1 Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois at Urbana-Champaign (UIUC), 2 Biomedical Magnetic Resonance Laboratory, UIUC, 3 Beckman Institute, UIUC, 4 National Cancer Institute, National Institutes of Health, Bethesda, MD, 5 Department of Medical Information Science, UIUC, and 6 Department of Molecular and Integrative Physiology, UIUC Identifying Tumor Permeability Heterogeneity With Macromolecular MRI Contrast Agents Michael Aref 1-3 , Martin Brechbiel 4 and Erik Wiener 1-3,5,6 Background Methods: Two Compartment Model Results: SI  [CA] Introduction Methods: Two Compartment Model Methods: Two Compartment Model Methods: SI  [CA] Conclusion Results: Two Compartment Model Summary Our results for Gd-DTPA agree with other published studies (for both the plasma and tumor compartments) and our PAMAM-TU-DTPA G = 4 results are consistent with predictions for an agent larger than Gd-DTPA. The dendrimer agent, PAMAM-TU-DTPA G = 4 can differentiate between two regions of tumor heterogeneity with a greater dynamic range than Gd-DTPA. In the case of tumor #3 (the data shown in the figure to the left), using Gd-DTPA measured only a 16% difference in PS between the ROI and the whole tumor, while the PAMAM-TU-DTPA G = 4 showed a 207% difference. For tumor #1, Gd-DTPA measured a 29% PS difference between the ROI and the whole tumor, while the PAMAM-TU-DTPA G = 4 showed a 86% difference. Selected Bibliography Baxter, L. T., et al. (1991) Microvasculature Research 41, 252-272. den Boer, J. A., et al. (1997) J Magn Reson Imaging 7, 702-715. Dvorak, H. F. (1990) in International Symposium on the Effects of Therapy on Biology and Kinetics of the Residual Tumor, Part A; Preclinical Aspects (Wiley-Liss, NY). Edell, S. L., et al. (1999) Delaware Medical Journal 71, 377-382. Folkman, J. (1994) J Clin Oncol 12, 441-443. Heywang, S. H., et al. (1989) Radiology 171, 95-103. Jain, R. K. (1990) Cancer and Metastasis Reviews, 253-266. Orel, S. G., et al. (1994) Radiology 190, 484-493. Roberts, T. P. L. (1997) J Magn Reson Imaging 7, 82-90. Stoica, G., et al. (1983) Am J Pathol 110, 161-169. Su, M.-Y., et al. (1994) Magn Reson Med 32, 714-724. Tofts, P. S. (1997) J Magn Reson Imaging 7, 91-101. Tofts, P. S., et al (1999) J Magn Reson Imaging 10, 223-232. Weidner, N. (1999) J Pathol 189, 297-299. Wiener, E. C., et al. (1994) Magn Reson Med 31, 1-8. Acknowledgments Mike Simmons and the St. Francis Medical Center, Peoria, IL, Dr. Andrew Webb, Hazardous Waste Research Center, UIUC, and support from PHS Grant Number 5 T32 CA 09067 awarded by the National Cancer Institute, DHHS, University of Illinois Block Fellowship, PHS Grant Number 1 R29 CA61918, and PHS Grant Number 5 P41 RR05964 awarded by the National Institutes of Health. Hypothesis Macromolecular agents will have a greater sensitivity in identifying local regions in mammary tumors permeability-surface area products compared to low molecular weight agents. Method To calculate the permeability-surface area products, we use a two compartment model and FLASH (Fast Low-Angle SHot) image signal intensities that have been converted to contrast agent concentration by an algebraic expression to examine the differences in regional tumor uptake of a low molecular weight agent, Gd-DTPA (MW = 938.014), and a macromolecular dendrimer based agent, PAMAM-TU-DTPA G = 4 (MW  35,000). Essentially our technique combines the two compartment model presented by Tofts and Kermode and Su et al ’s tumor tissue contrast agent concentration model. Folkman has shown that tumors are heterogeneous in their capillary density and surface area, since only a subset of tumor cells acquire angiogenic activity. High molecular weight dendrimer agents are blood pool agents and should have the greatest contrast enhancement in the areas of greatest capillary density and the greatest permeability in regions of neovascularization. High capillary density indicates poor prognosis. Angiogenic activity is a measure of metastatic potential. Extraction of a contrast agent by a tumor is dependent upon five factors: (1) capillary surface area, S (2) capillary permeability, P (3) capillary blood flow, F (4) transit time of the agent through the tumor interstitium due to diffusion and convection (5) plasma half-life, T 1/2 DIST T 1/2 EXCRE An algebraic expression was used to relate normalized signal intensity, S/S 0 (No Units), to contrast agent concentration, [CA] (mM): Where C 1 = e -TR/T 10 (No Units) is composed of the repetition time, TR (sec), and longitudinal relaxation time in the absence of contrast agent, T 10 , while C 2 = TR•r 1 (1/mM) is the product of the repetition time and the longitudinal relaxivity of the agent, r 1 (1/mMsec). In other words, C 1 is not agent dependent and should be approximately the same for any agent. The other coefficient, C 2 , is linearly proportional to the longitudinal relaxivity and is therefore agent dependent. We adjust the above expression, for temperature and contrast agent differences, by expressing the efficiency of one agent under a specific set of conditions to that of another agent under different experimental conditions, thus: With this expression we can adjust the signal intensity to concentration of Gd-DTPA ([CA a ]) calculation to one with any other Gadolinium-based agent ([CA b ]) at any temperature provided the relaxivities (r 1a,1b ) and longitudinal relaxation times (T 10a,10b ) for the two conditions are known. The T 1 data is used to scale contrast agent concentrations due to differences in the animal and vial, temperature, and agent type. Note the 5.5 fold difference between the relaxivities of Gd-DTPA and the macomolecular agent at 37 °C: To obtain the parameters, C 1,2 , serial dilutions of Gd-DTPA in Sephadex (to mimic tissue) were imaged. The S/S 0 was plotted versus [CA] and the data was fit for C 1,2 . The fit: The two compartment model is composed of the plasma compartment and the extravascular extracellular space (EES) compartment. From the two compartment model, ordinary differential equations for the rate of change can be written for the plasma and EES compartments. Solving these yields: The parameters are defined, as follows: [CA p (t)] (mM) is the time-dependent contrast agent concentration in the plasma compartment, [CA e (t)] (mM) is the time-dependent contrast agent concentration in the EES compartment, D (mmole/kg) is the initial dose, V p (L/kg) is the plasma volume, V e (L/kg) is the volume of distribution (EES) permeated by the agent, K p  e (L•kg -1 •min -1 ) is the isodirectional transfer rate between the plasma and EES compartments, and K p  k (L•kg -1 •min -1 ) is the unidirectional transfer rate from the plasma compartment to the kidneys. The concentration amplitudes, a 1,2 (kg/L), the distribution rate constant,  (min -1 ), and the excretion rate constant,  (min -1 ), are given by: Results: Two Compartment Model Recall, that the tumor compartment is composed of volume fractions of the plasma and EES compartments: In most tumors v p << v e , thus the plasma compartment drops out of the tumor compartment expression. The tumor’s EES volume fraction permeated by the agent, v e , defined as: The transfer rates incorporated in a 1,2 ,  and  are averages for the entire body and different from those in the tumor ROI (this is signified by replacing the subscript e with a t ). For the tumor compartment contrast agent concentration, [CA t (t)] (mM), The fitted plasma compartment behavior for Gd-DTPA (a) and PAMAM-TU-DTPA G = 4 (b). The fitted tumor compartment behavior for tumor #3, both a selected ROI and the whole tumor using Gd-DTPA (c) and PAMAM-TU-DTPA G = 4 (d). In a rat, the average V p = 0.0350 L/kg, which our measurements agree with. For Gd-DTPA V e > V p , since it is freely permeable, while for the dendrimer agent V e < V p , since this is a blood pool agent. The T 1/2 EXCRE also agree with other studies for Gd-DTPA and the G = 4 value falls between the values for G = 2 (T 1/2 EXCRE = 40 ± 10 min) and G = 6 (T 1/2 EXCRE = 200 ± 100 min) measured by Wiener et al . For the same tumor ROI, K p  t /V T Gd-DTPA > K p  t /V T PAMAM G = 4 and v e Gd-DTPA > v e PAMAM G = 4 since the dendrimer agent is larger it is less permeable and does not permeate as much of the tumor EES. Using K p  t /V T Gd-DTPA , the ratio of surface areas between the tumor ROI and the whole tumor for tumor #1 has a range of 1.0-1.3 and for tumor #3 has a range of 1.0-1.2. Using K p  t /V T PAMAM G = 4 , the ratio of permeabilities between the tumor ROI and the whole tumor for tumor #1 has a range of 1.4-1.8 and for tumor #3 has a range of 2.6-3.1. If PS << F (PS-limited), K p  t = P p  t S pt (L•kg -1 •min -1 ) the isodirectional transfer rate between the plasma and the tumor EES. That is, the transfer rate is equal to the permeability-surface area product (PS). In this study, we measure the transfer rate normalized to total tumor volume, K p  t /V T . Since, V T in the same tumor is the same for both agents and differences in PS Gd-DTPA between ROIs will be due to a combination of permeability and surface area effects, ratios of these PS can yield information about the ROIs’ surface area ratios. This information can be used with PS PAMAM G = 4 between the same ROIs, to find the ROIs’ permeability ratios. The plasma compartment is the fluid component of the vasculature, the agent is injected as a bolus into and is distributed into the EES and excreted through the kidneys. The EES compartment is the volume of distribution or the interstitial leakage space. That is, the areas outside the vasculature between the cells. The tumor compartment is experimental region of interest composed of a volume fraction of the plasma compartment, v p , (i.e. the capillary bed feeding the tumor) and the volume fraction of the EES, v e , that composes the interstitial leakage space of abnormal tissue. The rate of change of the concentration in a compartment is proportional to gains due to agent coming from other compartments and losses due to agent leaving the compartment.

1 Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois at Urbana-Champaign (UIUC), 2 Biomedical Magnetic Resonance Laboratory, UIUC,

3 Beckman Institute, UIUC, 4 National Cancer Institute, National Institutes of Health, Bethesda, MD,

5 Department of Medical Information Science, UIUC, and 6 Department of Molecular and Integrative Physiology, UIUC

Summary

Our results for Gd-DTPA agree with other published studies (for both the plasma and tumor compartments) and our PAMAM-TU-DTPA G = 4 results are consistent with predictions for an agent larger than Gd-DTPA.

The dendrimer agent, PAMAM-TU-DTPA G = 4 can differentiate between two regions of tumor heterogeneity with a greater dynamic range than Gd-DTPA. In the case of tumor #3 (the data shown in the figure to the left), using Gd-DTPA measured only a 16% difference in PS between the ROI and the whole tumor, while the PAMAM-TU-DTPA G = 4 showed a 207% difference. For tumor #1, Gd-DTPA measured a 29% PS difference between the ROI and the whole tumor, while the PAMAM-TU-DTPA G = 4 showed a 86% difference.

Selected Bibliography

Baxter, L. T., et al. (1991) Microvasculature Research 41, 252-272.

den Boer, J. A., et al. (1997) J Magn Reson Imaging 7, 702-715.

Dvorak, H. F. (1990) in International Symposium on the Effects of Therapy on Biology and Kinetics of the Residual Tumor, Part A; Preclinical Aspects (Wiley-Liss, NY).

Edell, S. L., et al. (1999) Delaware Medical Journal 71, 377-382.

Folkman, J. (1994) J Clin Oncol 12, 441-443.

Heywang, S. H., et al. (1989) Radiology 171, 95-103.

Jain, R. K. (1990) Cancer and Metastasis Reviews, 253-266.

Orel, S. G., et al. (1994) Radiology 190, 484-493.

Roberts, T. P. L. (1997) J Magn Reson Imaging 7, 82-90.

Stoica, G., et al. (1983) Am J Pathol 110, 161-169.

Su, M.-Y., et al. (1994) Magn Reson Med 32, 714-724.

Tofts, P. S. (1997) J Magn Reson Imaging 7, 91-101.

Tofts, P. S., et al (1999) J Magn Reson Imaging 10, 223-232.

Weidner, N. (1999) J Pathol 189, 297-299.

Wiener, E. C., et al. (1994) Magn Reson Med 31, 1-8.

Acknowledgments

Mike Simmons and the St. Francis Medical Center, Peoria, IL, Dr. Andrew Webb, Hazardous Waste Research Center, UIUC, and support from PHS Grant Number 5 T32 CA 09067 awarded by the National Cancer Institute, DHHS, University of Illinois Block Fellowship, PHS Grant Number 1 R29 CA61918, and PHS Grant Number 5 P41 RR05964 awarded by the National Institutes of Health.

Folkman has shown that tumors are heterogeneous in their capillary density and surface area, since only a subset of tumor cells acquire angiogenic activity.

High molecular weight dendrimer agents are blood pool agents and should have the greatest contrast enhancement in the areas of greatest capillary density and the greatest permeability in regions of neovascularization.

High capillary density indicates poor prognosis.

Angiogenic activity is a measure of metastatic potential.

Extraction of a contrast agent by a tumor is dependent upon five factors:

(1) capillary surface area, S

(2) capillary permeability, P

(3) capillary blood flow, F

(4) transit time of the agent through the tumor

interstitium due to diffusion and convection

(5) plasma half-life, T 1/2 DIST T 1/2 EXCRE

An algebraic expression was used to relate normalized signal intensity, S/S 0 (No Units), to contrast agent concentration, [CA] (mM):

Where C 1 = e -TR/T 10 (No Units) is composed of the repetition time, TR (sec), and longitudinal relaxation time in the absence of contrast agent, T 10 , while C 2 = TR•r 1 (1/mM) is the product of the repetition time and the longitudinal relaxivity of the agent, r 1 (1/mMsec). In other words, C 1 is not agent dependent and should be approximately the same for any agent. The other coefficient, C 2 , is linearly proportional to the longitudinal relaxivity and is therefore agent dependent.

We adjust the above expression, for temperature and contrast agent differences, by expressing the efficiency of one agent under a specific set of conditions to that of another agent under different experimental conditions, thus:

With this expression we can adjust the signal intensity to concentration of Gd-DTPA ([CA a ]) calculation to one with any other Gadolinium-based agent ([CA b ]) at any temperature provided the relaxivities (r 1a,1b ) and longitudinal relaxation times (T 10a,10b ) for the two conditions are known.

The T 1 data is used to scale contrast agent concentrations due to differences in the animal and vial, temperature, and agent type. Note the 5.5 fold difference between the relaxivities of Gd-DTPA and the macomolecular agent at 37 °C:

To obtain the parameters, C 1,2 , serial dilutions of Gd-DTPA in Sephadex (to mimic tissue) were imaged. The S/S 0 was plotted versus [CA] and the data was fit for C 1,2 . The fit:

The two compartment model is composed of the plasma compartment and the extravascular extracellular space (EES) compartment.

From the two compartment model, ordinary differential equations for the rate of change can be written for the plasma and EES compartments. Solving these yields:

The parameters are defined, as follows: [CA p (t)] (mM) is the time-dependent contrast agent concentration in the plasma compartment, [CA e (t)] (mM) is the time-dependent contrast agent concentration in the EES compartment, D (mmole/kg) is the initial dose, V p (L/kg) is the plasma volume, V e (L/kg) is the volume of distribution (EES) permeated by the agent, K p  e (L•kg -1 •min -1 ) is the isodirectional transfer rate between the plasma and EES compartments, and K p  k (L•kg -1 •min -1 ) is the unidirectional transfer rate from the plasma compartment to the kidneys. The concentration amplitudes, a 1,2 (kg/L), the distribution rate constant,  (min -1 ), and the excretion rate constant,  (min -1 ), are given by:

Recall, that the tumor compartment is composed of volume fractions of the plasma and EES compartments:

In most tumors v p << v e , thus the plasma compartment drops out of the tumor compartment expression.

The tumor’s EES volume fraction permeated by the agent, v e , defined as:

The transfer rates incorporated in a 1,2 ,  and  are averages for the entire body and different from those in the tumor ROI (this is signified by replacing the subscript e with a t ).

For the tumor compartment contrast agent concentration, [CA t (t)] (mM),

The fitted plasma compartment behavior for Gd-DTPA (a) and PAMAM-TU-DTPA G = 4 (b). The fitted tumor compartment behavior for tumor #3, both a selected ROI and the whole tumor using Gd-DTPA (c) and PAMAM-TU-DTPA G = 4 (d).

In a rat, the average V p = 0.0350 L/kg, which our measurements agree with. For Gd-DTPA V e > V p , since it is freely permeable, while for the dendrimer agent V e < V p , since this is a blood pool agent. The T 1/2 EXCRE also agree with other studies for Gd-DTPA and the G = 4 value falls between the values for G = 2 (T 1/2 EXCRE = 40 ± 10 min) and G = 6 (T 1/2 EXCRE = 200 ± 100 min) measured by Wiener et al .

For the same tumor ROI, K p  t /V T Gd-DTPA > K p  t /V T PAMAM G = 4 and v e Gd-DTPA > v e PAMAM G = 4 since the dendrimer agent is larger it is less permeable and does not permeate as much of the tumor EES.

Using K p  t /V T Gd-DTPA , the ratio of surface areas between the tumor ROI and the whole tumor for tumor #1 has a range of 1.0-1.3 and for tumor #3 has a range of 1.0-1.2.

Using K p  t /V T PAMAM G = 4 , the ratio of permeabilities between the tumor ROI and the whole tumor for tumor #1 has a range of 1.4-1.8 and for tumor #3 has a range of 2.6-3.1.

If PS << F (PS-limited), K p  t = P p  t S pt (L•kg -1 •min -1 ) the isodirectional transfer rate between the plasma and the tumor EES. That is, the transfer rate is equal to the permeability-surface area product (PS).

In this study, we measure the transfer rate normalized to total tumor volume, K p  t /V T .

Since, V T in the same tumor is the same for both agents and differences in PS Gd-DTPA between ROIs will be due to a combination of permeability and surface area effects, ratios of these PS can yield information about the ROIs’ surface area ratios. This information can be used with PS PAMAM G = 4 between the same ROIs, to find the ROIs’ permeability ratios.

The plasma compartment is the fluid component of the vasculature, the agent is injected as a bolus into and is distributed into the EES and excreted through the kidneys.

The EES compartment is the volume of distribution or the interstitial leakage space. That is, the areas outside the vasculature between the cells.

The tumor compartment is experimental region of interest composed of a volume fraction of the plasma compartment, v p , (i.e. the capillary bed feeding the tumor) and the volume fraction of the EES, v e , that composes the interstitial leakage space of abnormal tissue.

The rate of change of the concentration in a compartment is proportional to gains due to agent coming from other compartments and losses due to agent leaving the compartment.