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Optical imaging of radiolabeled drugs in tissue sections using the microImager
h [electronic resource] /
by Paul Dungel.
[Tampa, Fla] :
b University of South Florida,
ABSTRACT: The MicroImager is a fast, high resolution, real time, digital autoradiographic imaging tool with broad applications. This study utilizes the MicroImager to evaluate radiolabeled drug behavior in subcutaneous tissue. Experiments were conducted in conjunction with mathematical models to determine the diffusion coefficient (D) and elimination constant (k) for radiolabeled dexamethasone. Osmotic pumps containing [3H]dexamethasone were implanted into rat subcutaneous tissue over 6h, 24 h, and 60 h. Local tissue was explanted and slides were prepared for imaging. The MicroImager was then used to quantify the local concentration of 3H-dexamethasone in the tissue surrounding the tip of the osmotic pump. Betavision+ software was used to obtain local concentration profiles. These were then compared to a mathematical model to determine the diffusion coefficient and elimination constant for the radiolabeled drug. The diffusion coefficient for dexamethasone in rat subcutaneous tissue is 4.11 ¨ 1.77 x 10-10 m2/s. The elimination constant is 3.65 ¨ 2.24 x 10-5 s-1.A similar experiment was conducted to determine the diffusion coefficient through different means. [3H]dexamethasone was injected into the rat subcutaneous tissue for a 2.5 min and a 20 min period. A different mathematical model was applied and the diffusion coefficient was found to be 4.01 ¨ 2.01 x 10-10 m2/s.
Thesis (M.S.B.E. )--University of South Florida, 2006.
Includes bibliographical references.
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Adviser: Yvonne Moussy, Ph.D.
x Biomedical Engineering
t USF Electronic Theses and Dissertations.
Optical Imaging of Radiolabeled Drugs in Tissue Sections Using the MicroImager by Paul Dungel A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Biomedical Engineering Department of Chemical Engineering College of Engineering University of South Florida Major Professor: Y vonne Moussy, Ph.D. Francis Moussy, Ph.D. Mark Jaroszeski, Ph.D. Date of Approval: November 1, 2006 Keywords: autoradiography, dexamethasone, diffusion, subcutaneous tissue, tritium Copyright 2006, Paul Dungel
Acknowledgments I would like to thank and acknowledge Yvonne Moussy, Ph.D. for her encouragement and dedication to this project. I would also like to thank Lawrence Hersh, Ph.D. for his assistance in the mathematical modeling involve d in this research. Finally, I would like to thank my colleagues in the Biosensors and Biomaterials Labor atory and all others around the university for their s upport over the past two years.
i Table of Contents List of Tables iii List of Figures iv Abstract vi Chapter One MicroImager 1 Background of Radioimaging 1 Radiation 2 Emulsion Film Autoradiography 2 Phosphor Imaging 2 MicroImager Information 3 Operating Principles 3 Hardware Components of MicroImager 5 Scintillating Sheet 5 Image Intensifier Tube 5 CCD Camera 6 Software Components of MicroImager 6 Grid ROI 8 Circle ROI 8 Line Profile 9 Tracing 9 Previous Applications 10 Our Applications 11 Chapter Two Distribution of [3H]Dexamethasone in Rat Subcutaneous Tissue after Delivery from Osmotic Pumps 12 Introduction 12 Materials and Methods 13 Materials 13 Preparation of Osmotic Pumps 14 Subcutaneous Implantation 14 Autoradiographic Imaging and Analysis 15 Mathematical Model 16 Results 20 Discussion 24
ii Chapter Three Diffusion of [3H]Dexamethasone in Rat Subcutaneous Slices after Injection Measured by Digital Autoradiography 29 Introduction 29 Materials and Methods 29 Materials 29 Subcutaneous Injection 30 Autoradiographic Imaging and Analysis 30 Mathematical Model 31 Results 34 Discussion 36 Chapter Four Summary and Future Work 41 MicroImager 41 Osmotic Pump 41 Injection Study 42 Possible Future Work 42 References 43
iii List of Tables Table 1. Estimated D and k 21 Table 2. Penetration distan ce of radioactivity from th e tip of the catheter 23 Table 3. Diffusion coefficients for dexamethasone in various media 25 Table 4. Elimination constants of vari ous agents in subcutaneous tissue 26 Table 5. Estimated diffusion coefficient 36
iv List of Figures Figure 1. MicroImager with associated PC 3 Figure 2. Scintillating sheet on slide 5 Figure 3. The original autoradiogram of [3H]dexamethasone as acquired by the MicroImager (left) and the same image with a psuedocolor LUT applied (right) 7 Figure 4. Grid overlay on autoradiogram 8 Figure 5. Circle ROI overlay on autoradiogram 8 Figure 6. Line Profile on autoradiogram 9 Figure 7. An optical image of rat subcutaneous tissue (left) and the [3H]dexamethasone autoradiogram (right) with a ma nual trace of the optical image 10 Figure 8. Concentration versus dist ance profiles obtained by solving the transient diffusion and eliminati on equation (eq 3) for various times until steady state is reached are shown 18 Figure 9. Autoradiographic image from rat subcutaneous tissue obtained using the MicroImager after implantation of an osmotic pump containing [3H]dexamethasone for 6 hrs 20 Figure 10. Typical concentra tion profiles in the vicinity of the catheter tip at (a) 6 hr, (b) 24 hr and (c) 60 hr after implantation 22 Figure 11. A typical H&E steaned ti ssue section from our study 27 Figure 12. Concentration profiles for di ffusion when a concentrated bolus of solute is deposited within a small region 33 Figure 13. Image a shows a typical auto radiographic image obtained using the MicroImager 157 s after injection of [3H]dexamethasone 35
v Figure 14. Typical number of events ve rsus distance profiles obtained using the MicroImager at (a) 157 s and (b) 20 min after implantation 35 Figure 15. Concentration profiles at th e tail-end at (a) 157 s and (b) 20 min after injection. Data from only one angle per time period is shown 38
vi Optical Imaging of Radiolabeled Drugs in Tissue Sections Using the MicroImager Paul Dungel ABSTRACT The MicroImager is a fast, high resoluti on, real time, digital autoradiographic imaging tool with broad applications. This study utilizes the Micr oImager to evaluate radiolabeled drug behavior in subcutaneous tissue. Experiments were conducted in conjunction with mathematical models to determine the diffusion coefficient (D) and elimination constant (k) for radiolabeled dexamethasone. Osmotic pumps containing [3H]dexamethasone were implanted into rat subcutaneous tissue over 6h, 24 h, and 60 h. Lo cal tissue was explanted and slides were prepared for imaging. The MicroImager was then used to quantify the local concentration of 3H-dexamethasone in the tissue surr ounding the tip of the osmotic pump. Betavision+ software was used to obtain local concentration profiles. These were then compared to a mathematical model to determine the diffusion coefficient and elimination constant for the radiolabeled drug. The di ffusion coefficient for dexamethasone in rat subcutaneous tissue is 4.11 1.77 x 10-10 m2/s. The elimination constant is 3.65 2.24 x 10-5 s-1. A similar experiment was conducted to determine the diffusion coefficient through different means. [3H]dexamethasone was injected into the rat subcutaneous
vii tissue for a 2.5 min and a 20 min period. A di fferent mathematical model was applied and the diffusion coefficient was found to be 4.01 2.01 x 10-10 m2/s.
1 Chapter One MicroImager Background of Radioimaging The use of radioactive is otopes to investigate biologi cal phenomenon is important for several reasons. Radioactive tracers are in corporated into the s ubstance being studied and rarely inhibit the molecules motion or bi nding characteristics. Also, degradation of the signal does not decrease over time when us ing an appropriate isot ope. This provides for long term storage and analysis without loss of data. This valuable tool in contemporary medicine had its beginnings over 80 years ago. Autoradiography was first applied to systemic biolog ical investigation in 1924 by Lacassagne (1). Using photographic emulsions, Lacassagne studied Polonium distribution in tissues. Photographic emulsions have been used to ev aluate the presence and location of radiation in tissues ever since. Radiation Elements (Hydrogen, Carbon, Iodine, etc) can exist naturally as unstable isotopes of stable atoms. They can regain their stability by emitting energy in the form of radiation. This radiation can have different forms and different ener gies. Alpha, gamma, and beta radiation have differe nt characteristics and are associated with specific decay activities (2).
2 Alpha decay occurs when an alpha particle is emitted from the nucleus of an atom. An alpha particle is defined as 4 2He. Gamma radiation has no mass and is capable of the greatest penetrative distance. This type of radiation is co mmonly used in X-ray imaging. Beta radiation can have two forms. A particle is an electron while a + particle is a positron. Each of these has a mass 1/1840 that of a proton. If a particle is emitted from the nucleus, the transforma tion that occurs is that a ne utron changes to an electron and a proton. On the other hand, if a + particle is emitted, a proton splits into a positron and a neutron. The type of decay that occurs is dependant on the sp ecific element (2). Tritium, the radiolabel used in my experiments, emits particles that are then detected and analyzed. Emulsion Film Autoradiography The traditional method for visualizing ra diation has been photographic emulsions. A photographic emulsion incorporates Silver Bromide (AgBr) crys tals in a gelatin suspension. Upon exposure of the emulsion to a radioactive sample, areas of the crystal that are irradiated undergo a transformation. The free electron ( particle) oxidized the silver and creates metallic silver at these locations. After the latent image is processed, the results can be visualized. This proce ss can be time consuming and cumbersome (3). Phosphor Imaging Another modality has been developed th at operates similarly to emulsion film autoradiography. A sheet with a coating of excitable phosphor crystals is placed atop the sample. Upon exposure, low energy electron-ho le pairs are created by the interaction of
3 the phosphor with the incident radiation. Most recombine and luminescence can be observed locally. However, some of the new electrons become trapped and do not recombine. Upon stimulation with a He-Ne (re d) laser, these trappe d electrons are freed and find available holes. This creates a violet glow that is observed using fiberoptics. The signal from this system is then amp lified by a photomultiplier and then digitized using a scanner (4). Upon review, Kamarain en et al. (2006) found that compared to photostimulated luminescence, film autoradiography requires more time for optimizing, preparing, and analyzing film s because of poor sensitivity and low linearity (5). MicroImager Information Operating Principles Figure 1. MicroImager with associated PC
4 The recently developed MicroImager builds on previously developed imaging technology. As the MicroImager is fully digital, no film or phosphor screen is necessary. The sample is placed on a slide and covered with a thin sheet of scintillating paper. This paper converts beta particles to photons. These photons are amplified in an Image Intensifier Tube and enter a CCD Camera. Th e computer then assimilates the data into an observable image that is displayed to the user. This system has several advantages over traditional imaging modalities. Digital st orage of data is more compact, easier to transport, and easier to view than photogr aphic film or phosphor screens. The highresolution (~20m) and high speed of data acquisition (on the order of hours) is advantageous compared to previous tec hnology. Additionally, this system can be automated to process up to four samples in one run. High throughput data analysis is valuable because it provides the investigat or with time to focus on other tasks while acquiring important data. The MicroImager also has the unprecedente d ability to distinguish two different isotopes in one sample. If isotopes emitting radiation at different energy levels are used (i.e. 3H and 14C), the software can differentiate betw een the two. Each beta particle will have a different size light spot on the sc reen dependant on its energy. After user standards are prepared, the software can dete rmine the source of each spot and assign it to a specific isotope. This can not be done using film emulsions or phosphor imaging.
5 Hardware Components of MicroImager Scintillating Sheet A small, thin sheet of scintillating pape r is placed over the sample in order to properly image the sample. The MicroImage r employs scintillati ng sheets made of SiY2O5 due to its desired properties (6). The 10 micron thick sheet transforms beta decay from the sample into photons that then m ove through the image intensifier tube (IIT) on the way to the CCD camera. Image Intensifier Tube After the photons are rel eased from the scintillating sheet, they enter the image intensifier tube. This double microchannel plate tube is an optoelectronic device that amplifies the intensity of the incoming light by a factor of 30000 (6). The amplified image is then transferred to a phosphor sc reen that is lined with an 800 Angstrom aluminized layer. This creates a polarizing current that is picked up by the CCD camera. Figure 2. Scintilla ting sheet on slide
6 CCD Camera The Charge Coupled Device (CCD) Camera incorporated into the MicroImager has a 576 x 384 pixel screen to in tegrate incident light. The matrix structure of the CCD camera allows high speed, high resolution images to be acquired. An optical spot is detected by the CCD and then analyzed by an imbedded chip to determine the spots center of gravity (7). This enables the Micr oImager to have a spatial resolution of 15-20 m. The digital signal created is displayed on the PC screen and can then be processed using Betavision+ software. Software Components of MicroImager The images acquired with the MicroImager can then be processed using a dedicated software package called Beta Vision+ This software has broad applications for data analysis and visual interpretation. Quantification of the data can be conducte d in various ways. The final image is a composite of acquisitions done at numerous tim e points. One can view the entire set of data, or observe only a specific time segment of the acquisition. For example, if the sample was run for 10 hours, one can observe the final image with 10 hours of decay events. On the other hand, one can view th e first or last 3 hours of acquisitions. Furthermore, one can observe the middle 5 hours of acquisition. This feature can be valuable for several reasons. Fi rst, if decay events should remain constant over time, this can be confirmed by comparing initial acquisiti on with final acquisition. Secondly, if the radioactive tracer used has a short half-life, one can run the sample and observe the decrease in decay over time. This method en ables one to focus on data based on the time
7 it was obtained. In addition to the temporal distribution, more important data analysis is conducted on the spatial dist ribution of the signal. There are several different tools availabl e in Beta Vision+ to aid in spatial analysis of the image. Th e image of the decay events is acquired using a monochrome camera, yielding a black and white image. Th e intensity of different locations can be difficult to observe in grayscale images, so pseudocolor can be a pplied using a preset look-up-table (LUT) or a custom LUT. The rang e of this scale can be adjusted per user inputs. Additionally, there are many other processing and quantit ative tools available in the Beta Vision+ software. Among those that wi ll be discussed are the Grid ROI, Circle ROI, Line Profile tool and other tracing tools. Figure 3. The original autoradiogram of [3H]dexamethasone as acquired by the MicroImager (left) and the same image w ith a psuedocolor LUT applied (right). The image on the right more clearl y shows the variation in intensity
8 Grid ROI The Grid Region of Interest (ROI) tool is useful to iteratively analyze a region of the image. After clicking on the Grid ROI icon, the user can input the number of rows and columns desired in the rectangular region. Then, using the mouse, one can draw a grid on the desired area of the image. After this, the Result Viewer can be enabled to display information about each grid square. The data displaye d includes the area of each grid and counts within each gridsquare. This data can be exported to othe r programs such as Excel or Matlab for further analysis. Circle ROI The Circle Region of Interest (ROI) tool can also be used to gather data in specific locations on the image. Several Circle ROIs can be made to radiate from a central point. This is convenient wh en investigating the radial symmetry of the radioactive tracer. The data attained from i ndividual Circle ROIs can be exported to Excel and processed further. Figure 4. Grid overlay on autoradiogram Figure 5. Circle ROI overlay on autoradiogram
9 Line Profile Linear characterization of counts can be done using the Line Profile Tool. Upon clicking on the Line Profile tool icon, the user can draw a line of desired length along the image and obtain counts information along this line. The Beta Vision + software measures the counts within a 1 mm width at 0.02 mm intervals along the drawn line. Altern atively, there is another tool available which will measure the counts along a line. This PolyLine tool, how ever, allows the user to adjust the width of the area being analyzed. These line profile tools are useful for investigating linear distribution of isotope in the sample. Tracing Spatial correspondence to the actual sample is important in order to determine the validity of the data. An optical image can be acquired either prior to, or after radioimaging. This is done by shining an LED light on the sample to obtain an optical density image of the sample. This image is spatially aligned with the autoradiogram because they are both acquired with the sa me camera without moving the stage or the slide. With the standard package Betavision+ software, one can not directly overlay an optical image with an autoradiographic image. However, using the tracing tools in the measurement toolbar, one can correlate the tw o images. One can trace an ouline of the Figure 6. Line Profile on autoradiogram
10 optical image in one window and then unlink the trace. After this, one can select the autoradiograph, and the trace will transfer to the other image and be spatially representative of the sample in this image. This is essential for determining the location of isotope in a tissue sample. Previous Applications The MicroImager is a versatile imaging modality that has been used for a wide array of investigations. Salin et al. (2000) has used the MicroImager to quantitatively analyze the expression of two mR NA species using double isotope in situ hybridization (8). They labeled one oligonucleotide with 3H and another with 35S. Their results indicate the MicroImager is capable of accu rately discriminating between two different isotopes when used to investigate mRNA expression. In a different study, Salin et al. (2002) applied the MicroImager to conduct a microarray investigation using 3H and 35S. This study confirmed the high dynamic range and high resolution of the MicroImager are idea l for high density microarray analysis (9). Figure 7. An optical image of rat subcutaneous tissue (left) and the [3H]dexamethasone autoradiogram (right) with a manual trace of the optical image
11 Our Applications The investigations conducted in this study evaluate tr ansport characteristics of [3H]dexamethasone in rat subcutaneous tissu e. Several experiments were done to determine the elimination constant and diffusi on coefficient of dexamethasone in tissue. Different methods were investig ated that can be applied to different tissue types in the future. The high speed and high resolution of the MicroImager were critical for the success of these investigations.
12 Chapter Two Distribution of [3H]Dexamethasone in Rat Subcutaneous Tissue After Delivery from Osmotic Pumps Introduction Several recent reports suggest that controlled local re lease of dexamethasone may be useful for preventing inflammation around an implantable glucos e sensor (10-12). This decrease in inflammation is expected to increase glucose sensor function and lifetime. Local drug delivery may be achie ved using biodegradable polymer implants (13), hydrogels (14) and osmotic pumps (15) Local delivery of dexamethasone would permit high interstitial drug c oncentrations at the site of glucose sensor implantation without producing high sy stemic drug levels. For successful local treatment, dexameth asone must be released and penetrate through the tissue surrounding the implan ted glucose sensor. Additionally, the concentration of dexamethas one in the subcutaneous ti ssue surrounding th e implanted glucose sensor must be high enough to prevent inflammation to an imp lant. In a previous study using dexamethasone to suppress inflamma tion to an implant, local distribution of the drug in subcutaneous tissue was not de termined (10). Although dexamethasone is a commonly used anti-inflammatory agent, its lo cal concentration, diffu sion coefficient and rate of elimination have not been reported following subcutan eous release. The ability of dexamethasone to penetrate subcutaneous tissue can be measured and quantified by
13 comparison to mathematical models (13). This method allows a reliable estimate of the drug concentration in the tissue near the implanted glucose sensor. Experiments were set up to examine the controlled delivery of dexamethasone in normal rat subcutaneous tissue in order to develop a funda mental understanding of how the drug is transported in the subcutaneous tissue. Because the efficacy of controlled interstitial delivery depends on the distance the drug can penetrate into the tissue surrounding the implantabl e glucose sensor, [3H]dexamethasone was delivered from osmotic pumps that were implanted into the subcutaneous tissue of rats. Digital autoradiographic imaging was used to quantify the spatial distribution of radioactivity in the subcutaneous tissue at 6 hr, 24 hr and 60 hr after subcutaneous implantation. We investigated both the extent of penetration of dexamethasone and the effectiveness of simple transport models for quantification of penetration. From this quantification, the diffusion coefficient of dexamethasone in subcutaneous tis sue and the rate of elimination of dexamethasone from the subc utaneous tissue were determ ined. This information is necessary for the future de velopment of an optimal local delivery system of dexamethasone to reduce the inflammatory re sponse and enhance in vivo sensor function and lifetime. Materials and Methods Materials [3H]dexamethasone (392.46 MW), specifically [1,2,4,6,7-3H]dexamethasone, was obtained from Amersham Biosciences Corp. (Piscataway, NJ). The specific activity
14 was 88.0 Ci/mmol. Alzet osmotic pumps (1003D model) were obtained from Durect Corp. (Cupertino, CA). Preparation of Osmotic Pumps A solution of [3H]dexamethasone and sterile 0.9% (w/v) saline was loaded into the osmotic pumps (total volume 114 l) using the protocol provided by the manufacturer. Each pump cont ained a total activity of 127 Ci. The pumps provided a controlled delivery at a rate of 1.0 L/hr. To prevent the pump from causing a tissue reaction at the site of drug delivery, drug de livery was achieved via a 4 cm length of polyethylene tubing connected to the body of the pump. Subcutaneous Implantation Six male Sprague Dawley rats (Harlan, Indianapolis, IN, 375-399 g) were used for our studies. The rats were initially anesthetized by plac ing each rat in an induction chamber filled with a 5% mix ture of isoflurane in oxygen. During surgery anesthetization of the rats was maintained using a 2.5% mixture of isoflurane in oxygen. Two pumps containing radiolabeled dexameth asone were implanted subcutan eously on either side of the shoulders of the rat. A 3-4 cm incisi on was made between th e shoulder blades. A hemostat was inserted into the incision on the lateral aspect. By opening and closing the jaws of the hemostat a pocket in the subcut aneous tissue just larg e enough for the pump was created. A tunnel to inse rt the tubing was made using a blunt probe. Excess bleeding was removed with sterile cotton gauze. Th e osmotic pump was implanted tubing end first. The wound was closed with 4-6 surgical staples.
15 Two rats were euthanized at 6 hr, 24 hr, and 60 hr after implantation using CO2. The tissue around the tip of the catheter was removed, quickly frozen on dry ice and stored at -80 C to immobilize the tracers within th e tissue sample. The frozen tissue samples were mounted on a cryostat chuck and cut in 10 m sections. Sections taken at every 200 m were used for autoradiographic imaging. In addition, sections 50 m from those sections used for autoradiographic im aging were collected for hematoxylin-eosin (H&E) staining. All animal experiments were performed under the approval of the University of South Florida Animal Care and Use Program. Autoradiographic Imaging and Analysis Autoradiographic images of the tissue s ections were obtained using a recently developed real-time digital radioactivity-d etection system, the MicroImager (Biospace Mesures, Paris, France) (16, 17). With the MicroImager, acquisiti on of events can be visualized in real-time on a monitor screen. Each event is individually analyzed by the computer. An event is a radioactivity decay event (16). The acquisition of events need only proceed for as long as is necess ary to obtain a good image. In our case, autoradiographic images with between 380,715 to 686,390 events were acquired over 24 to 45 hours to obtain good images. An optical image of the same tissue sample using the MicroImager was also obtained. The spatial variation in drug concen tration from the osmotic pumps was quantified in the following way. The areas of subcutaneous tissue were identified on the optical image and then superimposed ont o the corresponding au toradiographic image.
16 The concentration profiles in the subcutane ous tissue surrounding the catheter tip were determined directly from the autoradiographic images using Beta Vision+ software (Biospace Mesures, Paris, France). A line prof ile tool (1 mm wide) was used from the center of the catheter tip to th e periphery of the subcutaneous tissue to obta in a number of events versus distance profile. The background number of events wa s subtracted from the number of events acquired. A number of events versus distance prof iles were performed at 15 increments around the catheter tip on each section selected for analysis. The number of events at the catheter tip opening was calibrated to the known concentration of the agent in the pump to obtain concentration versus distance profiles at 6 hr, 24 hr and 60 hr after implantation. Mathematical Model The concentration profiles of [3H]dexamethasone obtained using the MicroImager were compared to a mathematical model of drug diffusion and el imination. The model assumed: 1) constant drug con centration at the catheter tip/ti ssue interface; 2) first-order elimination of drug; 3) isot ropic diffusional tr ansport of drug thr ough the subcutaneous tissue; 4) negligible fluid convection; and 5) spherical symmetr y. The governing equation for the diffusion and elimination of a drug in subcutaneous tissue is: kC r C r r C D t C 22 2 (eq 1) where C is the concentration of the drug in the subcutaneous tissu e, D is the diffusion coefficient of the drug in subcutaneous tissue, r is the radial distan ce from the center of the catheter tip, k is the first-order el imination constant for the drug from the
17 subcutaneous tissue and t is the time after implantati on. The boundary and initial conditions are: C = 0 at t = 0; r a C = C0 at t > 0; r = a (eq 2) C = 0 at t > 0; r where a is the radius of the catheter and C0 is the concentration at the catheter tip. The solution of eq 1 using the boundary and in itial conditions of eq 2 is (22): kt Dt a r erfc D k a r kt Dt a r erfc D k a r r a C C 2 ) ( exp 2 ) ( exp 20 (eq 3) Assuming steady state, and applying the two boundary conditions from eq 2, eq 1 can be solved using a series solution. Alternativel y, the steady state solution can also be found from eq 3 by applying the limit t : D k a r r a C C ) ( exp0 (eq 4) The Brownian diffusion coefficient for dexamethasone in water was estimated from the Stokes-Einstein equation: A sN r T D 6 (eq 5) where rs = 0.657 M1/3 [x10-10 m] is the equivalent spheri cal solute radius, M is the molecular weight of de xamethasone (392.46 MW), is the ideal gas constant 8.314 JK-1mol-1, T is temperature, dynamic viscosity and NA is Avogadros number. The calculated diffusion constant of dexamethasone in water at 37C is D = 6.82x10-10 m2/s. The Stokes-Einstein equation underpredicts th e actual diffusion coefficient for small
18solutes of molecular weight less than seve ral hundred, and overpr edicts it for large solutes of molecular weight grea ter than several thousand (19). Measured concentration profiles for [3H]dexamethasone at t = 6 hrs, t = 24 hrs and t = 60 hrs were compared to the transi ent equation (eq 3). T ypical concentration profiles predicted by eq 3 for two values of for various times are shown in figures 8a and 8b. The dimensionless parameter where = D k a /, is analogous to the Thiele Figure 8. Concentration versus distance profiles obtained by so lving the transient diffusion and elimination equation (eq 3) for various times until steady state is reached are shown. Panels a and b demons trate the dependence of the penetration depth with the modulus = k/D a. Panel a ( = 0.2) has a larger penetration depth than panel b ( = 1)
19modulus obtained in analysis of heterogeneous catalysis (13) and is a predictor of the extent of drug penetration from the catheter tip. The radius of the catheter was approxima ted at 0.6 mm. Values for D and k were found in the following manner. First, initia l estimates for D and k were found. For the initial estimate of D, the diffusion constant for dexamethasone in water was used, D = 6.82x10-10 m2/s. This D was used in the steady-stat e solution of the diffusion equation (eq 4) to find an initial estimate for k. k was found by using the Marquardt-Levenberg technique (20) with two inde pendent variables, k and C0, to minimize the residual of the sum-squared-error between the predicted and experimental concentr ations. Second, these initial estimates for the k and D values were then used as the starting points for the Marquardt-Levenberg algorithm using the tran sient equation (eq 3) with the k, D, and C0 being the three independent variables over wh ich the residual of th e sum-squared-error between the predicted and experimental concen trations was to be minimized. The initial value for C0 was always the maximum concentrati on in the measured data set. The Marquardt-Levenberg algorithm effici ently searched over the k, D, and C0 space to find the point which best fits the data (21). This technique was repeated to find k and D for 6 hr, 24 hr, and 60 hr. For each of these time s, the calculations were repeated for the autoradiographic scans at various angles The Marquardt-Leve nberg algorithm was written in MATLAB.
20Results Radiolabeled dexamethasone spread through the subcutaneous tissue after implantation of the osmotic pu mp (fig. 9). The local concen tration of drug within the tissue was quantified from the autoradiographi c images using the Beta Vision+ software. The Beta Vision+ software was used to cons truct the number of even ts as a function of distance profiles. An event is a radioactivity decay event (16). The number of events was greatest at the tip of the catheter. A high num ber of events on the autoradiographic image represents a high drug concentr ation. The number of events at the tip of the catheter can be calibrated to the known c oncentration in the pump. Hence, the local concentration of the drug in the subcutaneous tissue su rrounding the catheter can be estimated by comparing the local number of events to the number of events at the catheter tip. In general, at distances more than a few millimeters from the catheter tip, the radioactivity was not significantly different from background. Figure 9 is representative of the autoradiographic images obtained using the MicroImager after implantation of the osmotic pumps for 6 hr, 24 hr, or 60 hr. Figure 9. Autoradiographic image from rat subcutaneous tissue obtaine d using the MicroImager after implantation of an osmotic pump containing [3H]dexamethasone for 6 hrs. The location and direction of the catheter tip is shown by the arrow. Each red dot represents a radioactivity decay event. Lighter shades indicate higher activity. The bar represents a distance of 1 mm.
21Concentration profiles obtained from the autoradiographic images of the subcutaneous tissue surrounding the catheter tip were examined and compared to the mathematical model of diffusion and first-orde r elimination to find th e best estimates for D and k. The best estimates obtained for D and k are given in Table 1. A single-factor analysis of variance (ANOVA) indicated that there was no significant difference between the 6 hr and 24 hr data for k (p > 0.05) or for D (p > 0.05). There was not enough data at 60 hr for comparison. The average, based on the 6 hr, 24 hr and 60 hr data, for the diffusion coefficient is D = 4.11 1.77 x10-10 m2/s and for the elimination constant is k = 3.65 2.24 x10-5 s-1. Table 1. Estimated D and k The diffusion coefficient and eliminati on constant was determined by fitting a model of diffusion and elimination to the con centration profiles measured near the tip of a catheter attached to an osmotic pump. Time after implantation n k [1/s] x 10-5 D [m2/s] x 10-10 6 hr 5 4.80 2.56 3.63 1.06 24 hr 6 2.52 1.65 4.92 1.97 60 hra 1 4.70 1.73 a Only one scan was suitable for analysis in this case, as th e subcutaneous tissue was very thin, allowing measurement wit hout boundary effects only in one case. To quantify differences in drug penetrat ion with time after release from the osmotic pump, the best fit con centration profiles were used to find the distance where the local concentration drops to 10% of its maximum value (figs. 10a, b, c). For the 6 hr case,
22the majority of the drug was c onfined to a region within 2.22 0.42 mm from the tip of the catheter (table 2). For th e 24 and 60 hr cases, the majority of the drug was confined to a region within 2.70 0.38 mm and 1.80 mm from the tip of the catheter, respectively. The penetration distance of [3H]dexamethasone increased from 6 hr to 24 hr, but decreased from 24 hr to 60 hr. Figure 10. Typical concentration profiles in the vicinity of the catheter tip at (a) 6 hr, (b) 24 hr and (c) 60 hr after im plantation. Data from only one angle per time period is shown. Combining data from all. 9 other scans would make the figure unreadable. The solid lines show the transient diffusion and elimination model (which reduces to th e steady state model as t) in which k, D and C0 was varied to minimize the residual of the sum-squarederror between the predicted and experimental values. The ordinate represents the location of catheter tip/tissue interface
23Table 2. Penetration distance of radio activity from the tip of the catheter The penetration distance is the distance where the local concentration drops to 10% of the concentration at the catheter tip. Th is radial distance wa s found using the best fit curve through the data and corr esponds to the location where C/C0 = 0.1. The dimensionless parameter, = D k a /, determines the extent of drug penetration and was found using the corresponding k and D values in Table 1. Time after implantation Penetration Distance [mm] = D k a / 6 hr 2.220.42 0.22 24 hr 2.700.38 0.14 60 hr 1.80a 0.31 a See note on table 1. Discussion Radiolabeled dexamethasone was introdu ced into the subcutaneous tissue by implantation of osmotic pumps. There was cons tant delivery of the agent from the pump via an attached catheter. High concentrations of the agent were located near the tip of the catheter. The local distributi on of the agent in the subc utaneous tissue surrounding the catheter tip was measured and analyzed. Th e distribution of the agent within the subcutaneous tissue near the catheter tip was consistent with the mathematical model of diffusion and first-order eli mination (figs. 10a, b, c). The mathematical model was compared to the experimental data in order to obtain valu es for the diffusion coefficient D, and the elimination constant k at 6 hr 24 hr and 60 hr after implantation. The experiment was terminated at the end of 60 hr as the concentration profile reached steady state at 60 hr (fig. 8a) (f urther discussion below).
24The diffusion coefficient, D, of dexameth asone in subcutaneous tissue at 6 hr and 24 hr after implantation was 3.63 1.06 x10-10 m2/s and 4.92 1.97 x10-10 m2/s, respectively. The 60 hr data suggests a D of 1.73 x10-10 m2/s. There was no significant difference between the 6 hr and 24 hr data fo r D (p > 0.05). A comparison with the 60 hr data was not made as the sample size was too small. Even tho ugh the concentration profile at 6 hr has not yet reached steady st ate (fig. 8a), the valu e found for D should not be different from that found for the 24 hr case which is ve ry close to steady state. (Note that at 6 hr, = 0.22 (table 2) and fig. 8a s hows concentration profiles for = 0.2 for various times.) The concentra tion profile at 60 hr has reac hed steady state (fig. 8a). D should have similar values at 6 hr, 24 hr a nd 60 hr because the best estimate for D and k for all cases was achieved usi ng the transient diffusion and elimination equation (eq 3). Since the transient equation takes time into acco unt, be it for a shor t time period or for a long time period, the D and k va lues for the same agent in the same tissue should be the same. D and k are assumed to be constants. As time becomes large, the transient equation (eq 3) reduces to the steady equation (eq 4). Hence, the average diffusion coefficient D = 4.11 1.77 x10-10 m2/s based on the 6 hr, 24 hr and 60 hr data, results in a reasonable value for dexamethasone in subcutaneous tissue. The diffusion coefficient of dexamethasone in subcutaneous tissue is slight ly less than in water but slightly greater than in brain tissue (table 3). Our diffu sion coefficient for de xamethasone in rat subcutaneous tissue is slightly greater than th e diffusion coefficient of sodium fluorescein (molecular weight 376) in ra t subcutaneous tissue D = 2.35 0.24 x 10-10 m2/s (24). Sodium fluorescein has a simi lar molecular weight as dexa methasone (molecular weight 392).
25Table 3. Diffusion coefficients fo r dexamethasone in various media The diffusion coefficient of dexamethasone in subcutaneous tissue was compared to the diffusion coefficient for dexamethas one in other media from the literature. Medium D [m2/s] Reference water 6.82 x 10-10 Stokes-Einstein equation subcutaneous tissue 4.111.77 x 10-10 This study brain tissue 2.0 x 10-10 Saltzman and Radomsky, 1991 (22) cellulose acetate membrane 3.15 x 10-11 a Barry and Brace, 1977 (23) a Interpolated for 37C The elimination constant, k, at 6 hr and 24 hr was 4.80 2.56 x10-5 s-1 and 2.52 1.65 x10-5 s-1, respectively. The 60 hr data suggests a k of 4.70 x10-5 s-1. There was no significant difference between the 6 hr and 24 hr data for k (p > 0.05). A comparison with the 60 hr data was not made as the sample size was too small. The average, based on the 6 hr, 24 hr and 60 hr data, for th e elimination constant is k = 3.65 2.24 x10-5 s-1. This value is quite reasonable despite the fact that the 6 hr case has not yet reached steady state for the reasons given in the paragraph above. Table 4 shows values for k of other agents in subcutaneous tissue. Our elimin ation constant for dexamethasone in rat subcutaneous tissue is slightly greater th an that of dexamethasone in rat brain k = 1.19 x 10-5 s-1 (26). Although only two rats were used for each time point, we did not observe any variation between the two rats as they were the same age, sex, size, and strain and were all from the same vendor. A deta iled study would be useful to demonstrate that the age, sex, size, strain and vendor ha ve no significant effect on the values of D and k. However, this extensive work is beyond the scope of this paper.
26Table 4. Elimination constants of vari ous agents in s ubcutaneous tissue The elimination constant of dexamethasone in subcutaneous tissue was compared to the elimination constant of other agents in subcutaneous tissue from the literature. Agent k [1/s] Reference RSAa 6.421.19 x 10-5 Kim and Burgess (2002) (16) Dexamethasone 3.652.24 x10-5 This study VEGFb 3.501.03 x 10-5 Kim and Burgess (2002) (16) a rat serum albumin b vascular endotheli al growth factor Dexamethasone penetrated an average distance of 2.22 0.42 mm at 6 hr, 2.70 0.38 mm at 24 hr and 1.80 mm at 60 hr into the subcutaneous tissu e near the implant (table 2). The difference between the penetration distances at 6 hr and 24 hr is most likely due to the fact that at 6 hr steady state has not yet been re ached and hence, the furthest extent of drug penetration has not yet been reached (fig. 8a). The reduction in penetration distance at 60 hr compared to that at 24 hr may be explained from an analysis of the H&E stained slides. Histopathological evaluation of the slides revealed that there were more inflammatory cells at 60 hr than for 24 hr after implantation. It s hould be noted that the actual amount of [3H]dexamethsone used for this study was very small. This amount of [3H]dexamethasone after 60 hr of delivery resu lted in slightly less than the maximum amount of radioactivity allowed in an anima l for normal disposal. This small amount of dexamethasone would not have had a significa nt effect on the number of inflammatory cells. The number of inflammatory cells may ha ve affected the transp ort characteristics. Kim et al. (25) also sugges ted that the bodys in flammatory response to local delivery devices located at a subcutaneous site may complicate drug release.
27The average based on the average values for D and k, is = 0.18. Since D and k values for the same agent in the same tissue are assumed to be constants, then = D k a / must also be a constant. Although the modulus determines the extent of drug penetration, the penetr ation distance for a given may be different at different times (figs. 8a, b). The maximum exte nt of drug penetration is no t reached until steady state is reached. At times prior to steady state, the pe netration distance is less then maximum. In general, the penetrati on distance increases as decreases (figs. 8a, b) because the rate of diffusion is greater than the ra te of elimination. The modulus is useful in predicting the extent of drug penetration between different drugs at steady state. The model also assumed isotropic diffusional transport of drug through the subcutaneous tissue. Figure 11 shows a typical H&E stained tissue se ction from our study. The subcutaneous tissue was homogeneous. Hence, the assumption that the tissue would be isotropic for diffusi onal transport seems reasonable. Our model of drug distribution within the subcutaneous tissu e assumes that drug transport occurs predominately by diffusion. The Peclet number (Pe = v a/D), where v is the velocity of the dexamethasone solution in the tissue and a is the radius of the catheter, was 0.18. Hence, this assumption is acceptable. Figure 11. A typi cal H&E stained tissue section from our study. The bar represents a distance of 100 m
28The model assumed spherical symmetry, a lthough the delivery of drug was from a pipe. As the model was consistent with the da ta (figs. 10a, b, c), this assumption appears to be acceptable. From other experiments in our laborat ory, we have determined the minimum dosage of dexamethasone that would prevent inflammation to a gluc ose sensor implanted subcutaneously. This dosage was found to be 0.12 mg per day (unpublished data). Knowledge of this minimum va lue along with the values of the diffusion coefficient and elimination constant found in this study, one can design an effective and efficient local drug delivery system around any implantable glucose sensor or implant whose function is affected by inflammation.
29 Chapter Three Diffusion of [3H]Dexamethasone in Rat Subcutan eous Slices after Injection Measured by Digital Autoradiography Introduction Many transport experiments are based on th e injection of a finite volume of substance into the tissue of interest whic h then diffuses away. Some examples of injection based diffusion experi ments are: the determination of the diffusion coefficient of small molecules in the brain (27); the de termination of the diffusion coefficient of growth factors in the brain (28); and the de termination of the diffusion coefficient of drugs in tumors (29, 30). Knowledge of the diffusion of a substance of interest in the tissue of interest is important for treatmen t efficacy. In this paper, we will derive a method in which the diffusion coefficient of an injected substan ce in tissue can be determined in a relatively simple manner. We will illustrate this technique by finding the diffusion coefficient of [3H]dexamethasone in rat subcutaneo us slices after an injection. Materials and Methods Materials [3H]dexamethasone (392.46 MW), specifically [1,2,4,6,7-3H]dexamethasone, was obtained from Amersham Biosciences Corp. (P iscataway, NJ). The specific activity was 88.0 Ci/mmol.
30 Subcutaneous Injection Three male Sprague Dawley rats (Harlan, Indianapolis, IN, 375-399 g) were used for our studies. The rats were euthanized using CO2 prior to the experiment. The 20 minute experiment: Three 40 l solutions of [3H]dexamethasone in sterile 0.9% (w/v) saline were used. Injections were made into subcutaneous tissue. Each solution contained a total activity of 0.65 Ci. The tissue around th e injection site was removed and frozen on dry ice. The average tim e from injection to when the tissue froze, as measured using a surface thermometer (Mannix Testing & Measurement, Lynbrook, NY), was approximately 20 minutes after injection. The 157 second experiment: Three subcutaneous secti ons were harvested. Each section was injected with 40 l solutions of [3H]dexamethasone in sterile 0.9% (w/v) saline and then frozen on dry ice. The aver age time from injection to when the tissue froze was approximately 157 s econds after injection. All tissue samples were then stored at -80 C to immobilize the tracers within the tissue sample. The frozen tissue samples were mounted on a cryostat chuck and cut in 10 m sections. Sections taken at every 200 m were used for autoradiographic imaging. All animal experiments were performed under the approval of the University of South Florida Animal Care and Use Program. Autoradiographic Imaging and Analysis Autoradiographic images of the tissue s ections were obtained using a real-time digital radioactivity-detection system, th e MicroImager (Biospace Mesures, Paris, France) (16, 17). With the MicroImager, acquisition of events can be visualized in real-
31 time on a monitor screen. The acquisition of even ts needs only to pro ceed for as long as is necessary to obtain a good image. In our case, autoradiographic images with between 1,593,815 to 1,918,869 events were acquired ov er 71 h 32 min to 72 hr 43 min to obtain good images. The spatial variation in dr ug concentration from the injection was quantified as follows. A grid was placed over the autora diographic image using the Beta Vision + software (Biospace Mesures, Paris, France) to determine the number of events in each 0.3 x 0.33 mm grid area. The grid area that c ontained the highest nu mber of events (or greatest radioactivity) was taken to be the center of the injection. The concentration profiles versus distance in the subcutaneous tissue surrounding the center of injection were determined directly from the autora diographic images usi ng the Beta Vision+ software (Biospace Mesures, Paris, France). A line profile tool (1 mm wide) was used from the center of the injection to the peri phery of the subcutaneous tissue to obtain a number of events versus distance prof ile. The background number of events was subtracted from the number of events acquired. The number of events can be calibrated to concentration. Mathematical Model The concentration profiles of [3H]dexamethasone obtained using the MicroImager were compared to a mathematical model of drug diffusion. The model assumed 1) that the diffusing substance is deposit ed within a sphere of radius a at t = 0; 2) isotropic diffusional transport of drug through the subc utaneous tissue; 3) negligible fluid convection; and 4) negligible elimination. A ssuming that the elimination is negligible is justified as tissue samples were obtained from a sacrificed rat. That is, the absence of
32 blood flow eliminates most clearance mechanisms normally present in vivo (28). Hence, the governing equation for diffusion of a drug in the subcutaneous tissue is: r C r r r D t C2 2 (eq 6) where C is the concentration of the drug in subcutaneous tissue, D is the diffusion coefficient of the drug in subcutaneous tissue, r is the radial distance from the center of the injection and t is the aver age time from injection to when the tissue froze. The initial concentration is Co in the sphere, 0 r < a and zero for r > a. The boundary conditions is C( t) = 0. The analytic solution for eq 6 using the above initial and boundary conditions is (18, 31): Dt a r Dt a r oe e r Dt Dt a r erf Dt a r erf C C4 / ) ( 4 / ) ( 2 / 1 2 / 1 2 / 1 2 / 12 2) ( 2 ) ( 2 ) ( 2 2 1 (eq 7) where a is the radius of the sphere. If r >> a, then expressi on (eq 7) becomes (18): Dt a Dt r e Dt m CDt r40 6 1 ) ( 82 2 4 2 / 32 (eq 8) where m = VCo = 4/3a3Co, and V is the injected volume. If the radius of the sphere tends to zero, a0, with m remaining constant (18): 2 / 3) ( 8 ) (4 2Dt me t r CDt r (eq 9) or 2 / 3 2 / 1 4 3) ( 6 ) (2Dt e a C t r CDt r o (eq 10)
33 Equation 9 is the same solution as for th e instantaneous point source in 3D (32). However, Nicholson (33) suggests that at meas urement locations sufficiently far from the source, eq 9 (or eq 10) will provide a useful approximation. Moreover, Thorne et al. (28) suggest that when the injection time is very br ief compared to the time of the subsequent diffusion measurements, the concentration can be described by eq 9 (or eq 10). Typical concentration profiles for [3H]dexamethasone predicted by eq 10 at t = 2.5 min, t = 5 min, t = 10 min, and t = 20 min are shown in Figure 12. The radius of the injected spherical volume was 2.1 mm. For eq 5 to be a useful approximation, data away from the source was used (33). For the 20 min experiment, a portion of the concentr ation profile from the tail-end was used in the mathematical model. This portion ranged from the tail-end to a position 3 mm towards the source from the first zero event value. For the 157 s experiment, first zero event va lue could not be used as reference point. Instead, a location on the profile where the profile bends from a steep curve to a plateau region was used as a reference. This bend was defined to occur at a position where the number of events was 100. Therefore, the portion of the concentration profile used in the mathematical model was from the tail-end to a distance 0.7 mm towards the source after the bend. The reason that the first zero even t value could not be used as a reference Figure 12. Concentration profiles for diffusion when a concentrated bolus of solute is deposited within a small region. The curves shown are a realization of eq 5 with D = 4.11 x 10-10 m2/s, a = 0.21 cm, and t = 2.5 min, 5 min, 10 min, and 20 min
34 point will be discussed further in the di scussion section below. The value for D was found in an iterative manner. First, an init ial estimate for D was needed. The diffusion constant for dexamethasone in water was used, D = 6.82x10-10 m2/s (34). This initial estimate for D was then used as the starting points for the Marquardt-Levenberg algorithm (20) with the D, and C0 being the two independent variables over which the residual of the sum-squared-error between the predicted and experimental concentrations was to be minimized. The initial value for C0 was always the maximum concentration in the measured data set. The Marquardt-Leve nberg algorithm efficiently searched over the D, and C0 space to find the point which best fits the data (21). This technique was repeated to find D for 157 s and 20 min. For each of these times, the calculations were repeated for the autoradiographic scans at various angles. The Marquardt-Levenberg algorithm was written in MATLAB. Results Radiolabeled dexamethasone spread through the subcutaneous tissue after injection. Figure 13 is representative of the autoradiographic images obtained using the MicroImager after injection of a radiolabeled drug. The local concentration of drug within the tissue was quantifi ed from the autoradiographic images using the Beta Vision+ software. The Beta Vision+ software was used to construct the number of events as a function of distance profiles. Fi gure 14 is representative of the number of events versus distance profiles obtained from the autoradiogr aphic images. An event is a radioactivity decay event (16). The number of events was gr eatest at the center of the injection. A high number of events on the autoradiographic im age represent a high drug concentration. The
35number of events can be calibrated to con centration to obtain concentration versus distance profiles. a b Figure 13. Image a shows a typical auto radiographic image obtained using the MicroImager 157 s after injection of [3H]dexamethasone. Image b shows an autoradiographic image 20 min after injection of [3H]dexamethasone. Red indicates higher activity than green. The ba r represents a distance of 2 mm Figure 14. Typical number of events ve rsus distance profiles obtained using the MicroImager at (a) 157 s and (b) 20 min af ter implantation. Data from only one scan is shown. Combining data from all other scans would make the figure unreadable. The ordinate re presents the location of the center of injection
36For the 20 min case, the concentration pr ofile from the tail-end to 3 mm towards the source was compared to the mathematical model of diffusion to find the best estimate for D. For the 157 s case, the concentration profile from 0.7 mm towards the source from the bend to the tail-end was compared to the mathematical model of diffusion to find the best estimate for D. The best estima tes obtained for D are given in Table 5. Table 5. Estimated diffusion coefficient The diffusion coefficient was determined by fitting a model of diffusion to the concentration profiles from th e tail-end of the profiles. Time after Injection n D [m2/s] x 10-10 157 s 18 2.68 1.08 20 min 22 4.01 2.01 Discussion When a substance is injected into tissue in a period that is effectively instantaneous it may exhibit two distinct behaviors: 1) form a fluid-filled cavity; or 2) infiltrate the extracel lular space of the tissue (33). Th e subsequent diffusion from each case can be described by its own set of expre ssions (33). In this study, we have assumed that the substance does not form a cavity but infiltrates the extracellular space and then diffuses away and hence, have used the a ppropriate solutions a nd their approximations for this case. The approximations to the case where subs tance infiltrates th e extracellular space lead to eq 10. The two criteria for eq 10 to provide a useful approximation are: 1) that the measurement locations be sufficiently far from the source (33); and 2) that the injection
37 time is very brief compared to the time of the subsequent diffusion measurements (28). To comply with criteria 1, the data near the tail-end of the concentration profiles was used as described below. The measurement di stance was kept as small as possible while large enough to provide meaningf ul data. To investigate crit eria 2, two diffusion times were chosen t = 157 s and t = 20 min. For our study, radiolabeled dexamethasone was introduced into the subcutaneous tissue by injection. Highest conc entrations of the agent were assumed to be the location of the center of the injection. This assu mption is supported by our theoretical curves (Figure 12). The local distri bution of the agent in the s ubcutaneous tissue surrounding the center of injection was measured (Figure 14). The local distribution of the agent at the tail end of the distribution was compared to the mathematical model of diffusion. For th e 20 min case, the ma thematical model was compared to the local distribution from the ta il-end to a distance 3 mm towards the center of the injection from the firs t zero event value. For th e 157s case, the mathematical model was compared to the local distributi on from the tail-end to a distance 0.7 mm towards the center of the in jection from a bend. The concentration profile bends from a steep curve to a plateau region. The bend was defined to be the position where the number of events had a value of 100 (see Figure 14a). The plateau region was defined as having a relatively flat pr ofile where the events values where between 0 and 100. The position of the first zero event value could not be used as a referen ce as the plateau region varied greatly in length. Hen ce, it would not be possible to set a specified measurement distance from the first zero event value. A plateau region was not seen with the 20 min data.
38The distribution of the agent within the s ubcutaneous tissue at the tail-end of the concentration profile was cons istent with the mathematical model of diffusion (Figure 15). The mathematical model was compared to the experimental data in order to obtain values for the diffusion co efficient D at 157s and 20 min after injection. The diffusion coefficient, D, of dexameth asone in subcutaneous tissue slices at 157 s and 20 min after injection was 2.69 1.08 x 10-10 m2/s and 4.01 2.01 x 10-10 m2/s, respectively. As mentioned above, there were two crit eria for eq 10 to provide a useful approximation. To comply with cr iteria 1, the data near the tail-end of the concentration profiles was used. However for a few of the concentration profiles for the t = 157 s case, using data 0.7 mm towards the source from th e bend meant using all the data as the profile was very steep (Figure 15a). Hence, criteria 1 for t = 157 s could not be complied with. For the 20 min case, there was an offs et ranging from 0.77 mm to 2.25 mm from the Figure 15. Concentration profiles at th e tail-end at (a) 157 s and (b) 20 min after injection. Data from only one angle per time period is shown. Combining data from all other scan s would make the figure unreadable. The solid lines show the diff usion model in which D and C0 was varied to minimize the residual of the sum-squared-error between the predicted and experimental values
39center of the injection. Although this offset is not large, it may be sufficient enough to comply with criteria 1. In addition, data in Nicholson (33) show th at the accuracy of eq 10, at measurement distances close to the source, increases with time. Criteria 2 required that the injection time be very brief compared to the time of the subsequent diffusion measurements. A lthough the injection tim e was not measured, the injection of 40 l of substance was very br ief. The two diffusion times were t = 157 s and t = 20 min. The t = 157 s concentration prof ile had a plateau region that was not seen in the t = 20 min concentration pr ofile. It could be that at t = 157 s, the injected substance formed both a fluid-filled cavity and infiltra ted the extracellular space to some degree producing the plateau region. If th is is the case, then eq 10 would not be the appropriate expression. This is a phenome non that needs to be investig ated further and is beyond the scope of this study. The concen tration profile at t = 20 min is similar in shape to the theoretical curves realized by using eq 10 (F igure 12), whereas the concentration profile for the t = 157 s is not similar due to the pl ateau region. Hence, we will assume that for t = 157 s the diffusion time was not long enough a nd that eq 5 does not provide a useful approximation in this case. A diffusion time of t = 20 min probably provides an adequate diffusion time and hence, eq 10 does provide a useful approximation. Therefore, the best estimate for the di ffusion coefficient of dexamethasone in subcutaneous tissue slices based on the t = 20 min data is D = 4.01 2.01 x10-10 m2/s. We previously found a diffu sion coefficient, D = 4.11 1.77 x10-10 m2/s, for dexamethasone in subcutaneous tissue using different experimental and mathematical techniques (34). The diffusion coefficient was determined by fitti ng a model of diffusion and elimination to the concentra tion profiles measured near the tip of a catheter attached
40to an osmotic pump containing [3H]dexamethasone that was im planted in rats for 6 h, 24 h and 60 h (34). These values for D are very similar suggesting that eq 10 provide an adequate approximation as long as the two criteria are met. Our mathematical model assumed that the diffusing substance was deposited within a sphere at t = 0. Figure 13a shows the shape of the injection at 157 s is relatively spherical. Hence, the assumption that the injected volume at t = 0 was spherical is acceptable. The mathematical model also assumed isotropic diffusional transport of drug through the subcutaneous tissue. Figure 13b show s the diffusion of the drug at t = 20 min and diffusion is relatively spherical away from the site of injection. Hence, our assumption of isotropic diffusi onal transport is reasonable. The elimination constant was assumed to be negligible as the injections were made in either harvested subc utaneous tissue or in a euthenized rat so that the normal clearance processes that depend on circula tion of blood was eliminated (33). In vivo concentration distributions are more complex and neither diffusion nor elimination can be neglected. In conclusion, eq 10 provides an ad equate approximation for measurement locations sufficiently far from the source a nd for diffusion times much longer than the injection time (28, 33). The main advantages of this injecti on technique to determine an approximation for the diffusion coefficient are that it is relatively si mple technique, and can be applied to any radiolabeled substan ce of interest injected into any tissue of interest.
41 Chapter Four Summary and Future Work MicroImager The MicroImager is a highly sensi tive autoradiographic imaging modality open to various applications. While the machin e is expensive, the cost of obtaining each image is low and can be done quickly. A ti ssue sample is placed on a slide and covered with a sheet of scintill ating paper. This is placed in the machine then autoradiography is performed. The PC associated system stores the data digi tally and is easily accessible for storage and processing. This autoradiographic machine can also be used to evaluate the distribution of two differ ent isotopes in a sample. Osmotic Pump Tritium labeled dexamethasone was placed within osmotic pumps and implanted into several Sprague Dawley rats. The implants were removed at several time intervals and surrounding tissue was obtained for eval uation. Samples were imaged using the MicroImager and spatial distribution of the radiolabeled dexamethasone was obtained. Mathematical models were created and best fit to experimental results. Using curve fitting, the diffusion coefficient and elimination constant of dexamethasone in subcutaneous tissue were obtained.
42 Injection Study Tritium labeled dexamethasone was injected into rat subcutaneous tissue to determine its behavior. After injection, the ti ssue was explanted and frozen very quickly. Two time points were tested as 2.5 min and 20 min. Mathematical models were obtained and matched to the experimental distribution curves. This study developed a new method to obtain the diffusion coefficient of dexamethas one in any rat subcutaneous tissue. This method can also be applied to different drugs in different tissues. Possible Future Work The MicroImager is a versatile imaging m odality with many possible applications. Building on this research, experiments can go forward to evaluate receptor-ligand interactions in the brain. For example, [3H]nicotine can be used to label nicotine receptors in the brains of adu lt and adolescent rats to inves tigate adolescent vulnerability to nicotine addiction ( Moussy and Wecker, personal communicat ion). In addition, future work can also investigate the dual imaging cap ability of this machine. Some work has already been done investigating this capability. [3H]glucose and 14[C]dextran were used to investigate the permeability of blood vessels (not publis hed). While minimal results were obtained, this study will be useful in preparing future investigations using dual labeling. Future work may include using ra diolabeled drugs for the treatment of brain tumors while simultaneously monitoring the metabolism at this site using radiolabeled glucose.
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