CRC Targeting and Imaging Group, Department of Oncology, Royal Free and University College Medical School, University College London, London, United Kingdom
CRC Targeting and Imaging Group, Department of Oncology, Royal Free and University College Medical School, University College London, Royal Free Campus, Rowland Hill Street, London NW3 2PF, United Kingdom===
The effectiveness of radioimmunotherapy (RIT) is known to depend on at least six factors: total absorbed dose and pattern of delivery, radiosensitivity, rate of repair of sublethal damage, ongoing proliferation during treatment, tumor heterogeneity, and tumor size. The purpose of this study was to develop a mathematic model that would relate the absorbed dose and its pattern of delivery to tumor response by incorporating information on each factor. This model was used to optimize therapeutic efficacy in mice by matching the antibody and radionuclide characteristics while ensuring recoverable marrow toxicity.
Pharmacokinetic data were acquired in mice for a range of antibodies that varied in molecular weight, specificity, affinity, and avidity, and for a range of tumor sizes. This information was combined with the properties of iodine-131, rhenium-86, and yttrium-90 to determine the pattern of dose delivery. Tumor response was characterized in terms of radiosensitivity, rate of repair, and proliferation. Values for these parameters were obtained from in vitro assays and were incorporated into a response model based on the linear-quadratic model. Storage phosphor plate technology was used to acquire images of antibody distribution in tumor sections. These were registered with corresponding images showing tumor morphology, which were subsequently used to delineate regions that were distinct in terms of their response to radiation: oxygenated, radiosensitive areas that contained viable cells and hypoxic areas containing resistant viable cells and necrotic cells. Beta point dose kernels were then used to estimate the absorbed dose distribution in these regions.
Therapy in normoxic areas was more effective than in hypoxic areas. The multivalent, tumor-specific antibodies, with intermediate clearance rates, delivered the highest absorbed dose to viable tumor cells. Antibody affinity and avidity facilitated the prolonged retention in radiosensitive areas of tumor, where most of the dose was deposited. The effectiveness of therapy could be enhanced further by matching the radionuclide with the antibody and tumor size.
Traditionally, the estimation of the absorbed dose has been used to characterize the biologic effect of radioimmunotherapy (RIT) in tumor and normal tissues.1, 2 However, the interaction between the physical absorbed dose and the subsequent biologic response is complex and dependent on numerous interrelated factors. This is emphasized by the finding that the efficacy of RIT is extremely dependent on tumor type.3, 4 Therefore, the measurement of a single parameter is unlikely to be an adequate method to characterize or predict the biologic effect. Rather, the interpretation of biologic effect requires the consideration of numerous parameters, some of which are addressed in this study.
Radiosensitivity may be described by two coefficients in the linear-quadratic formula,5 α and β, which describe the respective probabilities of cell death from a single radiation event and cell death from the interaction of two independent sublethal events. The ratio α/β then gives a measure of the proportion of lethal to repairable damage. Radiosensitive tissues have large values of α/β, which result in a high proportion of lethal damage following irradiation. As a result, RIT has achieved some impressive responses in sensitive tumors such as lymphomas,6 while the relative resistance of colorectal tumors has proved to be a major obstacle to successful therapy.7 This is also true for normal tissues; those with a large α/β ratio, such as bone marrow, tend to be major dose-limiting tissues.
Low values of α/β also indicate a higher proportion of repairable damage, and the tissue response becomes more dependent on dose rate. Typically, this is the case in normal tissues (with the exception of bone marrow) and also in radioresistant tumors that are spared when the dose rate is reduced. When the dose rate is low, the rate at which sublethal damage is repaired may become important, and tissues that repair quickly are less likely to have an accumulation of sublethal damage. In RIT, radiation is generally delivered at low dose rates, causing a considerable reduction in the biologic effect, particularly in resistant tissues that repair rapidly.
Another important consideration when interpreting the biologic effect of RIT is the rate of proliferation of tumors and normal tissues. As dose rates are low and treatment times are frequently long, a large proportion of the delivered dose may be expended in just overcoming proliferation.8 In order to reduce the cell number, the dose rate must be higher than the critical value that equilibrates proliferation. Proliferation rates vary greatly between different tumor types,9 and consequently so does the required critical dose rate.
Other factors that are known to influence therapeutic efficacy are the tumor size and heterogeneity. Large tumors are more difficult to treat effectively, as they contain more cells, while in small tumors much of the disintegration energy may escape due to the range of the emitted particle.10 Therefore, for any tumor size there is an optimal therapeutic radionuclide that increases the likelihood of effective therapy.11 Furthermore, as tumors start to outgrow their blood supply, the delivery of essential nutrients, such as oxygen and glucose, becomes increasingly inadequate. This creates cell populations that are more resistant in terms of their radiobiologic response. The systemic delivery of antibodies is also heterogeneous; antitumor antibodies preferentially localize in the well-perfused, radiosensitive areas, while nonspecific antibodies penetrate into the necrosis. In addition to the influence of antibody characteristics, the degree of heterogeneity of dose delivery is also dependent on the range of emission from the radionuclide.12
Clearly, the pattern of dose delivery and the heterogeneity of dose deposition and response are important factors when interpreting the biologic effect. This is of particular relevance in RIT, where the variation in dose rate and the heterogeneity of dose deposition depend on the radionuclide properties and characteristics of the antibody. Any method used to compare the efficacy of RIT with different that of antibodies and radionuclides should take the variations in dose rate and heterogeneity into account.
The purpose of this study was to incorporate information on the heterogeneity of dose deposition and response in tumor into an existing model that would relate absorbed dose and its pattern of delivery to biologic effect through response parameters (radiosensitivity, repair capacity, and proliferation). This model was then used to compare the efficacy of a range of antibodies and radionuclides in both radiosensitive and radioresistant areas of colorectal tumors in mice, and to investigate the influence of tumor size on efficacy while ensuring recoverable damage to bone marrow.
Antibody kinetics were described by a simple three-compartment model, representing blood, radiosensitive areas of tumor, and radioresistant areas of tumor (Fig. 1). The flow between compartments was defined by the flow rate constants. The concentration at any time (t) of antibody in blood [B(t)] and in radiosensitive [T1(t)] and radioresistant areas [T2(t)] was given by
where λB was the clearance rate from blood and λ1, λ2, λ3, and λ4 were the flow rate constants from the tumor compartments. Solving these simultaneous equations gave the mathematic form for the antibody kinetics in each compartment. Combining this information with the physical decay properties of the radionuclide enabled the calculation of the activity [A(t)] in each compartment. The dose rate in each compartment was given by
where S was the mean dose rate per unit activity (Gy Bq−1 s−1).
The response model was based on the linear-quadratic formula and the concept of the biologically effective dose (BED) (5) where the surviving fraction [S(t)] was given by
where RE(t) was the relative effectiveness and P(t) was given by13
where Tpot was the potential doubling time of the tumor (hr) and (dD(t)/dt)crit was the critical dose rate. When the actual dose rate reached the critical dose rate, net cell sterilization ended and the treatment was effectively over.
Materials and Methods
The monoclonal antibody A5B7 was used to produce the F(ab′)2 and Fab fragments by enzymatic digestion.1 Divalent (DFM) and trivalent (TFM) antibodies were produced by chemically cross-linking the Fab fragments of A5B7 using a maleimide linker.1 MFE-23 is a genetically engineered scFv produced by phage technology,14 consisting of the variable light and heavy chain, and is the smallest antibody fragment that retains full binding capacity. These antibodies bind to the cell surface antigen, carcinoembryonic antigen (CEA), and are not internalized into the cell. Two control antibodies were also used in this study: MOPC,15 a non-CEA-binding monoclonal immunoglobulin (Ig)G, and NFE, a non-CEA-binding scFv, created by inserting a point mutation into the antigen recognition site in MFE-23.16 The values of affinity, valency, and molecular weight for these molecules are shown in Table 1. Purification of all antibodies, except MFE-23 and NFE, was carried out by affinity chromatography using Protein A followed by gel filtration. MFE-23 and NFE were purified by immobilized metal ion chromatography (IMAC). Purity was confirmed using sodium dodecyl sulfate–polyacrylamide gel electrophoresis.
Table 1. Characteristics of the Antibodies Used in This Study
All antibodies were labeled with 125I to a specific activity of 60 kBq/μg. IgG, F(ab′)2, Fab, DFM, TFM, and MOPC were labeled using the chloramine T method, while MFE-23 and NFE were labeled using the iodogen method. Both labeling methods resulted in efficient incorporation of the radionuclide without reducing antigen-binding capacity.1, 17 Each radiolabeled antibody was sterilized by passage through a 0.22-μm acrodisc filter (Gelman Sciences, Northampton, United Kingdom). The percentage of incorporation of the isotope was determined by thin-layer chromatography, and the immunoreactivity of the labeled product was confirmed by applying a dilution to a CEA affinity column and measuring the percentage bound.
The human colorectal CEA–expressing adenocarcinoma cell line LS174T was grown subcutaneously as a xenograft model in the flanks of nude mice. Each radiolabeled antibody was administered via the tail vein when the tumors reached 0.5–1.0 cm3, and the mice were culled at selected time points after administration by cervical dislocation. There were four mice for each time point, and each mouse weighed approximately 20–25 g.
Tumors were fixed in 10% neutral formalin for 48 hours, processed to paraffin wax, and sectioned at 3 μm. Multiple sections were cut, dewaxed in inhibisol, and exposed on Molecular Dynamics (MD) phosphor plates (Molecular Dynamic Ltd., Chesham, United Kingdom), and the images were analyzed using MD ImageQuant and Interactive Data Language software. After scanning, all tissue sections were stained with hematoxylin and eosin to compare radiolabeled antibody distribution with tissue morphology. The stained sections were digitized using a Minolta RD175 digital camera mounted on an Axioskop microscope (Zeiss Ltd., Welwyn Garden City, United Kingdom), and reconstructed to form a composite image.
Before and after use, remaining images and background noise were erased from storage phosphor plates using the MD Image Eraser. The tumor sections were placed on the imaging plates. Intimate contact was achieved by using MD Exposure Cassettes. The latent images formed were converted to quantitative digital images using a MD 425 PhosphorImager. Background noise was subtracted from the image.
Each radioluminograph (RLG) and corresponding stained histologic section was registered using the cross-correlation method.18 This allowed accurate delineation of histologic features by defining regions of interest (ROIs).
Histologic examination of the tumor sections showed that each section could be easily delineated into two major zones: the first zone contained mostly viable, normoxic tumor cells, and the second mostly necrotic tumor cells (Fig. 2). This ROI was then copied onto the same position on the RLG. Pixel values were grouped for multiple sections from each tumor and also for separate necrotic or viable areas within each section. This enabled the calculation of the mean pixel value in viable areas relative to necrosis, which equated to the ratio of antibody concentration in viable relative to necrotic areas. For the purpose of this study, the pixel values in hypoxic areas were grouped with those in the necrosis.
The activity distribution was then represented by using a spheric tumor model19 that comprised a viable rim surrounding a central hypoxic or necrotic core. The total activity [A(t)] at any time point in the tumor was given by
where A0 was the injected activity, P(t) was the percentage of the injected activity per gram of tumor taken from previous biodistribution studies,20 and mt was the mass of the tumor (assuming a density of 1g/cm3). The activity distribution in tumor was constrained so that the activity per unit volume in the viable region relative to that in the necrosis was equal to the ratio of the antibody concentration in each region as given by the radioluminographs. The dose rate in the viable region relative to necrosis was then estimated using a dosimetry model for tumor.19
The total number of cells (N) in each region was given by the volume of the region divided by the cell volume, 15 μm3. For this purpose it was necessary to separate the hypoxic from the necrotic cells. Hypoxic cells were assumed to occupy a shell with a thickness of 300 μm (the difference between the diffusion ranges of glucose and oxygen21) between the viable and necrotic areas.
Biologically Effective Dose
BED in tumor and bone marrow was calculated for each antibody, along with iodine-131 (131I), rhenium-186 (186Re), and yttrium-90 (90Y). The antibody kinetics in marrow were assumed to follow those in blood where the pharmacokinetic model parameters, λ2 and λB in Equation 1, were obtained by fitting the model to the blood data. This was achieved using a nonlinear optimization procedure. The dose rate in marrow was then given in Equation 4, where the activity was assumed to be 0.36 times that in blood.22 The ratio of activity in marrow relative to blood is not constant and is known to vary by as much as 0.2–0.68. The value used in this study was the average from bone marrow biopsies from patients. S values for bone marrow were taken to be 1.7 × 10−11 Gy Bq−1 s−1, 1.17 × 10−11 Gy Bq−1 s−1, and 8.52 × 10−12 Gy Bq−1 s−1 for 131I, 186Re, and 90Y, respectively, and accounted for the contribution due to radioactivity in the rest of the mouse.23 The injected activity A0 was constrained so as to cause the same biologic effect at the nadir of cell population in marrow. The time at which the nadir of marrow survival (tnadir) occurred was given by setting the dose rate function equal to the critical dose rate and solving for t.
BED(tnadir) remained constant between antibodies and radionuclides and was set at a level that is known to cause recoverable marrow toxicity. In a previous experiment, 18.5 MBq of 131I-A5B7-IgG was injected into mice and caused a 10% weight loss and a reduction in white blood cell count to 30% of the pretreatment value before full recovery.2 In this case, BED(tnadir) was 2.28 Gy.
The injected activities were used to generate the dose rate functions in tumor. In normoxic tumor areas, the time at which the treatment ended (tmin) was given by setting the actual dose rate function to the critical dose rate given the value of the potential doubling time (Tpot). Any remaining hypoxic cells at tmin were assumed to be capable of reoxygenation and ultimately led to treatment failure.
By assuming that the probability of cell death from two separate sublethal interactions was related to the product of the dose rate function and a monoexponential repair function, and following the same derivation as Dale,24 expressions for RE(t) in marrow and in the normoxic and hypoxic areas of tumor were derived. The dose at time t [D(t)] was given by the integral of the dose rate function. The parameters describing response in marrow, normoxic tumor, and hypoxic tumor are given in Table 2. In hypoxia, the linear-quadratic coefficients were given by α/OER and β/(OER2),29 where OER was the oxygen enhancement ratio and was taken to be 2.5.30
Table 2. Radiobiologic Parameters
Superscript numbers refer to Howell et al.,25 Thames et al.,26 Dearling et al.,27 and Sharda et al.28
Assuming Poisson statistics, the probability of cure in each compartment was given by
where N0 was the initial number of cells and tfinal was the time at which the minimum surviving fraction occurred.
Registration of images of antibody distribution (Fig. 2A) and morphology (Fig. 2B) enabled the delineation of viable (V) and necrotic (N) areas. The degree of heterogeneity of antibody distribution in tumor varied depending on the antibody characteristics, with the most influential factors being specificity and valency. Specific antibodies preferentially localized in the viable radiosensitive areas at early time points, while nonspecific antibodies penetrated into the necrotic center. The highest ratio of antibody concentration in normoxic areas relative to necrotic areas was given by the trivalent antibody (Fig. 3). This ratio remained high longer than other antibodies but reduced over time and eventually became less than unity. Bivalent antibodies gave the next highest ratios, which again reduced over time. These were followed by the monovalent antibodies, which were retained less effectively in viable areas while the nonspecific antibodies showed no retention.
When information on the antibody kinetics in each tumor compartment were combined, compartment dimensions and the properties of the radionuclide gave the pattern of dose delivery. Figure 4 shows a typical dose rate function for a specific antibody where the dose rate was highest in viable areas but fell with the biologic clearance of the antibody and physical half-life of the radionuclide. At late time points, the dose rate in necrosis was higher than that in the viable areas.
Figure 5 shows the probability of achieving cure (Pc) in the radiosensitive and radioresistent areas of tumors, which ranged from 2 to 10 mm in radius for each antibody and radionuclide. When using 131I [Fig. 5a(i)], the trivalent antibody was effective in the normoxic areas, although there was evidence of a reduction in effect for large tumors. The bivalent antibodies, DFM and F(ab′)2, were effective over the entire range of tumor sizes, while the IgG was effective in the range of 3–4 mm with a reduction in effect either side of these values. The monovalent and nonspecific antibodies were ineffective.
In hypoxic areas [Fig. 5A(ii)], the trivalent antibody was ineffective and the bivalent antibodies, DFM and F(ab′)2, were effective in very small tumors only. There was little likelihood of the IgG curing these resistant cells and a negligible chance of the monovalent and nonspecific antibodies producing a cure.
Substituting the characteristics of 186Re [Fig. 5B(i)] resulted in a similar pattern, although the range of tumor sizes over which the therapy was most effective shifted toward larger tumors. The trivalent and bivalent antibodies eradicated all radiosensitive cells. Also, the monovalent antibodies that were ineffective with 131I became more effective with 186Re, although the effect of MFE-23 remained small. Again, the nonspecific antibodies elicited little response. In the hypoxic region, the DFM and F(ab′)2 were the best performers, and the range over which the therapy was effective was extended. Other antibodies produced little effect.
There was a further shift in the optimum range of tumor sizes when 90Y was used [Fig. 5C(i)]. Again, the trivalent and bivalent antibodies were most effective. However, there was a sharp decrease in effect in very small tumors. The monovalent and nonspecific antibodies were ineffective. In hypoxic areas, only the bivalent DFM produced any significant effect, although there was a considerable increase in the range at which this occurred [Fig. 5C(ii)].
The efficacy of RIT is dependent on numerous factors and cannot be assessed accurately by measuring a single parameter, such as the absorbed dose. We have used a mathematic model to relate the absorbed dose and pattern of delivery during RIT to the biologic effect by incorporating information on radiosensitivity, repair capacity, and proliferation. This model was extended to account for the heterogeneity of dose deposition and response in tumors. We used the model to assess the efficacy of a range of antibodies and radionuclides in radiosensitive and radioresistant areas of colorectal tumors in mice.
We used radioluminography to acquire experimental data on the extent of heterogeneity of antibody distribution within tumors. Tumor-specific antibodies preferentially localized in the well-perfused, radiosensitive areas rather than penetrating into the tumor. The extent of this effect was largely dependent on the valency of the antibody; the trivalent antibody was retained for longer and at higher concentrations in the viable areas, while the monovalent antibodies had increased mobility. This effect was primarily due to increased likelihood of an antibody interacting with an antigen near the blood supply, and the chance of this interaction increased with the number of binding arms of the antibody. As the antibody cleared from the blood, accretion in tumor stopped and the net flow was from the viable areas back into the circulation. As a result, the antibody concentration in viable areas fell below that in necrotic areas, as the antibodies could escape more readily from viable areas. In contrast, the nonspecific antibodies were not retained in viable areas, but penetrated into the necrosis, where there was an increased concentration at all times.
The TFM with 131I was effective in the radiosensitive areas of tumor over the entire range of tumor sizes. However, there was a slight decrease in effect at the largest tumor size. Indeed, this would continue to decrease due to the increase in cell number with larger tumors. The bivalent antibodies, DFM and F(ab′)2, were the most effective in normoxic areas due to the high injected activities and efficient localization and retention in those areas. The bivalent IgG was effective over a limited range due to the lower injected activity. Monovalent and nonspecific antibodies were ineffective in these areas because of low levels of accretion.
In hypoxic areas, the effect was drastically reduced due to the increased radioresistance of hypoxic cells. The trivalent antibody was ineffective, due also to its lack of penetration into the tumor and the limited injected activity caused by the long circulating half-time. Bivalent antibodies were effective in very small tumors only (∽1 mm radius), with DFM the most effective. Again, the monovalent and nonspecific antibodies had little likelihood of sterilizing all hypoxic cells.
The increased range of the emitted electron from 186Re caused a shift in the range of tumor sizes that were treated effectively toward larger tumors. The trivalent and bivalent antibodies were effective over the entire range and the monovalent antibodies became more effective in normoxic cells. The general increase in efficacy was probably due to the radionuclide half-life's complementing the antibody pharmacokinetics in tumor, where there was a higher dose rate effect while the antibody localization was high. The range of tumor sizes in which the hypoxic regions were effectively treated also increased. Again, the influence of dose rate was evident, but also a greater proportion of the beta energy emitted from the high-activity viable areas was absorbed in hypoxic areas. One exception to the general increase in effect was the performance of IgG in hypoxia. Due to the long circulating half-time, the IgG continued to penetrate into the tumor, and at late time points there was more in the necrotic and hypoxic areas. At later time points, the proportion of the total dose delivered was greater with a longer-lived radionuclide, as was observed with 131I.
There was a further shift in the range of tumor sizes over which antibodies were effective when the long-range beta emitter 90Y was considered. Larger tumors were treated more effectively and there was a rapid reduction in effect in small tumors (< 2 mm) with the TFM, F(ab′)2, and IgG due to the fact that most of the emitted beta energy escaped the tumor. In hypoxia, only DFM had a major effect; again, this effect was associated with a considerable shift toward larger tumors and was most effective in tumors with a 6-mm radius. The broad reduction in effect was due to the lower injected activity imposed by the additional marrow dose caused by cross-dose between organs in mice.
In summary, we have extended an RIT response model to account for heterogeneity in tumor. This took into account both the heterogeneity of dose deposition, from antibody distribution and radionuclide emission range, and the heterogeneity of response in normoxic and hypoxic cell populations. We acquired experimental data on dose distribution and showed that this was dependent on the antibody characteristics and radionuclide properties; specific, multivalent antibodies were retained longer in the normoxic, radiosensitive areas of tumor. The model showed that hypoxic cells were most likely to lead to treatment failure. The most effective antibody was bivalent and had a good balance between localization and clearance from blood. Furthermore, choosing the antibody characteristics and radionuclide properties to suit the tumor size could optimize the efficacy in both normoxic and hypoxic areas.
In RIT, the absorbed dose and dose rate are generally not sufficient to be lethal to all tumor cells, particularly in resistant, heterogeneous tumors. Therefore, other radiobiologic factors become important, such as proliferation and repair of sublethal damage. We need to understand the interaction between these parameters in order to relate the absorbed dose to the biologic effect and to optimize RIT. The model presented in this article allows the interaction between parameters to be assessed and provides a tool for optimizing therapy in animal models and in the clinic.