concentration was found to be negligible.
Fig. 2. Microscopic photograph of a device (F2) at the initial state (a) and after a long-term release test in water at 378C for 40 days (b).
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responsible for the high partition of CHX in the polymer phase. The solubility of CHX in the polymer phase was computed from the above data using Cs 5KCsolution . It was 8.5 and 1.6 mg / ml for water and pH 7.4 buffer, respectively. The permeability of CHX through the polymer membrane was determined to be 4.660.94310 211 cm 2 / s, from which the diffusion coefficient of CHX in the polymer phase was evaluated to be 1.5360.17310 210 cm 2 / s.
4.3. Release kinetics and mechanism
Fig. 3. Fraction of CHX remained in the solution versus time indicating dynamic absorption of CHX into polymer sheets.
Fig. 4 is a typical plot of CHX concentration in the polymer phase versus that in the solution used to calculate partition coefficient. A linear relationship is seen in the studied concentration range. The partition coefficient of CHX was determined to be 0.47 in water and 11.4 in pH 7.4 buffer (0.05 M), indicating a strong medium-dependence of partition. Similarly, the solubility of CHX in liquid, Csolution , also varies with the type of medium. It was 18.4 mg / ml in water and 0.14 mg / ml in pH 7.4 buffer (0.05 M) at 378C. The low solubility in the buffer is very likely
Fig. 4. Equilibrium CHX concentration in polymer phase versus that in water at 378C.
The results of short-term drug release from three devices with different formulations into pH 7.4 buffer (0.05 M) are shown in Fig. 5. For device F1, with no coating, the drug release is very fast; within 2 h, the UV absorbance of the drug solution is out of the measurable range of the instrument. In contrast, the drug release for device F2 and F3 is in a more controlled manner. After an initial burst in the first 2 h, the drug release reaches a nearly constant rate. As shown by the result of the long-term release test in Fig. 6, device F1 has released most of its payload within 10 days with a quick reduction in the release rate. Device F4, with a thick coating, provides a low release rate. This formulation may be suitable for long-term applications. However, its antibacterial effectiveness needs to be verified by
Fig. 5. The short-term release profiles of CHX from three devices with different formulations: F1, with no coating; F2, with coating; F3, with coating and other components. The experiments were carried out in 3 ml of pH 7.4 buffer (0.05 M) at 378C with mixing.
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Fig. 6. The long-term release profiles of CHX from devices with four different formulations: F1–F3 (see Fig. 5) and F4, with thick coating. The experiments were carried out in 0.35 ml of water at 378C with no mixing. The release medium was replaced by fresh water daily.
further investigation. CHX release from devices F2 and F3 appears to follow a similar pattern, i.e., a steady release rate following an initial burst. Especially for device F3, the steady release lasts about 30 days. Such a release pattern seems more desirable because the initial burst is beneficial to establishing an effective drug level in the solution; and the following slow but steady release is appropriate for maintaining the drug concentration at the therapeutic level. Therefore, more studies were carried out on the performance of devices F2 and F3. As mentioned above, the device is of a cylindrical geometry with a high drug loading (C10 4Cs ). In this case, the dispersed drug diffuses out from the cylindrical matrix, and thus a nonlinear release profile should be expected [28–30]. This release profile deviates from the present experimental observation, i.e., a relatively constant release rate following the initial burst. On the other hand, if membrane coating is a limiting barrier to the diffusion, a lag time instead of a burst should be observed [29,31,32]. Normally, an initial burst implies migration of the drug from the reservoir to the membrane. Therefore, we believe that, in our case, extraction of CHX from the core to the membrane in the coating process may take place, because of its relatively high solubility in ethanol (6.7%). Moreover, drug diffusion through the membrane coating may become the
301
Fig. 7. Effect of release medium on the release profiles of F2. The experiments were conducted in 3 ml of water or pH 7.4 buffer (0.05 M) at 378C with mixing.
limiting step at a later stage, so the release rate becomes rather constant. The partially membranecontrolled mechanism is also supported by the huge difference in the release rate between the coated (F2–F4) and uncoated device (F1), which is particularly obvious in Fig. 5.
4.4. Effect of release medium As presented above, the solubility and partition of CHX depend on the type of medium strongly. This dependence, in fact, affects release kinetics of CHX appreciably as evidenced by the in vitro data in Fig. 7. The release rate of CHX is much lower in pH 7.4 buffer than that in water. This kinetic behavior can be explained by theoretical [29] and numerical models [26]. It has been demonstrated that a higher partition in the polymer and / or a lower solubility in the liquid contribute to reduction in release rate [26,29]. We also observed, in the short-term tests in pH 7.4 buffer, acceleration in drug release after the release medium had been replaced by a fresh one. However, no change in the release rate was detected in the case of water. This result suggests that CHX solubility plays an important role in the release kinetics.
4.5. Model prediction Although experiments, such as that in a small vial
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with daily changed medium, were very carefully designed to gather kinetic data of release, these in vitro data are still not representative of in vivo situation. This is because, on one hand, the liquid volume in human dental root canals is much smaller even as compared to the smallest scale in our in vitro experimental setting. On the other hand, continuously taking samples from small cavities of root canal models and analyzing drug concentration in the fluid are very difficult, considering that the diameter of human root canals is in the vicinity of 0.1 cm and the average diameter of the device is |0.07 cm. Therefore, prediction of in vivo release behavior by mathematical modeling and computer simulation becomes indispensable, especially in the later stage of the development before any further pursuit of clinical trials. On the basis of our previous work [23–28], current experimental observation, and good understanding of the delivery system, mathematical models have been derived (see Section 3). Most of the parameters used in the model computation, such as partition coefficient, drug solubility, and diffusion coefficient in the polymer were determined by experiments (see Section 4.2). The thickness of the membrane coating, h m , in device F2 and F3 was evaluated to be 1.84310 23 cm. A concentrationdependent effective diffusion coefficient in the matrix core was applied, i.e., a higher D value in the layers with C1 #Cs than that in the layers containing the solid drug. This approach was taken based on our observation that pores were generated after the solid drug had been exhausted (see Section 4.1), and the concept that the effective diffusion coefficient (Deff ) can be related to porosity, ´, and tortuosity, t, by [26,31–35]
´ Deff 5 D0 ] t
C1 # Cs
(14)
where D0 is the drug diffusion coefficient in the liquid. In the absence of actual values of ´ and t, a factor less than one may be used in the place of ´ /t [26,35]. The values of Deff in the porous region, diffusion coefficient in the liquid, and boundary layer thickness were estimated by model-fitting of the in vitro experimental data.
4.5.1. Comparison of model prediction and in vitro experimental data To validate the model, computational procedures and programs, and to estimate the model parameters, the numerical solutions were compared with the experimental data from both long- and short-term release tests. 4.5.1.1. Long-term release in water. As mentioned above, the long-term release tests were conducted in 0.35 ml of water without mixing with the release medium being changed daily. The renewal of the medium was treated in the computation by reapplying the initial conditions (see Section 3.2.2). The following parameters were used in the computation: the diffusion coefficient in the membrane and in the core matrix before the solid drug was exhausted, D1 5D2 52.1310 210 cm 2 / s; the effective diffusion coefficient in the core matrix after the solid drug was exhausted, Deff 51310 27 cm 2 / s; the diffusion coefficient in the liquid, D3 51310 25 cm 2 / s; the partition coefficient between the polymer phase and water, K50.47; drug solubility in the polymer, Cs 5 8.5 mg / cm 3 ; the initial drug concentration in the polymer, C10 5440 mg / cm 3 , C20 550 mg / cm 3 ; the radius of the device, R m 50.035 cm; and the thickness of the membrane coating, h m 51.84310 23 cm. The values of D1 , D2 , K, Cs , C10 , R m , and h m were determined experimentally (see Section 4.2), and D3 , Deff , and C20 were estimated by model fitting. Fig. 8a shows that the release profile predicted by the model agrees well with the experimental data. 4.5.1.2. Short-term release in buffer. The short-term release was conducted in 3 ml of medium with mixing. In this case, a well-mixed environmental condition was applied and drug transport in the liquid beyond the boundary layer was due to convection rather than diffusion. The parameters used in the computation of drug release into pH 7.4 buffer (0.05 M) were as follows: the diffusion coefficient in the polymer phase, D1 5 D2 5 1.53 3 10 210 cm 2 / s, Deff 51310 27 cm 2 / s; the diffusion coefficient in the boundary layer, D3 5 1 3 10 25 cm 2 / s; the partition coefficient, K511.4; the drug solubility in the polymer, Cs 51.6 mg / cm 3 ; the initial drug concentration, C10 5440 mg / cm 3 , C20 550 mg / cm 3 ; the
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in the models and computational programs and procedures, we then moved to our ultimate goal of the modeling part of this work, i.e., the modeling and prediction of release kinetics of the device in root canals.
4.5.2. Prediction of release kinetics in root canals Before further pursuit of clinical trials, it is necessary to predict possible in vivo performance of the device, i.e., the dose it can deliver in root canals. As presented in Section 3.2.3. and Fig. 1c, drug removal by either tissue adsorption / absorption or leaking was considered by assuming drug permeation through a hypothetical layer. In the computation, the following parameters were used: the drug permeability, P51310 23 cm 2 / s; the length of the device and the canal, L51.2 cm; and the radius of the canal, r50.05 or 0.1 cm. While the device parameters were kept the same as those in preceding computation, the physicochemical and kinetic parameters for the buffer solution were used: K511.4, Cs 51.6 mg / cm 3 , D1 5D2 51.53310 210 cm 2 / s, Deff 51310 27 cm 2 / s, and D3 51310 25 cm 2 / s.
Fig. 8. Comparison of model-predicted release profile of F2 with that measured by experiment. (a) Long-term release in 0.35 ml of water with the medium being changed daily and (b) Short-term release in 3 ml of pH 7.4 buffer with mixing.
radius of the device, R m 50.035 cm; the membrane 23 thickness, h m 51.84310 cm; and the thickness of the diffusion boundary layer, h b 50.02 cm. The values of D1 , D2 , K, Cs , C10 , R m , and h m were determined by experiments (see Section 4.2), and D3 , Deff , C20 , and h b were estimated by model fitting. Fig. 8b illustrates that the release kinetics for the device in the buffer solution predicted by the model matches the experimental data well. The above results have not only confirmed that the model is mechanistically correct in describing the release kinetics of the device, but also validated the computational procedures. Having gained confidence
4.5.2.1. Comparison of in vivo release with in vitro release. The simulated in vivo release profiles are presented in Fig. 9 together with the in vitro experimental data from a long-term test (curve A in Fig. 9a) and a short-term test (top curve in Fig. 9b). Apparently, the in vivo release (curve C in Fig. 9a and bottom curve in Fig. 9b) is much slower than the in vitro ones, mainly because of the difference in the release environment. As discussed previously, the liquid volume in root canals is much smaller than that in the in vitro tests. As a consequence, drug accumulation in the liquid is much more severe, thus hindering the drug release. With consideration of the effect of the length of the device, curve B in Fig. 9a was obtained using the same length as that in the in vitro experiment, i.e., 1.8 cm. It is seen that the in vivo release rate is still much lower than the in vitro one. About 0.047 mg / day (day 1)–0.01 mg / day (day 25) of CHX is released from the device into the root canal, as compared with that in vitro (e.g., over 0.05 mg / day even at day 25). However, due to a small volume of liquid, e.g., 0.0048 ml for a root canal
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4.5.2.2. Investigation of factors influencing in vivo release kinetics. The in vivo release kinetics can be affected by environmental conditions or by changing the design parameters such as drug loading, membrane thickness and permeability, and matrix composition. Here we studied, by computer simulation, two factors that could influence the in vivo release rate. Since the size of canals may vary with the type of tooth and the filing depth, we computed the release profiles of device F2 with a length of 1.2 cm in two root canals, one with a radius of 0.05 cm and the other 0.1 cm. Fig. 10 shows that as the canal radius is doubled, that is, the liquid volume increases
Fig. 9. Comparison of model-predicted in vivo release profiles with in vitro data determined by experiment at 378C. (a) Longterm release. Curve A, in vitro release in 0.35 ml of water with daily-changed medium; curves B and C, simulated in vivo release in pH 7.4 buffer. (b) Short-term release in pH 7.4 buffer. Top curve, in vitro experimental data; and bottom curve, simulated in vivo data. The device is 0.035 cm in radius and 1.8 cm (curves A and B) and 1.2 cm (curve C) in length. The radius of the root canal is assumed to be 0.05 cm.
0.05 cm in radius and 1.2 cm in length (note that the volume of the device has been subtracted), the drug concentration in the canal could reach 26 mg / ml in 5 days. The in vivo drug concentration can be higher if a drug solution is introduced to the canal prior to the insertion of the device. Whether this concentration range is effective in killing the bacteria will be answered by further antimicrobial tests and clinical trials.
Fig. 10. The effect of membrane thickness and canal radius on the in vivo release kinetics of the device. The device is 0.035 cm in radius and 1.2 cm in length. The radius of the root canal is assumed to be 0.05 or 0.1 cm. The thickness of the membrane coating, h m 51.84310 23 cm or 0.92310 23 cm.
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305
Table 2 Turbidity of the broth as an indication of E. Faecalis concentration (n510 for Groups 1–6, n52 for Group 7) Group
1 2 3 4 5 6 7
Bur size (mm) 0.35
0.37
0.40
0.42
0.7260.12 0.6460.13 0.6560.16 0.01160.003 0.5360.09 0.6960.25 –
0.7660.07 0.6660.10 0.6260.07 0.01560.005 0.6960.14 0.5960.17 Not detectable
0.7660.10 0.6560.09 0.6960.08 0.00960.005 0.7760.16 0.6660.21 Not detectable
0.8460.06 0.7360.10 0.7160.08 0.009660.005 0.6760.21 1.0660.21 –
6.9 times, the change in release kinetics is negligible. This means that the device with the present design may be applied to large or small canals without need of significant modification, though the drug concentration in the cavity may be lower in a larger canal. If a higher or lower release rate is desired, we can vary the thickness of coating, which has been demonstrated by experiment (Fig. 6). In the modeling, we simulated the release behavior of two devices with coating thickness, h m 51.84310 23 and 0.92310 23 cm, respectively. The amount of drug delivered at the steady state is about 20% larger when a coating of a half thickness is applied. The above examples have demonstrated that the model simulation can predict in vitro and in vivo release behavior of the controlled-release device. If a desired drug concentration is found from antimicrobial tests, such simulation can provide a guidance for modifying the design of the device.
4.6. Antibacterial effect of the device The antibacterial effect of the controlled-release device was evaluated and is compared with other solutions in Table 2. In the table, the size of the bur used to remove the tissue from the root canals is an indication how deep the medicament has penetrated into the dentinal tubules and how effectively it has killed the bacteria. It is shown that no detectable turbidity is obtained from the samples that have been treated with the device. Though only two bur sizes were used to collect the dentine samples due to limited number of device available at that time, this preliminary test suggests that the device is superior to all the testing solutions. Surely, more experiments
are needed to establish right levels of CHX for killing the bacteria in root canals, from which optimal formulations can be developed to provide suitable release rate. This part of work is in progress.
5. Conclusions We have developed a controlled-release device for dental root canal therapy. The shape and the strength of the device is suitable for insertion into root canals of teeth. There is no sign of degradation of the device in the studied time periods (up to 40 days), so it is unlikely that residual pieces would be left in the root canal. The device with various formulations can provide short- and long-term release of antimicrobial agents such as CHX. A relatively steady in vitro release rate for over 40 days has been obtained using the formulation for long-term release. The result of an antimicrobial test using a bovine tooth model has indicated that the chlorhexidine-containing device appears to be an effective root canal medicament, superior to all the solutions tested. In addition to formulation, several key factors that influence release behavior of the device have been studied by in vitro release tests and modeling. The release rate of CHX is reduced in a smaller volume of liquid and in the absence of mixing. It is dependent on the type of release medium. A lower release rate in pH 7.4 buffer than that in water is probably caused by the lower solubility and the higher partition coefficient of CHX. Mathematical models have been developed for describing the in vitro and in vivo drug release from the cylindrical device into a liquid of limited volume with or without mixing. A moving boundary of a
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dispersed drug, a diffusion boundary layer, a timedependent boundary condition, and a concentrationdependent effective diffusion coefficient have been incorporated in the model to count the real situation in the course of drug release. The model-predicted in vitro release profiles agree well with the experimental data. The simulation result has predicted that an average 0.01 mg / day of CHX can be delivered for over 20 days in the cavity of a root canal using a device 1.2 cm in length and 0.035 cm in radius, loaded with |45% drug. The radius of the root canal has a negligible effect on the release rate. The amount of drug delivered to the canal can be tailored by changing the design parameters such as the thickness of the membrane coating.
Acknowledgements H.L. Wong is a recipient of MRC Summer Undergraduate Research Scholarship.
References [1] S. Friedman, in: D. Ørstavik, T.R. Pitt Ford (Eds.), Essential Endodontology, Blackwell Science, Oxford, UK, 1998, pp. 367–401. ¨ [2] U. Sjogren, D. Figdor, S. Persson, G. Sundqvist, Influence of infection at the time of root filling on the outcome of endodontic treatment of teeth with apical periodontitis, Int. Endod. J. 30 (1997) 297–306. ¨ [3] A. Bystrom, G. Sundqvist, Bacteriologic evaluation of the efficacy of mechanical root canal instrumentation in endodontic therapy, Scand. J. Dent. Res. 89 (1981) 321–328. ¨ [4] A. Bystrom, R. Claesson, G. Sundqvist, The antibacterial effect of camphorated paramonochlorophenol,camphorated phenol and calcium hydroxide in the treatment of infected root canals, Endod. Dent. Traumatol. 1 (1985) 170–175. [5] D. Ørstavik, M. Haapasalo, Disinfection by endodontic irrigants and dressings by experimentally infected dentinal tubules, Endod. Dent. Traumatol. 6 (1990) 142–149. [6] G. Sundqvist, D. Figdor, U. Sjogren, Microbiologic analysis of teeth with failed endodontic treatment and the outcome of conservative re-treatment, Oral Surg. Oral Med. Oral Pathol. Oral Radiol. Endod. 85 (1998) 86–93. [7] M. Haapasalo, D. Ørstavik, In-vitro infection and disinfection of dentinal tubules, J. Dent. Res. 66 (1987) 1375–1379. [8] S. Friedman, C.D. Torneck, R. Komorowski, Z. Ouzounian, P. Syrtash, A. Kaufman, In-vivo model for assessing the functional efficacy of endodontic filling materials and techniques, J. Endodon. 23 (1997) 557–561.
[9] K. Petersson, B. Lewin, J. Hakansson, B. Olsson, A. Wennberg, Endodontic status and suggested treatment in a population requiring substantial dental care, Endod. Dent. Traumatol. 5 (1989) 153–158. [10] P.J.M. Oosterwaal, F.H.M. Mikx, M.A. van’t Hof, H.H. Renggli, Short-term bactericidal activity of chlorhexidine gel, stannous fluoride gel and amine fluoride gel tested in periodontal pockets, J. Clin. Periodontol. 18 (1991) 97–100. [11] M.J.M. Schaeken, H.M.A.M. Keltjens, J.S. Van Der Hoeven, Effects of fluoride and chlorhexidine on the microflora of dental root surfaces and progression of root-surface caries, J. Dent. Res. 70 (1991) 150–153. [12] J.F. Siqueira, M. de Uzeda, Intracanal medicaments: evaluation of the antibacterial effects of chlorhexidine, metronidazole and calcium hydroxide associated with three vehicles, J. Endodon. 23 (1997) 167–169. [13] C.A.M. Barbosa, R.B. Goncalves, J.F. Siqueira, M. De Uzeda, Evaluation of the antibacterial activities of calcium hydroxide, chlorhexidine and camphorated paramonochlorophenol as intracanal medicament. A clinical and laboratory study, J. Endodon. 23 (1997) 297–300. [14] G.J. Parsons, S.S. Patterson, C.H. Miller, S. Katz, A.H. Kafrawy, C.W. Newton, Uptake and release of chlorhexidine by bovine pulp and dentin specimens and their subsequent acquisition of antibacterial properties, Oral Surg. 49 (1980) 455–459. [15] R.R. White, G.L. Hays, L.R. Janer, Residual antimicrobial activity after canal irrigation with chlorhexidine, J. Endodon. 23 (1997) 229–231. [16] R. Komorowski, S. Friedman, H. Grad, X.Y. Wu, Antimicrobial substantivity of chlorhexidine-treated bovine root dentin, J. Endodon. (in press). [17] M. Friedman, US Pat. No. 5,002,769. [18] I. Heling, M. Sommer, D. Steinberg, M. Friedman, M.N. Sela, Microbiological evaluation of the efficacy of chlorhexidine in a sustained-release device for dentine sterilization, Int. Endod. J. 25 (1992) 15–19. [19] I. Heling, D. Steinberg, S. Kenig, I. Gavrilovich, M.N. Sela, M. Friedman, Efficacy of a sustained-release device containing chlorhexidine and Ca(OH) 2 in preventing secondary infection of dentinal tubules, Int. Endod. J. 25 (1992) 20–24. [20] W.J. Loesche, US Pat. No. 4,568,535. [21] K.V. Roskos, B.K. Fritzinger, S. Ng, J. Heller, Development of a biodegradable poly(ortho ester) system for the treatment of periodontal disease, Proc. Int. Symp. Control. Release Bioact. Mater. 19 (1992) 337–338, and Refs. therein. [22] K.A. Gates, H. Grad, P. Birek, P.I. Lee, A new bioerodable polymer insert for the controlled release of metronidazole, Pharm. Res. 11 (1994) 1605–1609. [23] J. Huang, H.L. Wong, X.Y. Wu, H.A. Grad, R. Komorowski, S. Friedman, A device for controlled release of antibacterial drugs for dental root canal therapy, Proc. Int. Symp. Control. Release Bioact. Mater. 25 (1998) 778–779. [24] S. Friedman, H. Grad, J. Huang, X.Y. Wu, Patent Application. [25] X.Y. Wu, Y. Zhou, Finite element analysis of diffusional drug release from complex matrix systems. II. Factors influencing release kinetics, J. Control. Release 51 (1998) 57–72.
J. Huang et al. / Journal of Controlled Release 67 (2000) 293 – 307 [26] Y. Zhou, X.Y. Wu, Finite element analysis of diffusional drug release from complex matrix systems. I. Complex geometries and composite structures, J. Control. Release 49 (1997) 277–288. [27] X.Y. Wu, G. Eshun, Y. Zhou, Effect of interparticulate interaction on kinetics of drug release in microsphere ensembles, J. Pharm. Sci. 87 (1998) 586–593. [28] X.Y. Wu, Y. Zhou, Studies of diffusional release of a dispersed solute from polymeric matrices by finite element method, J. Pharm. Sci. 88 (1999) 1050–1057. [29] J. Crank, in: The Mathematics of Diffusion, 2nd Edition, Oxford University Press, London, 1975. [30] T.J. Roseman, W.I. Higuchi, Release of medroxyprogesterone acetate from a silicone polymer, J. Pharm. Sci. 59 (1970) 353–357.
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[31] L.T. Fan, S.K. Singh, in: Controlled Release: A Quantitative Treatment, Springer-Verlag, New York, 1989. [32] R.W. Baker, in: Controlled Release of Biologically Active Agents, Wiley, Toronto, 1989. [33] R.W. Baker, H.K. Lonsdale, Controlled release: mechanisms and rates, in: A.C. Tanquary, R.E. Lacey (Eds.), Controlled Release of Biologically Active Agents, Plenum, New York, 1974, pp. 15–71. [34] T. Higuchi, Mechanism of sustained-action medication, theoretical analysis of rate of release of solid drugs dispersed in solid matrices, J. Pharm. Sci. 52 (1963) 1145–1149. [35] R. Siegel, Modeling of drug release from porous polymers, in: M. Rosoff (Ed.), Controlled Release of Drugs, Polymers and Aggregates, VCH, Weinheim, 1989, pp. 1–51.
In vitro studies and modeling of a controlled-release device for root canal therapy a a a a, b b J. Huang , H.-L. Wong , Y. Zhou , X.Y. Wu *, H. Grad , R. Komorowski , S. Friedman b a
Faculty of Pharmacy, University of Toronto, Toronto, Canada M5 S 2 S2 Faculty of Dentistry, University of Toronto, Toronto, Canada M5 S 2 S2
b
Received 21 October 1999; accepted 26 January 2000
Abstract Endodontic disease is caused primarily by bacteria that interact with periradicular host tissues. Therefore, treatment of endodontic disease aims at the exclusion of bacteria from the root canal system. This work focused on in vitro studies and modeling of a controlled-release device for delivering antimicrobial agents in root canals. A cylindrical, needle-shaped device was prepared consisting of a matrix core and a polymer coating, loaded with 30–45% chlorhexidine (CHX). The composition of the core, a blend of water-permeable polymers, and the thickness of the coating were tailored to impart various release rates. A relatively steady release rate for over 40 days after an initial burst was achieved using a formulation for long-term release, which is desirable for establishing and maintaining the necessary therapeutic levels. Mathematical models were developed for both in vitro and in vivo drug release into a liquid of limited volume, taking into account a moving boundary of the dispersed drug and a time-dependent boundary condition. A concentration-dependent effective diffusion coefficient was used to count increased porosity as the solid drug had dissolved. The finite element method and computer programs were applied to solve the differential equations and predict the in vitro and in vivo release kinetics. The model prediction agreed well with the in vitro experimental data and provided guidance for designing the device for in vivo release in root canals. The result of in vitro antimicrobial tests, performed using a bovine tooth model, suggested that the device was effective in reducing growth of microbes. 2000 Elsevier Science B.V. All rights reserved. Keywords: Controlled-release device; Dental root canal; Antimicrobial; Modeling; Finite element method; Moving boundary; In vitro and simulated in vivo
1. Introduction Endodontic disease, such as pulpitis or periradicular periodontitis, is caused by infection or inflamma*Corresponding author. 19 Russell Street, Toronto, Ontario, Canada M5S 2S2. Tel.: 11-416-978-5272; fax: 11-416-9788511. E-mail address: [email protected] (X.Y. Wu)
tion of the dental pulp tissue and the bone supporting the tooth, which are affected by oral microorganisms invading the tooth. It is a very common occurrence that affects 70% of the population in countries with well-developed dental care modes, and by estimate, over 95% of the population in other parts of the world; and it is one of the major causes of tooth loss in these populations. Endodontic disease is an all-inclusive term for a
0168-3659 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0168-3659( 00 )00225-X
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variety of clinical conditions that are forms of either pulpitis or periradicular periodontitis. Pulpitis is an inflammation of the dental pulp that can be induced by mechanical, physical or microbial stimuli. If the stimulus is not eliminated in the early stage of pulpitis, the disease process will escalate beyond potential repair, leading to pulpal necrosis. Frequently at this stage, oral microorganisms infect the necrotic pulp and the pulp space inside the tooth, i.e., the pulp chamber and root canals. The bacteria in the root canal can further cause the development of periradicular periodontitis, an infective disease in the bone supporting the tooth. Symptoms that may be encountered in the various stages of the disease process frequently lead to the loss of the affected tooth. Untreated or intractable root canal infection may also lead to tooth loss. Periradicular periodontitis can be treated by debridement of the infected pulp tissue and disinfection of the root canal by a combination of three modes: (a) debriding the pulpal tissue and enlarging the root canal; (b) flushing the canal to kill microorganisms using antimicrobial irrigating solutions, mainly sodium hypochlorite; and (c) killing surviving microorganisms by applying antimicrobial medicaments to the root canal between consecutive treatment sessions. Such treatment is effective and results in complete healing of the diseased sites in 46–93% of the cases [1], yet up to 54% treatment failures are observed attributable to residual root canal infection [2]. This is because root canal microorganisms can persist mainly by residing in root canal irregularities and dentinal tubules, where they may be inaccessible to the files, irrigants, and conventional medicaments [2,3]. Most available root canal medicaments, such as camphorated parachlorphenol or iodine potassium iodide, are bactericidal. However, they are effective for only a few hours. After they have expired, microorganisms can repopulate the root canal [4]. Another commonly used medicament, calcium hydroxide, though it remains bioactive for weeks [4], is not very effective against specific enteric bacteria [5] that are frequently associated with failures of root canal treatment [6]. Also the ability of calcium hydroxide to affect microorganisms harbored in the dentinal tubules is questionable [7–9]. In contrast,
chlorhexidine effectively eliminates oral microorganisms when it is applied to treat gum disease [10,11] and its antimicrobial efficacy equals that of the conventional root canal medicaments [12,13]. Unlike the other medicaments, chlorhexidine binds to the dentin and thus induces substantive antimicrobial activity of the dentin surface [14]. Such activity can be obtained by irrigating the root canal with chlorhexidine [15]. Nevertheless, to resist re-infection, the canal has to be exposed to chlorhexidine for longer times, preferably 1 week [16]. In addition, for patients who may miss a scheduled revisiting time, an even longer time period of drug exposure is required in order to protect the canal from reinfection. Hence, a major therapeutic goal is to develop a vehicle to deliver chlorhexidine to root canals for extended periods of time. Sustained-release devices have been developed by several groups for treatment of periodontal disease [17–22]. It has been demonstrated that a biodegradable device containing chlorhexidine is more effective than calcium hydroxide in disinfection of root canal dentine in bovine teeth [17–19]. However, these devices were prepared for periodontal application and thus may not be suitable for root canal application. Firstly, unlike periodontal pocket, the fluid present in root canals is minimal, which may be insufficient to cause drug release by degradation or diffusion. Secondly, in the case of a degradable polymer as the carrier, the device may not be completely degraded when it is time to permanently fill the root canal. The remaining fragments may interfere with permanent filling and sealing of the root canal, resulting in leakage and thus ingress of bacteria. Consequently, infection of the filled root canal, constituting treatment failure, may occur [9]. Thirdly, owing to the size and shape of root canals, the materials and formulations useful for periodontal application may not warrant mechanical strength of the needle-shaped device for insertion into root canals. In addition to the aforementioned concerns about root canal device, delivering chlorhexidine is another challenge. Because of a strong, positive charge of chlorhexidine and its consequent binding capability, polymers used for delivery other antimicrobial agents such as metronidazole become unsuitable for chlor-
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hexidine. For example, cellulose acetate phthalate, used for sustained release of metronidazole, strongly binds with chlorhexidine, resulting in undetectable release of chlorhexidine (X.Y. Wu, H. Grad, P.I. Lee, unpublished data). Besides, chlorhexidine is incompatible with many pharmaceutical excipients such as dibutyl phthalate, which are commonly used to plasticize the polymers. These characteristics of chlorhexidine make it difficult to formulate a delivery composition for chlorhexidine. Our group has developed a non-degradable and retrievable device for sustained release of therapeutic agents in dental root canals [23,24]. To design suitable formulations for delivering sufficient medicament in the small cavity of root canals for days or weeks, extensive experimental tests and sophisticated computer modeling are needed. In this work, fundamental properties of chlorhexidine were characterized, including its solubility, partition between the polymers and the media, and permeability through the polymers. In vitro release kinetics was studied in various media of different volumes. Shortterm test (about 1 day) was conducted in a larger volume of liquid with stirring, simulating the extreme of high release rate. Long-term test (.40 days) was carried out in small vials without mixing, where the release medium was changed daily. The long-term test was designed to mimick in vivo condition with possible drug loss by tissue binding, drug absorption, or leaking through the temporary sealing. The antimicrobial efficacy of the device was assessed using in vitro bovine tooth model [16], and compared with conventional disinfection solutions. Mathematical models were developed to describe the kinetics of drug release in vitro and in vivo taking into consideration a moving boundary of the dispersed drug in a liquid of limited volume and a time-dependent boundary condition. The kinetics of drug release in root canals was predicted by computer simulation using the finite element method.
2. Experimental section
2.1. Preparation of the device The devices, with dimensions suitable for insertion
295
in dental root canals, e.g., 0.6–0.8 mm in diameter and 11–18 mm in length, were prepared using waterpermeable polymers such as ethyl cellulose and antibacterial agents such as chlorhexidine (CHX) and its salts [23,24]. In a typical preparation, chlorhexidine acetate (Wiler Fine Chemicals, Ontario, Canada) was dissolved or dispersed in a 10% ethyl cellulose (Dow Chemicals) solution in alcohol. Most of the solvent in the mixture was evaporated at room temperature in a fumehood, and the remaining gellike mixture was used to form the needle-like device. The device was then completely dried in a mold at room temperature. Four different formulations were prepared with different drug loading and drug release mechanisms. In formulation 1 (F1), the initial chlorhexidine concentration was 30%, no coating was applied. In formulation 2 (F2), the drug loading was |45%, and the device was coated with 10% ethyl cellulose solution. Formulation 3 (F3) was similar to F2 except for the addition of other components. Formulation 4 (F4) was also similar to F2 but with thicker coating. The thickness of the coating was evaluated based on mass balance before and after the coating, dimension of the device, and density of the polymer membrane.
2.2. Determination of solubility, partition coefficient and permeability Solubility of chlorhexidine in water or pH 7.4 buffer at 378C was determined using equilibrium solution method. Various amounts of solid drug were added to a known volume of liquid in different vials. The vials were incubated in a water bath at 378C for 2 days with stirring. After equilibration, i.e., no more drug could be dissolved, the drug concentration in the solution was assayed by UV-vis spectrophotometry following appropriate dilution. A known amount (e.g., 0.75 g) of polymer sheets was immersed in either water or pH 7.4 buffer (0.05 M) with different drug concentrations at 378C for at least 5 days. The remaining drug in the solution was then analyzed by spectrophotometry. The concentration of the drug in the polymer was calculated from mass balance and then plotted against drug concentration in the solution. The partition coeffi-
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cient of CHX between the polymer and the liquid was determined from the slope of the plot by linear regression. The permeability of CHX through the polymers was measured using side-by-side diffusion cells with a water jacket. The polymer membranes, prepared by casting polymer solutions in alcohol in glass rings, were mounted between the donor cell and the receptor cell. The concentration in the receptor cell was monitored by spectrophotometry. The permeability, P, defined as a product of partition coefficient, K, and diffusion coefficient, D, was evaluated from the slope of the plot of the amount of drug permeated versus time at the steady state.
2.3. In vitro release test 2.3.1. Short-term drug release test Each device was immersed into 3.0 ml of 0.05 M pH 7.4 buffer solution in a cuvette at 378C with vigorous stirring. The amount of drug released into the solution was continuously monitored with a diode array spectrophotometer (Hewlett-Packard 8452A) at 256 nm. The measurement lasted for more than 20 h, with a sampling interval of 10 min. 2.3.2. Long-term drug release test Each device was placed in 0.35 ml of deionized water at 378C without stirring in a small glass vial. At every 24 h, the drug concentration in the medium was determined by spectrophotometry after appropriate dilution. The device was immediately patted dry, and transferred into fresh water in a clean vial, followed by subsequent release test.
2.4. Antibacterial tests Haapasalo and Ørstavik’s method [7] was modified to prepare bovine tooth model for the antibacterial tests. The root segment was cut into 5-mm thick discs with a rotating diamond saw. Each disc had an external diameter of approximately 7 mm. The canals of the discs were enlarged with an ISO 033 round bur, to standardize the internal diameter. Absence of smear layer was confirmed by examination of a control disc with scanning electron microscopy. The discs were sterilized separately by autoclaving three times in test tubes containing brain heart infusion (BHI) broth for 30 min at 1218C. The discs were then coated with nail varnish on the outer surfaces, and mounted with sticky wax at the bottom of petri dishes. Two sets of tests were carried out to evaluate (1) conventional irrigation process in endodontic practice and (2) sustained exposure of various disinfectants.
2.5. Irrigation test Ten ml of testing solution were applied to the canal for 5 min and the excess amount of the solution was removed. A suspension of E. faecalis (ATCC 29212) in BHI broth was then introduced to the canal, and a fresh innoculum was added every other day.
2.6. Immersion test The discs were immersed in the testing solutions presented in Table 1 and thus the canals were filled by the solutions entirely. The discs were then left to stand for 7 days at 378C in air. At the end of the
Table 1 Conditions for irrigation and immersion tests using bovine root canal model Test
Irrigation
Group 1 Group 2
With sterile saline With 5.25% sodium hypochlorite With 0.2% chlorhexidine
Group 3
Immersion Group 4 Group 5
In 0.2% chlorhexidine In sterile saline
Group 6
In 5.25% sodium hypochlorite In water with insertion of the controlled-release device in the canal
Group 7
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testing time, sterile round burs, ISO sizes 035, 037, 040 and 042 were sequentially used to enlarge the canals of the discs. The dentine powder obtained with each bur was collected in separate test tubes containing 3 ml of sterile BHI broth, and incubated for 24 h at 378C in air. The optical density of the broth, proportional to the number of bacteria present, was then measured by a spectrophotometer at 540 nm. The mean optical density and the standard deviation were calculated for each group and statistically analyzed using Student’s t-test.
3. Theoretical section
3.1. General model The needle-shaped device, with a length to diameter ratio over 20, can be considered as a long cylinder where drug release from its two ends is negligible [25]. The device consists of a matrix core and a membrane coating. The drug is released from the device into a liquid of limited volume. The structure of the device and the definitions of various regions are schematically presented in Fig. 1a–c. Fig. 1a illustrates in vitro drug release into a wellstirred medium with a boundary layer resistance. In the figure, j is the moving boundary of the dispersed drug, R and R m are, respectively, the radius of the matrix core and that of the device; h m and h b denote the thickness of the membrane coating and that of the diffusion boundary layer, respectively; C1 , C2 , C3 , and C4 stand for the drug concentrations in four different regions, i.e., the matrix core, the membrane, the diffusion boundary layer, and the bulk liquid. The drug release is assumed to be diffusion controlled. Hence a diffusion model can be used with consideration of a moving boundary of the dispersed drug and a variable boundary condition owing to drug release into a finite liquid volume [25–28]. The governing equation of diffusion for an axisymmetrical, one-dimensional cylinder is given as follows [29],
S
≠C 1 ≠ ≠C ] 5 ] ] rD ] ≠t r ≠r ≠r
D
(1)
where r denotes the radial distance of the cylinder, D
Fig. 1. Schematic illustration of the structure of the device, a boundary layer, a moving boundary of a dispersed drug, and concentration profile of the drug. (a) In vitro release in a liquid of finite volume with mixing; (b) in vitro release in a liquid of finite volume without mixing; and (c) in vivo release in a root canal with drug removal.
and C are the diffusion coefficient (cm 2 / s) and solute concentration (g / cm 3 ), respectively. Eq. (1) and the following initial and boundary conditions are applicable to all three cases studied, i.e., in vitro release with mixing, in vitro release in a daily-changed medium with no stirring, and in vivo release.
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298
C1 5 C10
in the core, t 5 0
(2)
C2 5 C20
in the membrane, t 5 0
(3)
C30 5 C40 5 0 in the boundary layer and bulk liquid, t 5 0
(4)
≠C1 dj (C10 2 Cs )] 5 D1 ]] dt ≠r
(5)
C1 5 Cs
on j , 0 , t , t*
on j , 0 , t # t*
(6)
where C10 , C20 , C30 and C40 are the initial drug loading (g / cm 3 ) in the aforementioned four regions, respectively; Cs is the drug solubility in the polymer; D1 is the diffusion coefficient of the drug in the device; and t* is the time required for all the dispersed drug to dissolve. Furthermore, the drug concentration in the membrane and the liquid is linked by the following interfacial boundary conditions: ≠C2 ≠C3 D2 ]] 5 D3 ]] ≠r ≠r C2 5 KC3
on R m
t.0
t.0
on R m,
(7) (8)
where K is the partition coefficient of the drug between the polymer phase and the liquid. Because of the different external conditions in three different cases, additional boundary and / or initial conditions are needed, which are presented in the following section.
3.2. Additional initial and boundary conditions 3.2.1. In vitro release in a finite well-mixed liquid For in vitro release in a finite liquid volume with mixing, the whole system including the device and the liquid is a closed system. This means that there is no mass transport beyond the boundary, R s , ≠C ]]4 5 0 on R s ≠r
t$0
(9)
where Vb is the volume of the bulk liquid and S is the surface area of the cylinder at R b .
3.2.2. In vitro release with daily-changed medium The model for in vitro release in a non-mixed medium is portrayed in Fig. 1b, where the definitions of the parameters are the same as those in Fig. 1a. Please note that a boundary layer is absent in Fig. 1b since the entire liquid is assumed to be stagnant, though the boundary condition for the system remains: ≠C ]]3 5 0, on R s ≠r
t$0
(11)
When the release medium is replaced by a fresh, drug-free liquid after the release has proceeded for a time interval, t9 (e.g., 24 h), the initial condition for the medium is reapplied, C3 5 0, t 5 mt9, m 5 1, 2, 3, . . .
(12)
A non-uniform drug profile in the device is carried over from the previous release period and used as the initial condition for the device.
3.2.3. In vivo release in a root canal During in vivo release in a root canal, some of drug may be removed from the cavity due to tissue binding, drug absorption, or leaking from dentinal tubules or temporary sealing. Such an in vivo condition is taken into account by applying another layer outside the boundary, R s . Drug permeates through this layer with a permeability, P (P5DK), into the body fluid with a zero drug concentration and is then carried away by the fluid (see Fig. 1c). It is assumed that the drug permeation is governed by passive transport, i.e., diffusion. Hence, the diffusion equation such as Eq. (1) and corresponding initial and boundary conditions presented in Section 3.1 are applicable, yet a sink condition is added for the body fluid (see Fig. 1c), C 5 0, t $ 0
(13)
As depicted by Fig. 1a, drug concentration in the finite, well-mixed liquid is uniform and can be derived from mass conservation [28,29],
3.3. Treatment of moving boundary of the dispersed drug
≠C4 ≠C3 Vb ]] 5 2 SD3 ]] ≠t ≠r
To include the condition of moving boundary of the dispersed drug (Eqs. (5)–(6)) in the program, the
t.0
(10)
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entire polymer region was divided into many thin layers. The drug was allowed to diffuse out initially in the outermost thin layer, where the drug concentration was examined frequently using an iteration checking subroutine. Once the excess amount of solute, (C10 –Cs )d x, had been depleted, i.e., C1 5Cs in the current layer, the solute diffusion in the next thin layer was initiated. Such a procedure was repeated until all the dispersed drug dissolved. The finite element method was used to solve the diffusion equations with the initial and boundary conditions presented above. Computer programs and computational procedures from our previous work [25–28] were modified and used to obtain numerical solutions.
4. Results and discussion
4.1. Morphology of the device Fig. 2 is the microscopic photograph of a device (F2) before (a) and after (b) a long-term release in water at 378C for 40 days. It is seen that the device maintains the shape although it becomes more porous. This observation suggests that the device
299
unlikely disintegrates or ruptures during release, and it is mechanical stable. Such stability makes it possible to retrieve the device after its insertion in a canal for days or even weeks. Moreover, the obvious porous structure after CHX has been consumed (Fig. 2b) implies that the effective diffusion coefficient of CHX in the device may increase in the region where the solid drug has been exhausted.
4.2. Partition coefficient, diffusion coefficient, and solubility of CHX To ensure the incubation time for determination of CHX partition is sufficient to reach equilibrium, the reduction of CHX concentration in the solution was monitored by spectrophotometry. Fig. 3 shows the fraction of CHX remaining versus time reaches a plateau after about 3 days. Therefore, the polymer sheets were incubated with drug solutions for more than 5 days. To confirm that the reduction in CHX concentration is not due to drug adsorption onto the glass vials during incubation, the drug concentration in the solution in the absence of polymer was assayed after incubation for the same time periods. The change in drug concentration was found to be negligible.
Fig. 2. Microscopic photograph of a device (F2) at the initial state (a) and after a long-term release test in water at 378C for 40 days (b).
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responsible for the high partition of CHX in the polymer phase. The solubility of CHX in the polymer phase was computed from the above data using Cs 5KCsolution . It was 8.5 and 1.6 mg / ml for water and pH 7.4 buffer, respectively. The permeability of CHX through the polymer membrane was determined to be 4.660.94310 211 cm 2 / s, from which the diffusion coefficient of CHX in the polymer phase was evaluated to be 1.5360.17310 210 cm 2 / s.
4.3. Release kinetics and mechanism
Fig. 3. Fraction of CHX remained in the solution versus time indicating dynamic absorption of CHX into polymer sheets.
Fig. 4 is a typical plot of CHX concentration in the polymer phase versus that in the solution used to calculate partition coefficient. A linear relationship is seen in the studied concentration range. The partition coefficient of CHX was determined to be 0.47 in water and 11.4 in pH 7.4 buffer (0.05 M), indicating a strong medium-dependence of partition. Similarly, the solubility of CHX in liquid, Csolution , also varies with the type of medium. It was 18.4 mg / ml in water and 0.14 mg / ml in pH 7.4 buffer (0.05 M) at 378C. The low solubility in the buffer is very likely
Fig. 4. Equilibrium CHX concentration in polymer phase versus that in water at 378C.
The results of short-term drug release from three devices with different formulations into pH 7.4 buffer (0.05 M) are shown in Fig. 5. For device F1, with no coating, the drug release is very fast; within 2 h, the UV absorbance of the drug solution is out of the measurable range of the instrument. In contrast, the drug release for device F2 and F3 is in a more controlled manner. After an initial burst in the first 2 h, the drug release reaches a nearly constant rate. As shown by the result of the long-term release test in Fig. 6, device F1 has released most of its payload within 10 days with a quick reduction in the release rate. Device F4, with a thick coating, provides a low release rate. This formulation may be suitable for long-term applications. However, its antibacterial effectiveness needs to be verified by
Fig. 5. The short-term release profiles of CHX from three devices with different formulations: F1, with no coating; F2, with coating; F3, with coating and other components. The experiments were carried out in 3 ml of pH 7.4 buffer (0.05 M) at 378C with mixing.
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Fig. 6. The long-term release profiles of CHX from devices with four different formulations: F1–F3 (see Fig. 5) and F4, with thick coating. The experiments were carried out in 0.35 ml of water at 378C with no mixing. The release medium was replaced by fresh water daily.
further investigation. CHX release from devices F2 and F3 appears to follow a similar pattern, i.e., a steady release rate following an initial burst. Especially for device F3, the steady release lasts about 30 days. Such a release pattern seems more desirable because the initial burst is beneficial to establishing an effective drug level in the solution; and the following slow but steady release is appropriate for maintaining the drug concentration at the therapeutic level. Therefore, more studies were carried out on the performance of devices F2 and F3. As mentioned above, the device is of a cylindrical geometry with a high drug loading (C10 4Cs ). In this case, the dispersed drug diffuses out from the cylindrical matrix, and thus a nonlinear release profile should be expected [28–30]. This release profile deviates from the present experimental observation, i.e., a relatively constant release rate following the initial burst. On the other hand, if membrane coating is a limiting barrier to the diffusion, a lag time instead of a burst should be observed [29,31,32]. Normally, an initial burst implies migration of the drug from the reservoir to the membrane. Therefore, we believe that, in our case, extraction of CHX from the core to the membrane in the coating process may take place, because of its relatively high solubility in ethanol (6.7%). Moreover, drug diffusion through the membrane coating may become the
301
Fig. 7. Effect of release medium on the release profiles of F2. The experiments were conducted in 3 ml of water or pH 7.4 buffer (0.05 M) at 378C with mixing.
limiting step at a later stage, so the release rate becomes rather constant. The partially membranecontrolled mechanism is also supported by the huge difference in the release rate between the coated (F2–F4) and uncoated device (F1), which is particularly obvious in Fig. 5.
4.4. Effect of release medium As presented above, the solubility and partition of CHX depend on the type of medium strongly. This dependence, in fact, affects release kinetics of CHX appreciably as evidenced by the in vitro data in Fig. 7. The release rate of CHX is much lower in pH 7.4 buffer than that in water. This kinetic behavior can be explained by theoretical [29] and numerical models [26]. It has been demonstrated that a higher partition in the polymer and / or a lower solubility in the liquid contribute to reduction in release rate [26,29]. We also observed, in the short-term tests in pH 7.4 buffer, acceleration in drug release after the release medium had been replaced by a fresh one. However, no change in the release rate was detected in the case of water. This result suggests that CHX solubility plays an important role in the release kinetics.
4.5. Model prediction Although experiments, such as that in a small vial
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with daily changed medium, were very carefully designed to gather kinetic data of release, these in vitro data are still not representative of in vivo situation. This is because, on one hand, the liquid volume in human dental root canals is much smaller even as compared to the smallest scale in our in vitro experimental setting. On the other hand, continuously taking samples from small cavities of root canal models and analyzing drug concentration in the fluid are very difficult, considering that the diameter of human root canals is in the vicinity of 0.1 cm and the average diameter of the device is |0.07 cm. Therefore, prediction of in vivo release behavior by mathematical modeling and computer simulation becomes indispensable, especially in the later stage of the development before any further pursuit of clinical trials. On the basis of our previous work [23–28], current experimental observation, and good understanding of the delivery system, mathematical models have been derived (see Section 3). Most of the parameters used in the model computation, such as partition coefficient, drug solubility, and diffusion coefficient in the polymer were determined by experiments (see Section 4.2). The thickness of the membrane coating, h m , in device F2 and F3 was evaluated to be 1.84310 23 cm. A concentrationdependent effective diffusion coefficient in the matrix core was applied, i.e., a higher D value in the layers with C1 #Cs than that in the layers containing the solid drug. This approach was taken based on our observation that pores were generated after the solid drug had been exhausted (see Section 4.1), and the concept that the effective diffusion coefficient (Deff ) can be related to porosity, ´, and tortuosity, t, by [26,31–35]
´ Deff 5 D0 ] t
C1 # Cs
(14)
where D0 is the drug diffusion coefficient in the liquid. In the absence of actual values of ´ and t, a factor less than one may be used in the place of ´ /t [26,35]. The values of Deff in the porous region, diffusion coefficient in the liquid, and boundary layer thickness were estimated by model-fitting of the in vitro experimental data.
4.5.1. Comparison of model prediction and in vitro experimental data To validate the model, computational procedures and programs, and to estimate the model parameters, the numerical solutions were compared with the experimental data from both long- and short-term release tests. 4.5.1.1. Long-term release in water. As mentioned above, the long-term release tests were conducted in 0.35 ml of water without mixing with the release medium being changed daily. The renewal of the medium was treated in the computation by reapplying the initial conditions (see Section 3.2.2). The following parameters were used in the computation: the diffusion coefficient in the membrane and in the core matrix before the solid drug was exhausted, D1 5D2 52.1310 210 cm 2 / s; the effective diffusion coefficient in the core matrix after the solid drug was exhausted, Deff 51310 27 cm 2 / s; the diffusion coefficient in the liquid, D3 51310 25 cm 2 / s; the partition coefficient between the polymer phase and water, K50.47; drug solubility in the polymer, Cs 5 8.5 mg / cm 3 ; the initial drug concentration in the polymer, C10 5440 mg / cm 3 , C20 550 mg / cm 3 ; the radius of the device, R m 50.035 cm; and the thickness of the membrane coating, h m 51.84310 23 cm. The values of D1 , D2 , K, Cs , C10 , R m , and h m were determined experimentally (see Section 4.2), and D3 , Deff , and C20 were estimated by model fitting. Fig. 8a shows that the release profile predicted by the model agrees well with the experimental data. 4.5.1.2. Short-term release in buffer. The short-term release was conducted in 3 ml of medium with mixing. In this case, a well-mixed environmental condition was applied and drug transport in the liquid beyond the boundary layer was due to convection rather than diffusion. The parameters used in the computation of drug release into pH 7.4 buffer (0.05 M) were as follows: the diffusion coefficient in the polymer phase, D1 5 D2 5 1.53 3 10 210 cm 2 / s, Deff 51310 27 cm 2 / s; the diffusion coefficient in the boundary layer, D3 5 1 3 10 25 cm 2 / s; the partition coefficient, K511.4; the drug solubility in the polymer, Cs 51.6 mg / cm 3 ; the initial drug concentration, C10 5440 mg / cm 3 , C20 550 mg / cm 3 ; the
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in the models and computational programs and procedures, we then moved to our ultimate goal of the modeling part of this work, i.e., the modeling and prediction of release kinetics of the device in root canals.
4.5.2. Prediction of release kinetics in root canals Before further pursuit of clinical trials, it is necessary to predict possible in vivo performance of the device, i.e., the dose it can deliver in root canals. As presented in Section 3.2.3. and Fig. 1c, drug removal by either tissue adsorption / absorption or leaking was considered by assuming drug permeation through a hypothetical layer. In the computation, the following parameters were used: the drug permeability, P51310 23 cm 2 / s; the length of the device and the canal, L51.2 cm; and the radius of the canal, r50.05 or 0.1 cm. While the device parameters were kept the same as those in preceding computation, the physicochemical and kinetic parameters for the buffer solution were used: K511.4, Cs 51.6 mg / cm 3 , D1 5D2 51.53310 210 cm 2 / s, Deff 51310 27 cm 2 / s, and D3 51310 25 cm 2 / s.
Fig. 8. Comparison of model-predicted release profile of F2 with that measured by experiment. (a) Long-term release in 0.35 ml of water with the medium being changed daily and (b) Short-term release in 3 ml of pH 7.4 buffer with mixing.
radius of the device, R m 50.035 cm; the membrane 23 thickness, h m 51.84310 cm; and the thickness of the diffusion boundary layer, h b 50.02 cm. The values of D1 , D2 , K, Cs , C10 , R m , and h m were determined by experiments (see Section 4.2), and D3 , Deff , C20 , and h b were estimated by model fitting. Fig. 8b illustrates that the release kinetics for the device in the buffer solution predicted by the model matches the experimental data well. The above results have not only confirmed that the model is mechanistically correct in describing the release kinetics of the device, but also validated the computational procedures. Having gained confidence
4.5.2.1. Comparison of in vivo release with in vitro release. The simulated in vivo release profiles are presented in Fig. 9 together with the in vitro experimental data from a long-term test (curve A in Fig. 9a) and a short-term test (top curve in Fig. 9b). Apparently, the in vivo release (curve C in Fig. 9a and bottom curve in Fig. 9b) is much slower than the in vitro ones, mainly because of the difference in the release environment. As discussed previously, the liquid volume in root canals is much smaller than that in the in vitro tests. As a consequence, drug accumulation in the liquid is much more severe, thus hindering the drug release. With consideration of the effect of the length of the device, curve B in Fig. 9a was obtained using the same length as that in the in vitro experiment, i.e., 1.8 cm. It is seen that the in vivo release rate is still much lower than the in vitro one. About 0.047 mg / day (day 1)–0.01 mg / day (day 25) of CHX is released from the device into the root canal, as compared with that in vitro (e.g., over 0.05 mg / day even at day 25). However, due to a small volume of liquid, e.g., 0.0048 ml for a root canal
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4.5.2.2. Investigation of factors influencing in vivo release kinetics. The in vivo release kinetics can be affected by environmental conditions or by changing the design parameters such as drug loading, membrane thickness and permeability, and matrix composition. Here we studied, by computer simulation, two factors that could influence the in vivo release rate. Since the size of canals may vary with the type of tooth and the filing depth, we computed the release profiles of device F2 with a length of 1.2 cm in two root canals, one with a radius of 0.05 cm and the other 0.1 cm. Fig. 10 shows that as the canal radius is doubled, that is, the liquid volume increases
Fig. 9. Comparison of model-predicted in vivo release profiles with in vitro data determined by experiment at 378C. (a) Longterm release. Curve A, in vitro release in 0.35 ml of water with daily-changed medium; curves B and C, simulated in vivo release in pH 7.4 buffer. (b) Short-term release in pH 7.4 buffer. Top curve, in vitro experimental data; and bottom curve, simulated in vivo data. The device is 0.035 cm in radius and 1.8 cm (curves A and B) and 1.2 cm (curve C) in length. The radius of the root canal is assumed to be 0.05 cm.
0.05 cm in radius and 1.2 cm in length (note that the volume of the device has been subtracted), the drug concentration in the canal could reach 26 mg / ml in 5 days. The in vivo drug concentration can be higher if a drug solution is introduced to the canal prior to the insertion of the device. Whether this concentration range is effective in killing the bacteria will be answered by further antimicrobial tests and clinical trials.
Fig. 10. The effect of membrane thickness and canal radius on the in vivo release kinetics of the device. The device is 0.035 cm in radius and 1.2 cm in length. The radius of the root canal is assumed to be 0.05 or 0.1 cm. The thickness of the membrane coating, h m 51.84310 23 cm or 0.92310 23 cm.
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Table 2 Turbidity of the broth as an indication of E. Faecalis concentration (n510 for Groups 1–6, n52 for Group 7) Group
1 2 3 4 5 6 7
Bur size (mm) 0.35
0.37
0.40
0.42
0.7260.12 0.6460.13 0.6560.16 0.01160.003 0.5360.09 0.6960.25 –
0.7660.07 0.6660.10 0.6260.07 0.01560.005 0.6960.14 0.5960.17 Not detectable
0.7660.10 0.6560.09 0.6960.08 0.00960.005 0.7760.16 0.6660.21 Not detectable
0.8460.06 0.7360.10 0.7160.08 0.009660.005 0.6760.21 1.0660.21 –
6.9 times, the change in release kinetics is negligible. This means that the device with the present design may be applied to large or small canals without need of significant modification, though the drug concentration in the cavity may be lower in a larger canal. If a higher or lower release rate is desired, we can vary the thickness of coating, which has been demonstrated by experiment (Fig. 6). In the modeling, we simulated the release behavior of two devices with coating thickness, h m 51.84310 23 and 0.92310 23 cm, respectively. The amount of drug delivered at the steady state is about 20% larger when a coating of a half thickness is applied. The above examples have demonstrated that the model simulation can predict in vitro and in vivo release behavior of the controlled-release device. If a desired drug concentration is found from antimicrobial tests, such simulation can provide a guidance for modifying the design of the device.
4.6. Antibacterial effect of the device The antibacterial effect of the controlled-release device was evaluated and is compared with other solutions in Table 2. In the table, the size of the bur used to remove the tissue from the root canals is an indication how deep the medicament has penetrated into the dentinal tubules and how effectively it has killed the bacteria. It is shown that no detectable turbidity is obtained from the samples that have been treated with the device. Though only two bur sizes were used to collect the dentine samples due to limited number of device available at that time, this preliminary test suggests that the device is superior to all the testing solutions. Surely, more experiments
are needed to establish right levels of CHX for killing the bacteria in root canals, from which optimal formulations can be developed to provide suitable release rate. This part of work is in progress.
5. Conclusions We have developed a controlled-release device for dental root canal therapy. The shape and the strength of the device is suitable for insertion into root canals of teeth. There is no sign of degradation of the device in the studied time periods (up to 40 days), so it is unlikely that residual pieces would be left in the root canal. The device with various formulations can provide short- and long-term release of antimicrobial agents such as CHX. A relatively steady in vitro release rate for over 40 days has been obtained using the formulation for long-term release. The result of an antimicrobial test using a bovine tooth model has indicated that the chlorhexidine-containing device appears to be an effective root canal medicament, superior to all the solutions tested. In addition to formulation, several key factors that influence release behavior of the device have been studied by in vitro release tests and modeling. The release rate of CHX is reduced in a smaller volume of liquid and in the absence of mixing. It is dependent on the type of release medium. A lower release rate in pH 7.4 buffer than that in water is probably caused by the lower solubility and the higher partition coefficient of CHX. Mathematical models have been developed for describing the in vitro and in vivo drug release from the cylindrical device into a liquid of limited volume with or without mixing. A moving boundary of a
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dispersed drug, a diffusion boundary layer, a timedependent boundary condition, and a concentrationdependent effective diffusion coefficient have been incorporated in the model to count the real situation in the course of drug release. The model-predicted in vitro release profiles agree well with the experimental data. The simulation result has predicted that an average 0.01 mg / day of CHX can be delivered for over 20 days in the cavity of a root canal using a device 1.2 cm in length and 0.035 cm in radius, loaded with |45% drug. The radius of the root canal has a negligible effect on the release rate. The amount of drug delivered to the canal can be tailored by changing the design parameters such as the thickness of the membrane coating.
Acknowledgements H.L. Wong is a recipient of MRC Summer Undergraduate Research Scholarship.
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