The delivery of BCNU to brain tumors

Journal of Controlled Release 61 (1999) 21–41

The delivery of BCNU to brain tumors Chi-Hwa Wang a , *, Jian Li a , Chee Seng Teo a , Timothy Lee b a

Department of Chemical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore b Division of Neurosurgery, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore Received 15 October 1998; received in revised form 3 February 1999; accepted 2 April 1999

Abstract This paper reports the development of three-dimensional simulations to study the effect of various factors on the delivery of 1-3-bis(2-chloroethyl)-1-nitrosourea (BCNU) to brain tumors. The study yields information on the efficacy of various delivery methods, and the optimal location of polymer implantation. Two types of drug deliveries, namely, systemic administration and controlled release from polymers, were simulated using fluid dynamics analysis package (FIDAP) to predict the temporal and spatial variation of drug distribution. Polymer-based delivery provides higher mean concentration, longer BCNU exposure time and reduced systemic toxicity than bolus injection. Polymer implanted in the core gives higher concentration of drug in both the core and viable zone than the polymer in the viable zone case. The penetration depth of BCNU is very short. This is because BCNU can get drained out of the system before diffusing to any appreciable distance. Since transvascular permeation is the dominant means of BCNU delivery, the interstitial convection has minor effect because of the extremely small transvascular Peclet number. The reaction of BCNU with brain tissues reduces the drug concentration in all regions and its effect increases with rate constant. The implantation of BCNU / ethylene–vinyl acetate copolymer (EVAc) matrix at the lumen of the viable zone immediately following the surgical removal of 80% of the tumor may be an effective treatment for the chemotherapy of brain tumors. The present study provides a quantitative examination on the working principle of Gliadel  wafer for the treatment of brain tumors.  1999 Elsevier Science B.V. All rights reserved. Keywords: Tumor; 1-3-Bis(2-chloroethyl)-1-nitrosourea; Polymeric delivery; Systemic administration; Simulation

1. Introduction BCNU (1-3-bis(2-chloroethyl)-1-nitrosourea (carmustine)) is an important chemotherapeutic drug in treating brain tumors. Its main function is to inhibit the synthesis of DNA, RNA and protein similar to other alkylating agents. The traditional method of delivering BCNU to the pathological site is mainly through intravenous perfusion. The drawbacks asso*Corresponding author. E-mail address: [email protected] (C.-H. Wang)

ciated with it are the systemic toxicities characterized by delayed hematopoietic depression, cytotoxic effects on kidney, liver and central nervous system, and the short exposure time of tumor tissue to BCNU [1]. The research work of Blasberg et al. [2] showed that the intravenous perfusion of BCNU results in its penetration through only a short distance (|2 mm) from the ependymal surface into the local brain tissues, and hence the efficacy of this kind of drug delivery appears to be quite low. In an effort to overcome these disadvantages, intensive research has been undertaken by the sci-

0168-3659 / 99 / $ – see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S0168-3659( 99 )00098-X

22

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

entists for the design of more reliable and effective drug delivery systems. Among these, the controlled drug release from surgically implanted polymers seems to be a promising way for the treatment of tumors with several possible advantages over systemic administration. The polymer pellet can be directly implanted in the pathological site by surgery to give controlled release. By using a small amount of drug, a high local drug concentration can be achieved. In addition, controlled release obviates the need for longer distance transport which may cause severe systemic toxicity and the possible degradation of drug molecules. Furthermore, direct surgical implantation may circumvent the need for drug molecules to cross the blood–brain barrier (BBB). This may be very important in the case of brain tumors, where the high interstitial pressure at the center blocks the blood-borne drug delivery. The bio-compatibility of several polymer–drug systems and their efficiencies have been studied and verified through in vitro and in vivo studies [3–5]. Tamargo et al. [5] tested the bio-compatibility of EVAc (ethylene–vinyl acetate copolymer) and PCPP:SA (Poly(carboxyphenoxy-propane / sebacic acid)) matrices with the brain tissues in rats. Both these polymers appeared to be non-toxic and biocompatible with the rat brain. Using rats as hosts, Tamargo et al. [6] investigated interstitial chemotherapy of the 9L gliosarcoma in the brain using EVAc–BCNU and PCPP–BCNU systems. Their results showed that the controlled drug release from the polymer resulted in a significant delay in the tumor growth. The in vivo study of Yang et al. [7] showed that the polymeric delivery of BCNU could be obtained in a sustained manner for about 5 days. In addition, other studies on the controlled release of BCNU and other tracers have also been reported in the literature. Among them, GLIADEL  Wafer (PCPP:SA–BCNU) has been commercialized for the surgical treatment of recurrent malignant brain tumors [8,9]. Simulation studies on the distribution of neuroactive agents in tumors and normal brain tissues have also been of interest in the recent years. Levin et al. [10] studied the effect of blood flow rate and capillary permeability on the total exposure dose of BCNU. Saltzman and Radomsky [11] developed a one-dimensional model to study the drug release

process from polymers into the brain tissues. In their model, convection was assumed to be negligible and only diffusion and the drug elimination were considered. The assumption of negligible convective contribution in these models is questionable in certain cases, such as brain tumors, where the elevated interstitial pressure in tumor tissue may cause significant convective flux near the edge of tumors and hence may significantly affect the delivery of macromolecules [12]. Fung and co-workers [13,14] conducted a series of systematic studies both theoretical and experimental for the detailed local concentration profiles (rather than the mean concentration profiles reported by Grossman et al. [15]) of various drug molecules using different host animals. Their formulation was limited to a one-dimensional (radial) drug delivery problem, with the drug concentration profile being empirically correlated with the interstitial velocity. Upon comparison with the experimental data of Ferszt et al. [16] and Groger et al. [17], it was found that the convection component is significant during the first day of the controlled drug delivery. Kalayanasundaram et al. [18] presented a 2-D theoretical framework that includes a realistic rabbit brain geometry with salient anatomic features. Both the diffusive and convective contributions were included for the brain tissues. In addition, comprehensive simulated results were reported for the case of edema. Furthermore, their study accounted for the flow in the porous structure of brain tissue by solving an extended form of the Darcy’s law. Their formulation accounted for the clearance into the capillaries and enzymatic metabolism of the drug molecule by a constant ‘lumped’ parameter. Hence, the model did not capture the individual contribution of the transvascular transport mediated by the diffusion and convection of drug molecules. Moreover, although their model equations comprised the extended Darcy’s law for describing the momentum balance of interstitial fluid, the transient flow pattern in the brain was not addressed in detail. The implantation of a ‘single’ polymer may significantly increase the drug concentration in all parts (including the ipsilateral and the contralateral hemispheres) of a rabbit brain. In contrast, a similar arrangement may result in poor drug delivery with a tumor-bearing human brain, due to the dramatic

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

difference in the size of the brain. In the latter case, a more practical application is the polymer implantation in conjunction with the surgical removal of the major part of the tumor, if the target is a tumorbearing brain [8,9]. Under such considerations, a few polymer carriers in the form of wafers are inserted in the surgical cavity, followed by the permeation of interstitial fluid in the whole surgical cavity. The delivery of drug molecules to the target tissues is achieved through the sustained direct contact between the target tissues and a ‘drug-rich’ film formed at the lumen of the surgical cavity and the wafer. In such a problem, the anatomical structure of tumor is much more important than the detail structure of the remaining part of the healthy normal brain tissues. This is because it is almost impossible to supply the drug molecules efficiently to the regions away from the polymer carriers (or the surgical cavity) due to the physical size of the human brain (.5 cm). The aim of this study is to carry out computer simulations to quantitatively analyze and compare the BCNU delivery through the polymeric implant and systemic bolus injection. The effects of elevated interstitial pressure, convective flux, blood drainage and intracellular kinetics are studied. One of the objectives of the present work is to address the problem of geometrical limitation. In the present study, three-dimensional simulations using MRI images of a primitive neuroectodermal tumor (PNET) are conducted and the results are compared with those reported in the literature [13,14]. The model geometry is not limited to a perfect shape (i.e. sphere or slab). The tumor and normal tissues in this model can be of any arbitrary shape, thus allowing us to make a realistic prediction on the pressure and BCNU distributions. In addition, the present simulation platform also explores the possibility of optimizing the drug delivery through computer simulations.

2. Mathematical model The model geometry (Fig. 1a) is established from the MRI pictures of a PNET (Courtesy, Department of Surgery, National University Hospital, Singapore). The white dotted curve (V ) approximately encircles the periphery of the tumor. Fig. 1b shows the simulation geometry of the surgical model. It is

23

reconstructed from seven MRI pictures with 80% of the tumor being removed through surgery. Polymer pellets are implanted in the cavity of the tumor. It has been assumed that the BCNU is released from the surface of the polymer and is distributed uniformly in the interstitial fluid of the surgical cavity. Domains A, B and C show the surgical cavity, remaining viable zone of the tumor and the surrounding normal tissues, respectively [12]. The computations with typically 7800–9800 elements were conducted using a finite-element software package, fluid dynamics analysis package (FIDAP) [19]. Fig. 1c shows the schematic diagram of the model. In these simulations, a non-uniform blood perfusion is considered by incorporating a necrotic core in the center of a tumor. The equation for the mass conservation of interstitial fluids is [20–22], =? U 5 Fv 2 Fl

(1)

where U is the velocity of the interstitial fluid; Fv is the fluid gain from the blood per unit volume of the tumor tissues and Fl is the fluid removal from lymphatics per unit volume of the tumor tissues. The constitutive relation for Fv is based on the formulation of Starling’s hypothesis and can be found in Ref. [21], Fv 5 Kv S /V [Pv 2 Pi 2 sT (pv 2 pi )]

(2)

where Kv is the hydraulic conductivity of the microvascular wall, Pv is the vascular pressure, pv and pi are the osmotic pressures of plasma and the interstitial fluid, S /V is the exchange area of the blood vessels per unit volume of the tumor tissue, sT is the osmotic reflection coefficient for the plasma proteins. The modified continuity equation takes into account the source and sink terms due to the existence of blood and lymphatic vessels. This is because interstitial fluid can permeate from blood vessels into tumor tissues, and lymphatic vessels can also reabsorb the fluid back into the systemic circulation. Since the brain does not have a well-defined lymphatic system (the ventricular system and pattern of fluid circulation in the brain is quite unique compared to other organs), the fluid removal from lymphatics per unit volume of tumor tissues can be assumed to be negligible,

24

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

Fig. 1. The reconstructed finite element mesh plot of calculation geometry: (a) MRI picture. The white dotted curve (V ) encircles the tumor. (b) Mesh plot for the surgical model: (A) surgical cavity; (B) remaining viable zone of tumor; and (C) surrounding normal tissues. The black dot represents the implanted polymer. (c) Schematic diagram of the model. V1 , V2 and V3 refer to internal boundaries. V4 is the external boundary. N1 –N4 are the unit normal vectors corresponding to V1 – V4 .

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

Fl ¯ 0

(3)

The interstitium is approximated as a rigid porous medium, and hence the semiheuristic volume-averaged momentum equation can be applied [19,23],

S

D

r ≠U m m ] ] 1 U ?=U 5 2=Pi 1 r f 1 ] = 2 U 2 ] U ´ ≠t ´ l CE 2 ]] ruUuU (4) l 0.5 where l is the permeability of the interstitium; U and Pi are the velocity vector and the pressure of the interstitial fluid, respectively; ´ is the porosity; m and r are the viscosity and the density of the interstitial fluid, respectively; CE is the Ergun coefficient; f is the body force. The literature reported a steady-state value of roughly 10 26 cm s 21 for the velocity of interstitial fluid through the brain tissues [16,17]. This indicates that the macroscopic and the microscopic inertial forces may be less important relative to other terms. Furthermore, the body force and the Brinkman viscous term (the third term on the R.H.S. of Eq. (4)) are both assumed to be negligible as compared to others. The present model assumes the time scale of transient pressure equilibration following the surgical removal of tumor to be short enough, and hence the steady-state flow field of interstitial is established much faster than that of the concentration field. Under the above simplifications, the resulting Darcy’s law can be directly applied to determine the relationship between interstitial fluid velocity and the pressure gradient, U 5 2 K=Pi

(4a)

where the hydraulic conductivity, K5 l /m. The pressure field can be solved by substituting Eq. (4a) into Eq. (1) and analyzed as a steady-state problem. The mass conservation equation for the drug is written as, ≠C ]i 5 D= 2 Ci 2=? (UCi ) 1 Fs 2 Fls 2 R(Ci ) ≠t

(5)

where Ci is the drug concentration, D is the diffusivity of drug molecules in the interstitium, Fs and

25

Fls are the supply of drug from blood stream and the loss of drug from lymphatic vessel per unit tumor volume, respectively. For the closures of Fs and Fls in the necrotic core, viable zone and normal tissues, we refer to the work of Baxter and Jain [21], Fs 5 Fv (1 2 s )Cv 1 PS /V(Cv 2 Ci )Pev /(e P ev 2 1) (6) The transcapillary Peclet number is defined as: Fv (1 2 s ) Pev 5 ]]] PS /V

(7)

where P is the vascular permeability coefficient, Cv is the concentration of drug in the plasma and s is the osmotic reflection coefficient for the drug molecules. This dimensionless quantity represents the ratio of convective and diffusive transport. Due to the existence of the blood–brain barrier, the value of BCNU transvascular permeability (Table 1) is smaller than the corresponding value in other organs and tissues. Similar to the argument for Eq. (3), there is no well-defined lymphatic system in the brain tissue, and hence Fls is assumed to be negligible, Fls ¯ 0

(8)

The chemical reaction of drug with tissues may be written in the following form [11]: Vmax Ci Vmax Ci R(Ci ) 5 ]]] 1 Ke Ci ¯ ]] 1 Ke Ci Km 1 Ci Km 5 k*Ci

(9)

where Vmax and Km are the Michaelis–Menten parameters and Ke is a first-order elimination due to non-enzymatic reactions; k* is the effective rate constant. Eq. (9) can be simplified into a first-order reaction if the drug concentration is low enough (Ci
C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

26

Table 1 Parameter values used in BCNU simulation a Parameter

Baseline value

Reference

2.11310 26 cm kPa 21 s 21 N 2.70310 27 cm kPa 21 s 21 T 200.00 cm 21 N 70.00 cm 21 B 2.07 kPa 2.66 kPa T 2.00 kPa N 1.33 kPa T 3.23310 27 cm 2 kPa 21 s 21 N 6.40310 28 cm 2 kPa 21 s 21 T 0.82 N 0.91 T 6.75310 25 cm 2 s 21 N 2.5310 26 cm 2 s 21 0.10 T 8.31310 25 cm s 21 , N 1.06310 25 cm s 21 P 7.90310 29 mol cm 23 E 1.57310 29 mol cm 22 s 21 E 1.26310 5 s E 0.29 cm 2 P 7.74310 3 s B 1.31310 24 s 21

[20] [20] [22] [22] [22] [21] [21] [21] [20] [20] [20] [20] [11,20–22] [11,20–22] 2 [11,20–22] [11,20–22] 1 [7] [7] [7] [1] [1,10,11]

T

Kv

vascular hydraulic conductivity

S /V

exchange area

Pv pv pi

vascular pressure osmotic pressure (plasma) osmotic pressure (interstitial fluids)

K

interstitium hydraulic conductivity

sT

plasma osmotic reflection coefficient

D

diffusion coefficient

s P

drug osmotic reflection coefficient vascular permeability

C 0v F0 t Sp ts k*

plasma drug concentration initial drug flux from polymer release time constant polymer surface area decay time constant effective rate constant

a

2, estimated based on molecular weight; 1, estimated by the bolus injection of 100 mg BCNU for a 60-kg patient; B, tumor and normal tissues; E, EVAc–BCNU (30%) system; N, normal tissues; P, plasma; T, tumor.

and flux across all internal boundaries (V1 , V2 and V3 ). At the external boundary of normal tissues (V4 ), a no-flux condition is used. The mathematical formulation for the internal boundary V2 is given by,

drug-carrying polymer is assumed to be EVAc with a 30% BCNU loading. The flux of drug (F ) is specified by the data of [7] as an exponential decay function with a time constant t.

CiuV 22 5 CiuV 12

(10a)

F 5 F0 e 2t / t

PiuV 22 5 PiuV 12

(10b)

where F0 is the initial release flux and t is the time constant. The initial concentration of BCNU in the brain tissue (normal and tumor) is assumed to be negligible. In order to compare the results of different cases, a coefficient known as ISN is calculated together with the mean value of the drug concentration [24],

≠Pi 2 KB ] ] ≠N2

U U

≠Ci 2 DB ] ] ≠N2 (u i Ci )uV 12

V2 2

≠Pi 5 2 KC ] ] ≠N2

U

(10c)

V1 2

≠Ci 1 (u C ) 2 5 2 DC ] u i i V 2 ] ≠N2 V2 2

U

V1 2

1 (10d)

Similar expressions are applied to the other internal boundaries (e.g. V3 ). At the polymer–tissue interface (V1 ), on the other hand, the boundary condition is set up by matching the flux of drug with the in vivo experimental data of Yang et al. [7]. The

]]]] N ] (Ci 2C)2 i 51 ISN 5 ]]]] ]]] ] œN(N 2 1) ?C

œO

OC

(11)

(12)

N

i

] i 51 C 5 ]] N

(13)

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

] where C and Ci are the mean and local values of concentration throughout each sub-domain and N is the total number of nodal points in the mesh geometry. The ISN coefficient is proportional to the coefficient of variation for the spatial distribution. The smaller the ISN is, the greater the homogeneity of drug distribution will be [12,24]. Two types of drug delivery are studied, namely systemic bolus injection and the polymeric release. In the first case, BCNU is delivered to the tumor through a systemic bolus injection, in which the drug concentration in plasma decays with time, Cv 5 C v0 e 2t / t s

(14)

where C 0v is the drug concentration in plasma at t50 and ts is the time constant. The dosage is based on the intravenous injection of 100 mg BCNU for a 60-kg patient. In the second case, EVAc polymer matrices with 65 mg BCNU loading are implanted in the necrotic core, viable zone of tumor and the lumen of the viable zone of tumor, immediately following the surgical removal of 80% of the tumor to study the effect of implantation location. The parameter values used in this study are summarized in Table 1.

3. Results and discussion The simulated pressure and velocity profiles of interstitial fluid are reported in an earlier study and, therefore, are not reproduced here [12]. The steadystate solution shows that the interstitial fluid pressure in the viable zone of tumor (about 1.3 kPa) is significantly higher than the surrounding normal tissue which has a pressure reading of about zero gage pressure. The pressure drop occurs within a very thin boundary layer between the tumor and the normal tissue. These results appear to agree well with the previous animal experiments [25] and theoretical studies [21]. Simulations on the BCNU distribution are conducted for both the systemic bolus injection and polymer in the necrotic core, viable zone of tumor and surgical model. The three-dimensional simulation geometry is constructed from seven MRI pictures of a PNET. In the next few sections, simulation

27

results on a cross-section of an intact PNET (on the same plane as V in Fig. 1a) will be discussed first, followed by the three-dimensional simulation results for both the intact and surgical tumor models presented in a subsequent section.

3.1. Baseline simulation Baseline simulation refers to the case where there is no intracellular kinetics. This case illustrates the net effect of diffusion and convection. Fig. 2 shows the detailed distribution of BCNU at t530 h for the cases of (a) necrotic core implantation; (b) viable zone implantation; and (c) systemic bolus injection. The BCNU delivery from a single polymer pellet (for implantation in either the viable zone or the core) seems to be quite insufficient for the entire tumor. The penetration of drug is limited to a few millimeters in the tumor tissues away from the surface of the polymer. This is quite different from the simulation results of [18] which show the penetration throughout the major part of the brain. This difference is primarily due to the geometry. Kalyanasundaram et al. [18] reported the computational geometry based on the model of a rabbit brain. The penetration depth of BCNU is, therefore, of a comparable size to the entire brain. It is not surprising that they have to incorporate the salient anatomical structure of the brain (ventricle, white and gray matters, etc.) for a more accurate prediction on the overall drug distribution. In the present work, in contrast, the size of human brain tumor is about 4 cm in diameter, much larger than the penetration depth achieved by a single polymer implant. In this case, the penetration is limited to the vicinity of tumor and the detailed anatomical structure of the tumor (core, viable zone) is, therefore, much more important than the remaining part of the brain. Figs. 3a,b shows the temporal variation of BCNU concentration profiles (measured from the interface of polymer and tissue) for the cases of necrotic core and viable zone implantation. For both cases, BCNU concentration at the polymer surface decreases to about 50% of the original value after 24 h and to a very small value at the end of 250 h. In contrast, the BCNU distribution for the case of systemic bolus injection appears to be much more homogeneous. The concentration profiles are shown

28

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

Fig. 2. Spatial distribution of BCNU concentration: (a) core implantation, (b) tumor implantation and (c) systemic bolus injection.

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

in Fig. 3c as a function of a local coordinate (indicated by horizontal lines, scaled from 0 to 5.34 cm). The viable zone of the tumor (henceforth abbreviated as tumor) shows the highest concentration while the necrotic core (henceforth abbreviated as core), expectedly, shows the lowest drug concentration. A sharper BCNU concentration gradient occurs within the necrotic core. This is because there is no blood perfusion in the core and the only way for BCNU molecules to reach the core is through diffusion from the viable zone. In contrast, the drug transport in other regions is mediated primarily by the transvascular permeation. The exposure time of tissue with BCNU is very short. This is because of the short half-life of BCNU in the plasma (1.5 h) and its fast drainage into blood vessels. Apart from the systemic toxicity, the efficiency of bolus injection also appears to be quite low. After 24 h, the mean concentration of BCNU is almost negligible. The core shows the greatest degree of non-homogeneity of BCNU distribution, the transient ISN values in the range from 0.01 to 0.04. On the other hand, BCNU distribution is very uniform in the normal tissue, ISN values keeping below 10 25 . The tumor region’s ISN is between the corresponding values of other two regions, hovering around 0.002. In systemic administration, the drug is supplied from the blood vessels and, since the core has no functional blood vessels, its only source of BCNU is via diffusion from the tumor. Diffusion takes time and this give rise to greater heterogeneity. The tumor’s ISN is larger by virtue of the larger amount of exchange surface in it (S /V is 200 cm 21 in the tumor compared to 70 cm 21 in the normal tissues [21,26–28]) and its smaller volume.

3.2. Penetration depth In order to conduct sensitivity analysis for the penetration depth of different drug molecules, two types of drugs with significantly different molecular weight are investigated in this section. The penetration depth is defined as the average distance measured from the surface of polymer at which the value of (Cs 2Ci ) /(Cs 2Cb ) is 99%. Here Cs and Cb refer to the drug concentrations on the polymer surface and the surrounding normal tissues, respectively [12].

29

Fig. 4 shows the comparison of the penetration depths between Immunoglobulin G (IgG) and BCNU for the case of polymer implantation in the viable zone of the tumor. Both cases are reported for the same model geometry (indicated in Fig. 2b by a red box). Fig. 4a shows the IgG distribution at 50 h [12] while Fig. 4b shows the corresponding BCNU distribution at 30 h after implantation. BCNU has a much lower molecular weight (MW5214) as compared to the IgG (MW5146 000). Despite the fact that IgG’s diffusivity is nearly 10 6 times smaller than that of BCNU, it shows much greater penetration depth of nearly 2.2 cm (at 100 h after the polymer implantation) compared to BCNU’s 0.5 cm (t5100 h). This is because BCNU has a much higher transvascular permeability and, therefore, is reabsorbed to the systemic circulation much easily. BCNU molecules, being lipid soluble and very permeable, get into the bloodstream before they can travel far enough. In the case of IgG [12], although it diffuses very slowly, it takes more time to cross the capillary walls into the bloodstream.

3.3. Relevant experimental data in the literature Most of the previous modeling works have been focused on the drug delivery to normal tissues. According to Baxter and Jain [20–22], the transport of drug in normal and neoplastic tissues may be significantly different, due to the interstitial convective transport induced by the elevated pressure and heterogeneous blood flow. This certainly has raised the question: whether the data collected in studies of normal tissue can be extended to other pathological conditions such as brain tumors. Fung et al. [13] compared the concentration profiles of carmustine at the site of microinjection (from the edge of polymer) for both normal and tumor-bearing brains. Similar profiles were found for both the cases at 6 h and 24 h after the microinjection of carmustine. The same study indicated that high concentration of BCNU were measured near the polymer for the entire 30 days of experimental period. In a subsequent work, Fung et al. [14] presented a similar study with BCNU delivery to monkey brain, using a slab rather than a sphere for the geometry of polymer. BCNU concentrations in both the ipsilateral and the contralateral hemispheres were reported.

30

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

Fig. 3. Temporal variation of BCNU concentration profiles: (a) core implantation, (b) tumor implantation and (c) systemic bolus injection.

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

31

Fig. 4. Penetration depth of IgG and BCNU: (a) IgG, t550 h and (b) BCNU, t530 h.

Neglecting the interstitial convection, they compared the simulated BCNU concentration with one-dimensional experimental results. In addition, the drug concentration at polymer–tissue interface and the ‘high dose distance’ were recorded as a function of time. A comprehensive schematic diagram was also shown to illustrate the detailed drug delivery pathway from the polymer pellet to the brain. The characteristic time scales associated with these transport pathways were compared. In that work, the transient concentration profiles were fitted into the expression of an unsteady analytical solution to obtain the value of a diffusion / elimination modulus. While these fitted results were not significantly different from the experimental data (this module was varied to compare most favorably with the experimental data), the estimated values of a diffusion / elimination modulus show some variation with

time, indicating the basis of this pseudo steady-state estimation may be questionable at some times. The simulation results in the present study are compared with the penetration profiles reported by Fung et al. [14]. Before presenting any further information, it is necessary to point out the fundamental difference between these two studies. Fung et al. [14] considered a normal brain tissue implanted with a biodegradable polymer pellet (PCPP:SA), whereas the present work considers the brain tumor tissue implanted with a non-biodegradable polymer. Due to the difference in the polymers, the release flux and mass loading of drug in the present study are quite different from that used by Fung et al. [14]. In order to facilitate the comparison between the two studies, the concentrations were normalized with their initial values and were plotted against the distance from the polymer–

32

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

tissue interface (Fig. 5). Cs(t 50) refers to the BCNU concentration on the polymer surface at t50. The experimental penetration profile by Fung et al. [14] is always higher than the profiles simulated in the present work. This is expected, as in the normal tissue, the capillary exchange surface area per unit volume of tumor is about three times lower than that in the tumor tissue (S /V|200 cm 21 and 70 cm 21 for the tumor and normal tissues, respectively [21,26– 28]), already mentioned elsewhere in the text. In addition, based on the experimental data of dextran [11,28], the transvascular permeability of the normal

tissue is about eight times lower than that of the tumor tissue (P|8.3310 25 cm s 21 and 1.0310 25 cm s 21 for the tumor and normal tissues, respectively). Hence, when compared to the tumor tissue, drug in the normal tissue can be retained for longer periods of time. These reasons together with the fact that the diffusivity of BCNU in the tumor tissue is much higher than that in the normal tissue, could explain the difference between our simulated results and the experimental values from Fung et al. [14]. If the polymer degradation mechanism (bulk and surface degradation) can be better understood, the

Fig. 5. Penetration of BCNU in the normal and tumor tissues. The solid lines and the squares refer to the results of normal and tumor tissues, respectively.

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

relevant data can be incorporated in the boundary condition for the polymer–tissue interface to give a better prediction in the transient drug penetration profiles. Apparently, extensive works on the brain drug delivery problem have been conducted during the past few years. Most of these studies were based on animal models. For instance, the tissues of either rat or rabbit were used by Grossman et al. [15], Fung et al. [13] and Kalayanasundaram et al. [18]; while the tissues of monkey were used by Fung et al. [14]. Inherently in all these studies there are problems in the applicability of extending animal experiment results for clinical application. Most of the previous studies involve the implantation of a single polymer and the examination of the drug distribution and penetration depth of various neuroactive agents through simulations and experimentation (e.g. quantitative autoradiography). These studies have provided valuable insight into the detailed drug distribution in relatively small animal models. However, some of these findings may not be directly extended to clinical applications due to the geometry (size) difference between the animal model and the human beings.

33

transcapillary term. This accounts for the more significant effect of lymphatic drainage on macromolecule transport in other organs. In the case of polymer implanted in the viable zone of tumor, there was no noticeable difference in the drug distribution when the interstitial convection and transcapillary convection terms in the BCNU mass conservation equation were omitted. Similar results were obtained for core implantation. In both the cases, the model consists of only pure diffusion and a pseudo-first-order elimination given by Eq. (9). This phenomenon could be due to the very small Pev in BCNU delivery. The limiting case of zero Pev refers to the absence of transvascular convection. Pev in the neoplastic and normal tissues is only about 0.03–0.3. The small Pev is in turn due to the large transcapillary permeability of BCNU. This small value of Pev would predict a very limited role of transvascular convection in BCNU delivery and distribution. This finding is in contrast to the more significant contribution by convection observed in the delivery of macromolecule IgG, owing to the much larger (3–25) Pev values [12].

3.5. Effect of intracellular kinetics 3.4. Effect of transcapillary permeation For the polymeric delivery of BCNU, Cv is very small and hence the transcapillary term is always a sink for the drug. Further, for small Pev , as in the case of BCNU, Eq. (6) reduces to: PS Fs ¯ 2 ]Ci V

(15)

The simulation results generally confirms the above analysis and are also consistent with those of Blasberg et al. [2], where the ECF-capillary half-life was calculated as only 1 min, as already stated elsewhere in the text. In contrast to other organs, there is no well-defined lymphatic system in the brain tissues. This makes the transcapillary permeability of the BCNU molecule the key factor in the drug delivery problem. However, the effect of lymphatic vessels is very significant in the transport of larger molecules like IgG in organs other than the brain [12]. Using an order of magnitude analysis, the lymphatic term is almost 18 times larger than the

This case is compared with the baseline simulation to study the effects of tissue / drug chemical reactions. Since the reaction term is simply modeled as a first-order elimination, Eq. (9) predicts that the effect of intracellular kinetics is to reduce the mean concentration of BCNU in the tissues. In the case of tumor implantation, the values of the mean concentration are lower than those of baseline values by 6% for normal tissues, 5% for the necrotic core and only 1% for the tumor (percentages quoted are averaged values for the various time steps). The value of k* (1.31310 24 s 21 ) is almost negligible compared to the transcapillary exchange. When the simulation is repeated with a k* value 10 times larger than the original value, the reduction in the drug concentration was more significant. In the case of tumor implantation, the mean concentrations of the tissue, necrotic core and tumor are 38, 15 and 5% lower than the baseline values, respectively. Fig. 6 shows the mean concentrations with an increment in k* values in the normal tissue, tumor

34

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

Fig. 6. Effect of intracellular kinetics on mean concentration for all three sub-domains for the case of tumor implantation. Concentrations are normalized with respect to baseline concentration, Co : (a) normal tissue, (b) tumor and (c) core.

and necrotic core for the tumor implantation (normalized with respect to baseline values at each time step), respectively. Since BCNU is extraneous to the

human body, it is eliminated very quickly. As reported by Goodman et al. [1], it takes only 24 h for BCNU to be degraded and excreted in the urine.

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

Apparently, the literature values for k* is too small to notice any significant effect.

3.6. Lumped first-order elimination model Saltzman and co-workers [11,14] carried out pioneering modeling work on drug delivery to normal brain tissues. The present study differs from their work in that clusters of neoplastic tissues (embedded in normal tissues) rather than normal tissues are investigated. In their models, there were no separate terms for transcapillary exchange and interstitial convection. Instead, a lumped first-order elimination term incorporating the effects of intracellular kinetics (due to non-enzymatic reactions) and transcapillary exchange was used. Even though there is no clear theoretical ground for such simplifications, their simulation results have yielded concentration profiles matching the experimental data. In order to examine the robustness of the present model and to check whether the lumped first-order elimination can obtain quantitatively similar results with the present study, a few comparisons have been carried out. The differences in the drug concentration, ISN, and penetration depth are illustrated. Fig. 7 shows the results with different values of the lumped first-order elimination constant, k*. When k* is zero, there is no escape for the drug from the interstitial space by elimination and hence the concentration of the BCNU builds up with time. With k* not zero, BCNU is eliminated and the mean concentrations first rises and then falls. The rise is because the polymer releases BCNU faster than it is being eliminated by reaction. When k* is increased to 100-fold, the peak disappears as the elimination is now too fast. The pattern is now very similar to tumor implantation used in the present model. Therefore, the temporal evolution of drug distribution depends highly on the value of k*. The effect of k* on the penetration distance is equally substantial. With the rate constant k*, the maximum penetration distance reaches nearly 15d p before falling to about 10d p at 250 h (d p refers to the diameter of polymer cylinder). The same trend is seen when k* is increased by 10 times, except that the maximum penetration distance is now only about 3.5d p . When k* is multiplied by 100, the penetration distance is nearly constant at 1d p , reminiscent of the

35

present model. This is because BCNU is eliminated so fast that it does not have sufficient time to diffuse through the tumor tissues. Fig. 7c shows the variation of penetration distance with time. To capture the nature of the system in a better manner, k* may include the effect of transcapillary exchange and the intracellular kinetics. Between these, the transcapillary term is the more important one as it is the dominant term in the case of BCNU, as discussed in the previous sections. Under such circumstances, it is imperative that the k* used is able to describe the dominant term accurately. In situations where all terms of transcapillary exchange and intracellular kinetics are equally important, detailed modeling would be more suitable.

3.7. Three-dimensional simulation The first two cases studied are the polymer in the viable zone and the core of the tumor. The aim is to study the effect of polymer location on the BCNU ] distribution. Fig. 8a shows C distribution for the case ] of polymer in the viable zone of tumor. All C values ] decrease with time, with C in the viable zone being the highest, followed by that of normal tissues and necrotic core. ISN in the viable zone is the highest of all three ISNs (Table 2). Simulation results of ] polymer in the core case are shown in Fig. 8b. C in the core is about two orders of magnitude higher ] than that of other regions and all C values decrease with time. Since there is no systemic circulation in the core, BCNU molecules that are trapped in the core gradually diffuse into the viable zone and then into the normal tissues. Because of the fast drainage ] of drug into the blood vessels, C values in the viable zone and normal tissue are much lower than that in the core. ISN of viable zone is the highest followed by that of core (Table 2). ISN of normal tissue remains at a low value. Another case studied is the surgical model that shares the same geometry as the other two cases described in this section except that 80% of the tumor is removed through surgery. This case is modified from the Gliadel  wafer treatments [8,9]. Polymer matrices are applied to the lumen of recurrent brain tumors immediately after surgery. The ‘surgical model’ presented here is used to simulate the drug distribution after polymer implantation.

36

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

] Fig. 7. Lumped first-order model with different values of k: (a) C, (b) ISN and (c) penetration depths.

These simulation results may be used to generate information on the optimization of the treatment for surgeons before operation. ] Fig. 8c shows the temporal evolution of C in the surgical model. Since necrotic core has been totally ] removed through surgery, it shows only the C values of the remaining viable zone and the surrounding

normal tissues. Similar to the case of polymer in the ] ] viable zone, all C values decrease with time, with C in the viable zone being higher than that of the normal tissues. The BCNU concentration in the normal tissues is high enough to cause local toxicity. However, the overall systemic toxicity is greatly reduced since the release is localized. Similar to

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

37

Fig. 8. Mean concentrations for the case of: (a) polymer in the viable zone; (b) polymer in the necrotic core; and (c) surgical model.

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

38

Table 2 Mean ISN values for the cases of polymer in core, viable zone and the surgical model Polymer in core

Polymer in viable zone

Surgical model

Tissue

Tumor

Core

Tissue

Tumor

Core

Tissue

Tumor

0.001

0.2

0.025

0.001

0.2

0.1

0.001

0.04

polymer in the viable zone case, ISN in the viable zone is the highest and that in normal tissue remains at a lower value (Table 2). The time-averaged BCNU mean concentration is 93% of that in tumor implantation. The lower BCNU concentration can be attributed to the dilution factor as the polymer is now grafted unto the entire inner lumen and not implanted in a single zone like before. However, the mean BCNU concentration in the normal tissue is nearly halved. This means that the normal tissues are not exposed to higher BCNU concentration while maintaining a similar BCNU concentration in the tumor. Therefore, the surgical model suggests a better method of polymer-based treatment. From the ISN values, it is even more advantageous to use the surgical model. The ISN values in the tumor are on an average only 20% of the ISN values in the tumor implantation, since BCNU can now diffuse into the normal tissues from many sites. This indicates much greater uniformity in the spatial distribution of the drug. The ISN values for the normal tissues are about 104% of those in tumor implantation. Given the short penetration of BCNU, most of the BCNU would be absorbed by either the tumor tissues or blood circulation before reaching the normal tissues. The temporal evolution of BCNU is shown in Fig. 9 where the tumor is ‘cut’ through the centre to illustrate the interior concentration distribution. The mean concentration decreases with time and becomes insignificant after t.250 h. Here, different color refers to different level of BCNU concentration. In interpreting these results, one needs to recall that the velocity field is assumed to reach a steady state a short while after the surgical operation. Upon the completion of surgical operation, the interstitial pressure in the viable zone of tumor is the highest, and hence the interstitial fluid flows towards both normal tissues (outward flow) and the surgical cavity (inward flow). This trend continues until the interstitial fluid in the surgical cavity has reached equilib-

rium with the viable zone and a new steady state in the flow field is established. BCNU release kinetics (from polymer carriers) also has finite effect on its delivery to brain tumors. The present study assumes that the released drug is well mixed, and hence the concentration gradient in the cavity fluid is neglected. Based on the in vivo data by Yang et al. [7], the transient BCNU flux is calculated by the overall mass conservation of drug molecules in the cavity. The post-surgery chemotherapy is achieved by the sustained exposure between a ‘drug-rich’ fluid and the viable zone of the tumor.

3.8. Clinical implications The simulation results provided in the present study are based on the controlled drug release from a non-biodegradable polymer. These are certainly different from the Gliadel  wafer treatments which are based on biodegradable polymers. The successful Gliadel  wafer treatments on malignant glioma were shown to improve the 6-month survival rate of recurrent patients from 47 to 60%, and the 12-month survival rate of primary patients from 19 to 63% [9]. It is anticipated that the patients with different size of brain tumors may require significantly different drug dosage in their treatments. The optimal treatment is achieved by allowing most of the viable zone exposed to a drug concentration higher than the therapeutic level, concurrently, the leakage of drug to the surrounding normal tissue is less than a prespecified toxic level. This is indeed an optimization problem with multiple constraints. The simulation model presented in this work provides some insight into the optimization of drug dosage form in the Gliadel  wafer treatments. Any such application that has the potential of improving the patient survival rate under Gliadel  wafer treatments is certainly of significant clinical value and deserves further research work.

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

39

Fig. 9. Temporal evolution of drug concentration: (a) t51 h, (b) t550 h, (c) t5100 h, (d) t5150 h, (e) t5200 h and (f) t5250 h.

40

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41

4. Conclusions Simulation studies on BCNU delivery to tumors have been conducted. Compared with systemic bolus injection, controlled release from polymer can give higher local BCNU concentration for a longer time and with reduced systemic toxicity. The penetration depth of BCNU depends significantly on the transvascular permeability, and it is much smaller than that of IgG. Intracellular kinetics can decrease the overall BCNU concentration, and its reduction rate depends on the effective rate constant. Interstitial convection plays only a small role in BCNU distribution in the tumor and its elimination from the tumor via the capillaries. This is drastically different from the delivery of macromolecules where the contribution by convection is significant. The surgical model indicates that grafting BCNU / EVAc to the sides of the lumen after the surgery is more effective than implanting the polymer without removing any part of the tumor. This work also generates quantitative analysis to explain why the Gliadel  wafer treatment is preferred over traditional chemotherapy. In this study, a steady flow field was assumed to calculate the transient drug concentration distribution. This may not be the case in actual growing tumors. Hence, if possible, we should examine the effect of unsteady flow field. Very often, the treatment for cancer involves using a ‘cocktail’ of drugs. The model can be further extended to other potential anticancer agents by simulating a combination of two or more drugs instead of just one.

Acknowledgements This work has been supported by National Medical Research Council under grant number NMRC / 0232 / 1997 (RP970658). We also thank Kamalesh Sengothi, Theodore Chen and Dr Suryadevara Madhusudana Rao for their technical support.

References [1] G.A. Taylor, T.W. Goodman, A.S. Rall, P. Nies, in: Goodman Gilman’s The Pharmacological Basis of Therapeutics, 8th ed., Macmillan, New York, 1990, p. 1221.

[2] R.G. Blasberg, C. Patlak, J.D. Fenstermacher, Intrathecal chemotherapy: brain tissue profiles after ventriculocisternal perfusion, J. Pharmacol. Exp. Ther. 195 (1975) 73–83. [3] K.W. Leong, B.C. Brott, R. Langer, Bioerodible polyanhydrides as drug-carrier matrices. I. Characteristics, degradation, and release characteristics, J. Biomed. Mater. Res. 19 (1985) 941–955. [4] K.W. Leong, P. D’amore, M. Marletta, R. Langer, Bioerodible polyanhydrides as drug-carrier matrices. II. Biocompatibility and chemical reactivity, J. Biomed. Mater. Res. 20 (1986) 51–64. [5] R.J. Tamargo, J.I. Epstein, C.S. Reinhard, M. Chasin, H. Brem, Brain, Biocompatibility of a biodegradable, controlled-release polymer in rats, J. Biomed. Mater. Res. 23 (1989) 253–266. [6] R.J. Tamargo, J.S. Myseros, J.I. Epstein, M.B. Yang, M. Chasin, H. Brem, Interstitial chemotherapy of the 9L Gliosarcoma: Controlled release polymers for drug delivery in the brain, Cancer Res. 53 (1993) 329–333. [7] M.B. Yang, R.J. Tamargo, H. Brem, Controlled delivery of 1,3-bis(2-chloroethyl)-1-nitrosourea from ethylene-vinyl-acetate copolymer, Cancer Res. 49 (1989) 5103–5107. [8] H. Brem, S.P. Piantadosi, C. Burger, M. Walker, R. Selker, N.A. Vick, K. Black, M. Sisti, S. Brem, G. Mohor, P. Muller, R. Morawetz, S.C. Schold, Placebo-controlled trial of safety and efficacy of intraoperative controlled delivery by biodegradable polymers of chemotherapy for recurrent gliomas, Lancet 345 (1995) 1008–1012. [9] Guilford Pharmaceuticals, Gliadel  wafer summary (1995 and 1996). [10] V.A. Levin, J. Stearns, A. Byrd, A. Finn, R.J. Weinkam, The effect of phenobarbital pre-treatment on the antitumor activity of 1,3-bis(2-chloroethyl)-1-nitrosourea (BCNU), 1-(2chloroethyl)-3-cyclohexyl-1-nitrosourea (CCNU) and 1-(2chloroethyl)-3-(2,6-dioxo-3-piperidyl-1-nitrosourea (PCNU), and on the plasma pharmacokinetics and biotransformation of BCNU, J. Pharmacol. Exp. Ther. 208 (1979) 1–6. [11] W.M. Saltzman, M.L. Radomsky, Drugs released from polymers: diffusion and elimination in brain tissue, Chem. Eng. Sci. 46 (1991) 2429–2444. [12] C.H. Wang, J. Li, Three-dimensional simulation of IgG delivery to tumors, Chem. Eng. Sci. 53 (20) (1998) 3579– 3600. [13] L.K. Fung, M. Shin, B. Tyler, H. Brem, M. Saltzman, Chemotherapeutic drugs released from polymers: Distribution of 1,3-bis(2-chloroethyl)-1-nitrosourea in the rat brain, Pharm. Res. 13 (5) (1996) 671–682. [14] L.K. Fung, M.G. Ewend, A. Sills, E.P. Sipos, R. Thompson, M. Watts, M. Colvin, H. Brem, M. Saltzman, Pharmacokinetics of interstitial delivery of carmustine, 4-hydroperoxycyclophosphamide, and paclitaxel from a biodegradable polymer implant in the monkey brain, Cancer Res. 58 (1998) 672–684. [15] S.A. Grossman, C. Reinhard, M. Colvin, M. Chasin, R. Brundrett, R.J. Tamargo, H. Brem, The intracerebral distribution of BCNU delivered by surgically implanted biodegradable polymers, J. Neurosurg. 76 (1992) 640–647.

C.-H. Wang et al. / Journal of Controlled Release 61 (1999) 21 – 41 [16] R. Ferszt, S. Neu, J. Cervos-avarro, J. Sperner, The spreading of focal brain edema induced by ultraviolet irradiation, Acta Neuropathol. 42 (1978) 223–239. [17] U. Groger, P. Huber, H.J. Reulen, Formation and resolution of human peritumoral brain edema, Acta Neuropathol. Suppl. 60 (1994) 373–374. [18] S. Kalyanasundaram, V.D. Calhoun, K.W. Leong, A finite element model for predicting the distribution of drugs delivered intracranially to the brain, Am. J. Physiol. 273 (1997) R1810–1821. [19] Fluid Dynamics International, Inc. (1995) FIDAP User Manual. [20] R.K. Jain, L.T. Baxter, Mechanisms of heterogeneous distribution of monoclonal antibodies and other macromolecules in tumors: significance of elevated interstitial pressure, Cancer Res. 48 (1988) 7022–7032. [21] L.T. Baxter, R.K. Jain, Transport of fluid and macromolecules in tumors. I Role of interstitial pressure and convection, Microvasc. Res. 37 (1989) 77–104. [22] L.T. Baxter, R.K. Jain, Transport of fluid and macromolecules in tumors. II Role of heterogeneous perfusion and lymphatics, Microvasc. Res. 40 (1990) 246–263.

41

[23] M. Kaviany, in: Principles of Heat Transfer in Porous Media, Springer, New York, 1991, pp. 62–64. [24] K. Fujimori, D.G. Covell, J.E. Fletcher, J.N. Weinstein, Modelling analysis of the global and microscopic distribution of Immunoglobulin G, F(ab9) 2 and Fab in tumors, Cancer Res. 49 (1989) 5656–5663. [25] K. Hori, M. Suzuki, I. Abe, S. Saito, Increased tumour tissue pressure in association with the growth of rat tumours, Jpn. J. Cancer Res. 77 (1986) 65–73. [26] D. Hilmas, E.L. Gilette, Morphometric analyses of the microvasculature of tumors during growth and after Xirradiation, Cancer 33 (1974) 103–110. [27] J.R. Pappenheimer, E.M. Renkin, L.M. Borrero, Filtration, diffusion and molecular sieving through peripheral capillary membranes: A contribution to the pore theory of capillary permeability, Am. J. Physiol. 82 (1951) 13–46. [28] L.E. Gerlowski, R.K. Jain, Microvascular permeability of normal and neoplastic tissues, Microvasc. Res. 31 (1986) 288–305.