Parametric Images of Antibody Pharmacokinetics Based on Serial Quantitative Whole-Body Imaging and Blood Sampling

MATERIALS AND METHODS

Data Acquisition

Patient data were obtained from a clinical trial using ¹¹¹In-labeled, biotinylated rituximab (Mabthera; Roche), a chimeric monoclonal B-cell–specific anti-CD20 antibody. Details have been published elsewhere (8). Data from 2 patients were used in this study. Patient 1 had a transformed mucosa-associated lymphoid tissue lymphoma, stage III, originating in the stomach, with tumor manifestations in the mediastinum, abdomen, and retroperitoneal nodes, which were enlarged. Patient 2 had a transformed follicular lymphoma, stage III, with enlarged cervical, retrocrural, paraaortic, iliac, and inguinal nodes and with the hepatoduodenal ligament affected. The activity administered to patients 1 and 2 was 156 and 153 MBq, respectively, measured in a calibrated well chamber (CRC-15; Capintec). The labeling efficiency was determined by instant thin-layer chromatography and high-performance liquid chromatography to be 93% and 97% for patients 1 and 2, respectively. The labeling procedure also included a step in which diethylenetriaminepentaacetic acid (DTPA) was added to bind any free ¹¹¹In. Blood samples were collected at 5 and 45 min and at 3, 6, 24, 48, 72, 144, and 168 h after injection. The samples were weighed, and the activity was measured in a calibrated well-type NaI(Tl) detector (1282 CompuGamma CS; Wallac). Anteroposterior whole-body images were acquired on 6 occasions: 1, 24, 48, 72, 144, and 168 h after injection (Fig. 1). A dual-head SPECT system equipped with an x-ray unit for simultaneous anatomic imaging (Discovery VG; GE Healthcare) was used. Imaging was performed in a 15% energy window centered over the ¹¹¹In 245-keV photopeak, in a 256 × 1,024 matrix with a pixel width of 2.2 mm. A transmission image used for pixel-based attenuation correction was also acquired using the x-ray unit in scanogram mode. Based on the geometric mean of anteroposterior images, activity images were calculated in units of Bq/pixel (16). Images were registered at several steps for quantifying activity and for coaligning the time series of the images. The registration method was designed for whole-body images and included nonrigid transformations for each leg, the trunk, the shoulders, and the head, with mutual information as a similarity measure (15).

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FIGURE 1. 

Image data for patient 1. (A) Attenuation map obtained from CT scanogram image. (B) Geometric mean of anteroposterior raw-count images, showing 3 of total of 6 images, acquired at 1.5, 48, and 163 h after injection. (C) Quantitative images in units of MBq/pixel spatially registered to attenuation map.

RESULTS

For the blood curves, the biexponential function (Eq. 5) described the data well, with a correlation coefficient of more than 0.998 for both patients.

Figure 2 shows parametric images of α, K′₁, k₂, and V′_d for patient 1, resulting from the pharmacokinetic modeling. To illustrate the meaning of the parameters, Figure 3 displays these images together with plots of locations that exhibit representative time–activity curves, subjectively selected by navigating through the image. Figure 3 shows that at time zero all the activity is in the vascular space. The activity value is equal to , for example 8·10⁻⁵·156 MBq ≈ 12 Bq for Figure 4A. At early times, the extravascular activity increases. In terms of the curves, the parameter K′₁ influences the slope of the tangent to the initial part of the extravascular time–activity curve, which can be seen mathematically by setting a_ev to zero in Equation 10. As time passes, the washout from extravascular space gradually has more impact, and at about 50–100 h after injection the slope of the extravascular curve, that is, the rate of change (Eq. 10), decreases toward zero. At later times, the extravascular curve either becomes parallel to the blood curve, corresponding to smaller k₂ values, or has a negative slope, corresponding to larger k₂ values. The value of V′_d is the ratio of the extravascular to vascular activities at equilibrium and can be estimated from the diagrams as the activity ratio at late time points.

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FIGURE 2. 

Parametric images for patient 1. (A) α: fractional blood volume (−). (B) K′₁: normalized extravasation rate constant (h⁻¹). (C) k₂: rate constant of washout from extravascular to vascular space (h⁻¹). (D) V′_d: extravascular-to-vascular activity ratio at equilibrium, equal to K′₁/k₂, and closely related to volume of distribution (−). Gray scales are to right of each image, with maximum and minimum values displayed. Patient 1 had tumor in abdomen, corresponding to high-contrast region on V′_d image (D).

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FIGURE 3. 

At top, from left to right, are the parametric images α, K′₁, k₂, and V′_d, showing positions corresponding to time–activity curves for liver (A), heart (B), lung (C), kidney (D), intestinal tract (E), and tumor (F). Decay-corrected activity values from measured images are displayed as crosses. Solid line is fitted total-activity curve (a_i(t)), long dashed line is vascular activity (a_v,i(t)), and short dashed line is extravascular activity (a_ev,i(t)). Correlation coefficient was between 0.97 and 0.99, and no filtering was used for the positions marked.

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FIGURE 4. 

Distributions of measures of goodness of fit. (A) Filter width applied for successful optimization of patient 1. Black corresponds to no filtering, and white is maximum level applied (19-pixel-wide average filter). (B) Squared correlation coefficient between measured and fitted time–activity curves of patient 1; black implies high correlation. (C) Frequency histogram of filter width required for successful time–activity curve optimization of both patients.

Figure 3A displays a time–activity curve at a position in the liver. The value of K′₁ is 0.01 h⁻¹. At the later time points, the extravascular activity is higher than the vascular activity, with a V′_d of 2. Figures 3B and 3C show time–activity curves of the heart and lung. Both time–activity curves are dominated by the vascular compartment, with slow and low extravasation, as reflected by low values of K′₁. Figure 3D shows the time–activity curve for the cortex of the right kidney. The value of K′₁ is similar to that of the liver, but the washout rate is somewhat higher, yielding a V′_d close to 1. Figure 3E is the time–activity curve for a location selected on the basis of the increased values in the K′₁ and k₂ images. Both the extravasation and the washout rates are high, with a K′₁ of 0.2 h⁻¹and a k₂ of 0.02 h⁻¹. The location corresponds to the intestinal tract, but we still do not know the actual tissue associated with this fast turnover. Figure 3F is the time–activity curve for a location that corresponds to the abdominal tumor manifestation. It appears that this region has not yet reached equilibrium at 200 h after injection. K′₁ is high and the washout rate is low, yielding a V′_d of 35 for the chosen pixel location.

Figures 4A and 4B show distributions of the measures of the goodness of fit, that is, the level of filtering required to obtain convergence, and the squared correlation coefficient. Figure 4C shows a frequency histogram of the number of pixel time–activity curves requiring various levels of filtering. The majority of the pixels, about 80%, require no filtering to obtain convergence. About 3%–5% require average filtering using a width of up to 9 pixels, corresponding to the average from a 2 × 2 cm² neighborhood, and these pixels are primarily near the patient contour and in the distal legs (Fig. 4A). This could be due to differences in the torsion of the legs between acquisitions—differences that are not properly accounted for by image registration. The correlation coefficient (Fig. 4B) is mostly close to 1.0, although smaller values are obtained at the patient contour because of misregistration. Also noticeable are a point in the abdominal tumor region and an area in the intestinal tract on the patient's left side that exhibit rather poor values of 0.4–0.6.

Figure 5 shows 2 measured raw images and parametric images from patient 2. In general, for the normal organs of patient 2 the shapes of the time–activity curves, separated into vascular and extravascular activity components (not shown), are similar to those of patient 1. For both patients, the α image, Figures 2A and 5C, describing the distribution of blood in the body, is similar to the image obtained at the first time point (Figs. 1B and 5A), with high-intensity areas appearing in blood-rich regions such as the heart, liver, and large vessels. In the K′₁ images (Figs. 2B and 5D), high values appear along segments of the patient contour and along the edge of the liver and spleen. In regions where the activity gradient is high, any spatial misregistration between the images acquired at different time points will yield a high variability in the measured time–activity data. If the regions near the patient contour are not considered to be of interest, the value of K′₁ may be set to zero, where contour pixels are identified using the attenuation map and applying a mathematic erosion operator (22). Also, to decrease the influence of the pixels where the optimization is poor, the possibility of discriminating the pixels where the correlation coefficient is below a user-defined value is included. This procedure has been applied by setting K′₁ to zero for all pixels with a squared correlation coefficient below 0.5 in Figure 5. Furthermore, to be able to visualize V′_d for pixels where K′₁ is large while k₂ approaches zero, such as in the abdominal tumor region of patient 1 in Figure 2, the possibility of replacing k₂ by a distance-weighted average of its closest neighbors is included, accomplished by applying a morphologic closing operator (22) to the k₂ image.

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FIGURE 5. 

Patient 2. (A and B) Raw-count geometric-mean images acquired at 1.1 and 164 h after injection. (C–F) Parametric images α (C), K′₁ (D), k₂ (E), and V′_d (F), with lower limbs excluded for space reasons. Arrows a–i indicate positions at which parameter values were obtained: a = liver (α = 5 × 10⁻⁵, K′₁ = 1 × 10⁻², V′_d = 1.2), b = heart (α = 6 × 10⁻⁵, K′₁ = 6 × 10⁻³, V′_d = 0.6), c = lung (α = 1 × 10⁻⁵, K′₁ = 4 × 10⁻³, V′_d = 0.3), d = kidney (α = 2 × 10⁻⁵, K′₁ = 3 × 10⁻², V′_d = 1.4), e = intestinal tract (α = 7 × 10⁻⁶, K′₁ = 8 × 10⁻², V′_d = 3), f = paraaortic malignancy (α = 8 × 10⁻⁶, K′₁ = 9 × 10⁻², V′_d = 11), and g, h, and i = iliac, inguinal, and cervical nodes, respectively (α = 1 × 10⁻⁵, K′₁ = 5 × 10⁻², V′_d = 7–10).

Regions that exhibit homogeneous uptake patterns are distinguishable in the K′₁ and k₂ images of both patients. However, the images give the impression of being noisy, mostly because of the high variability in tissues that do not accumulate ¹¹¹In-mAb. The variability is less pronounced in the V′_d images (Figs. 2D and 5F), where the artifacts due to spatial mismatch almost disappear. Spatial mismatch and image noise due to low count values produce variability in the data points in the time–activity curves, resulting in greater uncertainty in the parameter values obtained. We have noticed that K′₁ and k₂ correlate positively and that this correlation leads to reduced variability in V′_d. For the K′₁ and k₂ images, the general intensity of the lungs is similar in the 2 patients, although there is a high variability because of image noise. The appearance of the liver is similar for the 2 patients, with values of V′_d between 1.2 and 2. Both patient images exhibit streaks of unexpectedly high K′₁ and k₂ values in the intestinal tract, although these cancel out in the V′_d image, where corresponding streaks are not seen. In both patients, the heart and kidneys exhibit V′_d values of less than 1 and around 1, respectively. Interestingly, in the V′_d image of patient 2 (Fig. 5F) the kidney (d) appears to be separated into 2 distinct areas with different kinetic rate constants, corresponding to the location of the renal pelvis and cortex. In patient 2, 4 of the sites of enlarged nodes clearly exhibit high V′_d values, indicated in Figure 5F. The shape of the time–activity curve (not shown) of the paraaortic malignancy (f) resembles the time–activity curve in Figure 3F, with a V′_d of 11 for the selected location. The cervical, iliac, and inguinal nodes (i, g, and h, respectively) present flatter time–activity curves with V′_d values of 7–10.

Figure 6 shows images of the cumulated activity separated into its vascular and extravascular components. The Ã_v images reflect the distribution of blood and appear similar for the 2 patients. The Ã_v images are essentially a scaling of the α images, because in Equation 14 that is the only quantity that varies with image position. The Ã_ev images differ for the 2 patients and appear similar to the V′_d images. For patient 1, values are increased in the abdominal tumor region and also at positions corresponding to the mediastinal tumor manifestations, which were not visualized as well on the V′_d image. For patient 2, clearly increased values are obtained in positions corresponding to the 4 enlarged nodes indicated on the V′_d image.

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FIGURE 6. 

Cumulated activity images in patients 1 (A–C) and 2 (D and E). (A) Total cumulated activity (only patient 1 shown). (B and D) Vascular component Ã_v. (C and E) Extravascular component Ã_ev. Ã_ev images exhibits high contrast values in positions corresponding to confirmed malignant regions, for patient 1 (C) in abdomen and 2 locations in mediastinum, and for patient 2 (E) at cervical, paraaortic, iliac, and inguinal nodes.

DISCUSSION

We have developed a method to calculate whole-body images of the distribution of parameter values of a 1-tissue-compartment model, and we have applied this method to data from patient studies with ¹¹¹In-mAb. We have shown that compartmental modeling on a pixel level is feasible for this type of data. This tool is good for gaining a comprehensive picture of the pharmacokinetic and for analyzing it at a pixel level without defining ROIs beforehand.

Although the method has been thoroughly tested, the quantitative parameter values presented here are not considered to be fully representative of the tissues: The specific locations were chosen only to illustrate the essence of the parametric images. In an ongoing project, histograms of rate constant distributions in selected ROIs are being quantitatively analyzed in detail and compared with SAAM II–based compartmental modeling (University of Washington). The parameter values obtained have generally been in agreement, although more evaluation remains to be done.

The K′₁ and k₂ images may be difficult to interpret individually (Figs. 2 and 5), partly because of noise and spatial mismatches that cause the optimization to converge to variable parameter values for some regions. On the V′_d images, which describe the extravasated amount of ¹¹¹In-mAb in relation to the vascular amount, the correlation found between K′₁ and k₂ leads to reduced noise. The Ã_ev images (Fig. 6) have a smoother appearance and reveal malignant regions in patient 1 that were difficult to distinguish on the V′_d image. V′_d and Ã_ev in combination are concluded to be the quantities best suited for parametric imaging for radioimmunodetection.

The images of cumulated activity also provide quantitative information on the extravascular fraction of total cumulated activity. This information may have implications for dosimetry in situations where the therapeutic effect depends on the proximity of the radiopharmaceutical to the target cells, for example, for radionuclides emitting particles with a short range. Furthermore, for dosimetric applications, parametric images can be of use for defining regions with similar kinetic behavior for a subsequent ROI-based analysis. For example, in Figure 5F, the border of the kidney is clearer than on the activity images, and separation of the cortex and pelvis in this image also appears feasible. Moreover, high-intensity regions seen in the intestinal tract in Figures 2B and 5D but not distinguishable on the activity images can be delineated and then be accounted for as an overlapping region for a subsequent ROI-based pharmacokinetic analysis of the kidneys and liver.

The current 1-tissue-compartment model, although appearing adequate for describing the pharmacokinetic in most image positions, is probably not sufficient for all tissues. Two factors in particular may make the underlying kinetics deviate from a 1-tissue-compartment model, requiring caution in interpreting the parameter values quantitatively. First, because data are obtained from planar images, the parameter values reflect the extravasation and washout rates of all tissue represented by the pixel, including activity in under- or overlying tissues. For the current study, the general background is relatively low, however, making the background kinetics less influential. Also, at least a portion of most organs is nonoverlapping and may provide representative quantitative organ rate constants. The extent to which overlap influences the bias and precision of the parameter values is currently being investigated. Furthermore, it will be of interest to implement the modeling in 3-dimensional SPECT or PET images.

Second, the underlying assumption is that extravasation and washout are governed by mechanisms that behave similarly for all tissues and organs and are linear with the supply of ¹¹¹In-mAb. For most normal tissues and organs, it is mainly passive mechanisms that are responsible for the transport. Tumors are, however, expected to be capable of binding, and in such cases the disappearance from the extravascular compartment is no longer linear with the total amount of ¹¹¹In-mAb because not all is available for washout. The parameter k₂ of the current formulation then underestimates the true washout rate by the lymphatics. Hence, the parameter V′_d becomes high and, in accordance with the high observed values, is unlikely to be due to passive transport only. Furthermore, if the binding is saturable because of a limited number of binding sites, the kinetics become nonlinear. A model description that separates the extravascular compartment into a free compartment and a bound compartment (including saturation) would probably be more appropriate for describing the kinetics of the tumors, as is seen in Figure 4B, in which 2 regions, one near the abdominal tumor and another in the intestinal tract, show low correlation values. Likewise, in Figures 3E and 3F one can envisage that a more complex model would have provided a better fit at later time points. However, at this stage, and given the few data points, the current model was chosen to obtain stability.

A special concern in mAb parametric imaging is that turnover is comparatively slow, on the order of days or even weeks. Parametric imaging in general has been applied mostly in situations where the physiologic process of interest is relatively fast, so the sequential imaging can be performed with the patient in position. Calculation of mAb parametric images requires registration of the images from different time points. A potential source of error is then spatial mismatch, which causes inaccurate parameter values, particularly at locations with a pronounced signal gradient. The registration method applied has shown good accuracy (15), and visual inspection of the registrations shows that generally they appear to be accurate. However, organ movement within the body is not accounted for and generates mismatch errors, for example, the rim at the top of liver in Figures 2B and 5D.

Concerning optimization, convergence is reached for about 80% of the pixel positions without filtering (Fig. 4). However, the advantage of gradual filtering is that parameter values are obtained for all pixels, thus producing a better image quality than would be obtained if the remaining 20% were not calculated. Also, the data-based initial estimates produce good and stable solutions, improving image quality.

CONCLUSION

Compartmental modeling on a pixel level is feasible for planar mAb images, provided that accurate image-based activity quantification and image registration are performed. The resulting parametric images, V′_d and Ã_ev in particular, are believed to have a potential for use in radioimmunoimaging and radioimmunotherapy.

APPENDIX