Late-fluorescence mammography assesses tumor capillary permeability and differentiates malignant from benign lesions

Axel Hagen; Dirk Grosenick; Rainer Macdonald; Herbert Rinneberg; Susen Burock; Peter Warnick; Alexander Poellinger; Peter M. Schlag

doi:10.1364/OE.17.017016

Late-fluorescence mammography assesses tumor capillary permeability and differentiates malignant from benign lesions

Axel Hagen, Dirk Grosenick, Rainer Macdonald, Herbert Rinneberg, Susen Burock, Peter Warnick, Alexander Poellinger, and Peter M. Schlag

Optics Express
Vol. 17,
Issue 19,
pp. 17016-17033
(2009)
•https://doi.org/10.1364/OE.17.017016

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Axel Hagen, Dirk Grosenick, Rainer Macdonald, Herbert Rinneberg, Susen Burock, Peter Warnick, Alexander Poellinger, and Peter M. Schlag, "Late-fluorescence mammography assesses tumor capillary permeability and differentiates malignant from benign lesions," Opt. Express 17, 17016-17033 (2009)

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Related Topics
Table of Contents Category
- Medical Optics and Biotechnology
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Mammography (170.3830)
- Spectroscopy, fluorescence and luminescence (170.6280)
- Fluorescence (260.2510)

About this Article
History
- Original Manuscript: July 8, 2009
- Revised Manuscript: August 20, 2009
- Manuscript Accepted: August 24, 2009
- Published: September 9, 2009
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 4, Iss. 11

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Open Access

Abstract

Using scanning time-domain instrumentation we recorded fluorescence projection mammograms on few breast cancer patients prior, during and after infusion of indocyanine green (ICG), while monitoring arterial ICG concentration by transcutaneous pulse densitometry. Late-fluorescence mammograms recorded after ICG had been largely cleared from the blood by the liver, showed invasive carcinomas at high contrast over a rather homogeneous background, whereas benign lesions did not produce (focused) fluorescence contrast. During infusion, tissue concentration contrast and hence fluorescence contrast is determined by intravascular contributions, whereas late-fluorescence mammograms are dominated by contributions from protein-bound ICG extravasated into the interstitium, reflecting relative microvascular permeabilities of carcinomas and normal breast tissue. We simulated intravascular and extravascular contributions to ICG tissue concentration contrast within a two-compartment unidirectional pharmacokinetic model.

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References

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2008 (4)

H. Rinneberg, D. Grosenick, K. T. Moesta, H. Wabnitz, J. Mucke, G. Wübbeler, R. Macdonald, and P. Schlag, “Detection and characterization of breast tumours by time-domain scanning optical mammography,” Opto-Electronics Review 16(2), 147–162 (2008).

S. A. Carp, J. Selb, Q. Fang, R. Moore, D. B. Kopans, E. Rafferty, and D. A. Boas, “Dynamic functional and mechanical response of breast tissue to compression,” Opt. Express 16(20), 16064–16078 (2008).
[PubMed]

E. E. Uzgiris, “Tumor microvasculature: endothelial leakiness and endothelial pore size distribution in a breast cancer model,” Breast Cancer: Basic and Clinical Research 1, 83–90 (2008).

B. Alacam, B. Yazici, X. Intes, S. Nioka, and B. Chance, “Pharmacokinetic-rate images of indocyanine green for breast tumors using near-infrared optical methods,” Phys. Med. Biol. 53(4), 837–859 (2008).
[PubMed]

2007 (5)

A. Hagen, O. Steinkellner, D. Grosenick, M. Möller, R. Ziegler, T. Nielsen, K. Lauritsen, R. Macdonald, and H. Rinneberg, “Development of a multi-channel time-domain fluorescence mammograph,” Proc. SPIE 6434, 64340Z (2007).

S. P. Poplack, T. D. Tosteson, W. A. Wells, B. W. Pogue, P. M. Meaney, A. Hartov, C. A. Kogel, S. K. Soho, J. J. Gibson, and K. D. Paulsen, “Electromagnetic breast imaging: results of a pilot study in women with abnormal mammograms,” Radiology 243(2), 350–359 (2007).
[PubMed]

A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. R. Arridge, M. D. Schnall, and A. G. Yodh, “Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,” Opt. Express 15(11), 6696–6716 (2007).
[PubMed]

A. Cerussi, D. Hsiang, N. Shah, R. Mehta, A. Durkin, J. Butler, and B. J. Tromberg, “Predicting response to breast cancer neoadjuvant chemotherapy using diffuse optical spectroscopy,” Proc. Natl. Acad. Sci. U.S.A. 104(10), 4014–4019 (2007).
[PubMed]

C. Zhou, R. Choe, N. Shah, T. Durduran, G. Yu, A. Durkin, D. Hsiang, R. Mehta, J. Butler, A. Cerussi, B. J. Tromberg, and A. G. Yodh, “Diffuse optical monitoring of blood flow and oxygenation in human breast cancer during early stages of neoadjuvant chemotherapy,” J. Biomed. Opt. 12(5), 051903 (2007).
[PubMed]

2006 (4)

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11(4), 044005 (2006).
[PubMed]

B. W. Pogue, S. C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11(3), 033001 (2006).

M. R. Dreher, W. Liu, C. R. Michelich, M. W. Dewhirst, F. Yuan, and A. Chilkoti, “Tumor vascular permeability, accumulation, and penetration of macromolecular drug carriers,” J. Natl. Cancer Inst. 98(5), 335–344 (2006).
[PubMed]

R. Duncan, “Polymer conjugates as anticancer nanomedicines,” Nat. Rev. Cancer 6(9), 688–701 (2006).
[PubMed]

2005 (4)

D. Grosenick, H. Wabnitz, K. Th. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol. 50(11), 2451–2468 (2005).
[PubMed]

C. Perlitz, K. Licha, F. D. Scholle, B. Ebert, M. Bahner, P. Hauff, K. T. Moesta, and M. Schirner, “Comparison of two tricarbocyanine-based dyes for fluorescence optical imaging,” J. Fluoresc. 15(3), 443–454 (2005).
[PubMed]

P. Taroni, A. Torricelli, L. Spinelli, A. Pifferi, F. Arpaia, G. Danesini, and R. Cubeddu, “Time-resolved optical mammography between 637 and 985 nm: clinical study on the detection and identification of breast lesions,” Phys. Med. Biol. 50(11), 2469–2488 (2005).
[PubMed]

D. Grosenick, K. Th. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, Ch. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50(11), 2429–2449 (2005).
[PubMed]

2004 (1)

G. Brix, F. Kiessling, R. Lucht, S. Darai, K. Wasser, S. Delorme, and J. Griebel, “Microcirculation and microvasculature in breast tumors: pharmacokinetic analysis of dynamic MR image series,” Magn. Reson. Med. 52(2), 420–429 (2004).
[PubMed]

2003 (5)

M. Möller, H. Wabnitz, A. Kummrow, D. Grosenick, A. Liebert, B. Wassermann, R. Macdonald, and H. Rinneberg, “A four-wavelength multi-channel scanning time-resolved optical mammograph,” Proc. SPIE 5138, 290–297 (2003).

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, S. Merritt, B. J. Tromberg, G. Gulsen, H. Yu, J. Wang, and O. Nalcioglu, “In vivo quantification of optical contrast agent dynamics in rat tumors by use of diffuse optical spectroscopy with magnetic resonance imaging coregistration,” Appl. Opt. 42(16), 2940–2950 (2003).
[PubMed]

H. E. Daldrup-Link and R. C. Brasch, “Macromolecular contrast agents for MR mammography: current status,” Eur. Radiol. 13(2), 354–365 (2003).
[PubMed]

H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, “Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom, and clinical results,” Appl. Opt. 42(1), 135–145 (2003).
[PubMed]

X. Intes, J. Ripoll, Y. Chen, S. Nioka, A. G. Yodh, and B. Chance, “In vivo continuous-wave optical breast imaging enhanced with Indocyanine Green,” Med. Phys. 30(6), 1039–1047 (2003).
[PubMed]

2002 (1)

D. Feng, J. A. Nagy, H. F. Dvorak, and A. M. Dvorak, “Ultrastructural studies define soluble macromolecular, particulate, and cellular transendothelial cell pathways in venules, lymphatic vessels, and tumor-associated microvessels in man and animals,” Microsc. Res. Tech. 57(5), 289–326 (2002).
[PubMed]

2001 (1)

Z. M. Bhujwalla, D. Artemov, K. Natarajan, E. Ackerstaff, and M. Solaiyappan, “Vascular differences detected by MRI for metastatic versus nonmetastatic breast and prostate cancer xenografts,” Neoplasia 3(2), 143–153 (2001).
[PubMed]

2000 (5)

M. Gurfinkel, A. B. Thompson, W. Ralston, T. L. Troy, A. L. Moore, T. A. Moore, J. D. Gust, D. Tatman, J. S. Reynolds, B. Muggenburg, K. Nikula, R. Pandey, R. H. Mayer, D. J. Hawrysz, and E. M. Sevick-Muraca, “Pharmacokinetics of ICG and HPPH-car for the detection of normal and tumor tissue using fluorescence, near-infrared reflectance imaging: a case study,” Photochem. Photobiol. 72(1), 94–102 (2000).
[PubMed]

P. Vaupel and M. Höckel, “Blood supply, oxygenation status and metabolic micromilieu of breast cancers: characterization and therapeutic relevance,” Int. J. Oncol. 17(5), 869–879 (2000) (review).
[PubMed]

P. Carmeliet and R. K. Jain, “Angiogenesis in cancer and other diseases,” Nature 407(6801), 249–257 (2000).
[PubMed]

H. Hashizume, P. Baluk, S. Morikawa, J. W. McLean, G. Thurston, S. Roberge, R. K. Jain, and D. M. McDonald, “Openings between defective endothelial cells explain tumor vessel leakiness,” Am. J. Pathol. 156(4), 1363–1380 (2000).
[PubMed]

V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. U.S.A. 97(6), 2767–2772 (2000).
[PubMed]

1999 (3)

S. B. Colak, M. B. van der Mark, G. W. 't Hooft, J. H. Hoogenraad, E. S. van der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1143–1158 (1999).

D. Grosenick, H. Wabnitz, H. H. Rinneberg, K. Th. Moesta, and P. M. Schlag, “Development of a time-domain optical mammograph and first in vivo applications,” Appl. Opt. 38(13), 2927–2943 (1999).

C. C. Michel and F. E. Curry, “Microvascular permeability,” Physiol. Rev. 79(3), 703–761 (1999).
[PubMed]

1998 (3)

S. Yoneya, T. Saito, Y. Komatsu, I. Koyama, K. Takahashi, and J. Duvoll-Young, “Binding properties of indocyanine green in human blood,” Invest. Ophthalmol. Vis. Sci. 39(7), 1286–1290 (1998).
[PubMed]

H. Daldrup, D. M. Shames, M. Wendland, Y. Okuhata, T. M. Link, W. Rosenau, Y. Lu, and R. C. Brasch, “Correlation of dynamic contrast-enhanced MR imaging with histologic tumor grade: comparison of macromolecular and small-molecular contrast media,” AJR Am. J. Roentgenol. 171(4), 941–949 (1998).
[PubMed]

L. Götz, S. H. Heywang-Köbrunner, O. Schütz, and H. Siebold, “Optical mammography on preoperative patients (Optische Mammographie an präoperativen Patientinnen),” Akt. Radiol. 8, 31–33 (1998).

1997 (2)

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, and M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94(12), 6468–6473 (1997).
[PubMed]

P. Ott and R. A. Weisiger, “Nontraditional effects of protein binding and hematocrit on uptake of indocyanine green by perfused rat liver,” Am. J. Physiol. 273(1 Pt 1), G227–G238 (1997).
[PubMed]

1996 (1)

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AJR Am. J. Roentgenol. (1)

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E. E. Uzgiris, “Tumor microvasculature: endothelial leakiness and endothelial pore size distribution in a breast cancer model,” Breast Cancer: Basic and Clinical Research 1, 83–90 (2008).

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D. K. F. Meijer, B. Weert, and G. A. Vermeer, “Pharmacokinetics of biliary excretion in man. VI. Indocyanine green,” Eur. J. Clin. Pharmacol. 35(3), 295–303 (1988).
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Eur. Radiol. (1)

H. E. Daldrup-Link and R. C. Brasch, “Macromolecular contrast agents for MR mammography: current status,” Eur. Radiol. 13(2), 354–365 (2003).
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J. Biomed. Opt. (3)

B. W. Pogue, S. C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11(3), 033001 (2006).

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J. Pharmacokinet. Biopharm. (1)

P. Ott, L. Bass, and S. Keiding, “The kinetics of continuously infused indocyanine green in the pig,” J. Pharmacokinet. Biopharm. 24(1), 19–44 (1996).
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X. Intes, J. Ripoll, Y. Chen, S. Nioka, A. G. Yodh, and B. Chance, “In vivo continuous-wave optical breast imaging enhanced with Indocyanine Green,” Med. Phys. 30(6), 1039–1047 (2003).
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Microsc. Res. Tech. (1)

Nat. Rev. Cancer (1)

R. Duncan, “Polymer conjugates as anticancer nanomedicines,” Nat. Rev. Cancer 6(9), 688–701 (2006).
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Nature (1)

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C. C. Michel and F. E. Curry, “Microvascular permeability,” Physiol. Rev. 79(3), 703–761 (1999).
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Fig. 1 Time course of molar ICG concentration in plasma of arterial blood, recorded at the finger pad of a 72-year-old patient by transcutaneous pulse densitometry. The entire time course is divided into five periods corresponding to the initial (native) phase, the period during which the ICG bolus is administered (bolus phase), the infusion period (vascular phase), the washout phase after termination of the infusion and the extravascular phase when the ICG arterial plasma concentration has returned to zero. Periods during which absorption and fluorescence mammograms were taken are indicated by vertical bars. The red solid line represents a mono-exponential fit of the ICG decay after the infusion was stopped.

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Fig. 2 Schematic of scanning time-domain laser and fluorescence mammograph.

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Fig. 3 Fluorescence raw mammogram (a) based on diffusely transmitted, time-integrated fluorescence intensity, absorption raw mammogram (b), corresponding to time-integrated transmitted laser intensity and corresponding ratio mammogram of (a) and (b) without edge correction (c) and with edge correction (d). Unlike ratio images, absorption and fluorescence mammograms are dominated by hemoglobin absorption. The carcinoma (arrow) is visible in laser and ratio mammograms but invisible in the fluorescence mammogram due to cancellation effects. Each mammogram is normalized to the center region of the breast.

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Fig. 4 Open unidirectional compartmental model (right hand side, solid lines) for simulating local ICG concentrations. Model consists of local vascular (plasma) compartment and local extravascular-extracellular space (EES), with apparent capillary plasma flow per unit volume of tissue (F_pρ), apparent permeability-surface-area product (PSρ) and (bound) ICG outflow rate (k_out) entering as parameters (s. Table 1). Left hand side (dashed lines) illustrates (global) open redistribution compartment model used by Ott et al. [23] to interpret ICG plasma disappearance curve.

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Fig. 5 Fluorescence ratio images taken (a) in the vascular phase, i.e. during ICG infusion (Scan 3, s. Figure 1), and (b) in the extravascular phase, i.e. about 30 min post infusion (Scan 5, Fig. 1), of 72-year-old patient; (c) x-ray mammogram shown for comparison with arrow indicating the position of the invasive ductal carcinoma. In (a) fluorescence originates predominantly from ICG in vasculature, in (b) fluorescence predominantly reflects ICG that extravasated into the interstitium. The higher fluorescence intensity of the carcinoma reveals its higher permeability for ICG bound plasma proteins. Distance between image-ticks is 2 cm.

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Fig. 6 Mammogram showing reciprocal photon counts of a late time window of the TPSF recorded at 660 nm prior to ICG administration (a). The intrinsic absorption contrast reveals structures that can also be seen in the fluorescence ratio image taken during the vascular phase (b). Distance between image-ticks is 2 cm.

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Fig. 7 X-ray-mammogram (cranio-caudal projection) of the left breast of a 51-year-old patient bearing an invasive ductal carcinoma. The tumor is hardly visible due to very dense glandular tissue.

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Fig. 8 Fluorescence ratio images in cranio-caudal projection taken (a) in the vascular phase and (b) in the extravascular phase 54 min after termination of ICG infusion. Axial reconstruction of Gd-DTPA enhanced MR breast scan (c) showing maximum intensity projection. In contrast to x-ray mammogram (s. Figure 7), late-fluorescence ratio mammogram (b) and MR image reveal the ductal carcinoma indicated by arrows in (c). Distance between image-ticks is 2 cm.

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Fig. 9 Fluorescence ratio mammograms in cranio-caudal projection taken (a) in the vascular phase and (b) in the extravascular phase, 26 min after termination of ICG infusion, of a 52-year-old patient with benign fibroadenoma. The lesion does not lead to a focused area with higher fluorescence intensity above background, i.e. is invisible in the ratio images, indicating that ICG extravasated at a rate comparable with normal breast tissue. Distance between image-ticks is 2 cm.

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Fig. 10 (a,b) Simulated time course of concentration corresponding to (a) vascular contribution (v_pC_p(t)), and (b) extravascular contribution (v_eC_e(t)) to total ICG concentration in carcinoma (), breast parenchyma () and normal breast tissue (fat) () during (0 ≤ t ≤ 25 min) and after ICG infusion, with simulation input parameters listed in Table 1; (c,d) Simulated concentration contrast of (c) intravascular (v_pC_p(t)) and extravascular (v_eC_e(t)) contributions and (d) of total ICG concentration normalized to total ICG concentration C_t in normal breast tissue (fat) for carcinoma (), breast parenchyma () and fat (). In (c,d) vertical gray bars indicate periods during which optical mammograms of the 72-year-old patient were recorded (case 1, Scan 3, Scan 5, s. Figure 1).

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Tables (2)

Table 1 Simulation input parameters

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Table A1 Coefficients and abbreviations used in analytical solutions of rate equations

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Equations (9)

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\frac{d C_{A}^{s s}}{d t} = - k_{e l i m} C_{A}^{s s} + S_{i n f} = 0

d C_{p} (t) / d t = k_{F} C_{A} (t) - (k_{F} + k_{p}^{P S ρ}) C_{p} (t)

d C_{e} (t) / d t = k_{e}^{P S ρ} C_{p} (t) - k_{o u t} C_{e} (t)

C_{A}^{b o l u s} (t) = A_{1} \exp (- m_{1} t) + A_{2} \exp (- m_{2} t)

C_{A} (t) = \frac{S_{i n f}}{k_{e l i m}} {1 - q \exp (- m_{1} t) - (1 - q) \exp (- m_{2} t)}

C_{p} (t) = A_{0} - A_{m 1}^{(1)} \exp (- m_{1} t) - A_{m 2}^{(1)} \exp (- m_{2} t) + A_{F}^{(1)} \exp {- (k_{F} + k_{p}^{P S ρ}) t}

\begin{array}{c} C_{e} (t) = B_{0} + B_{m 1}^{(1)} \exp (- m_{1} t) + B_{m 2}^{(1)} \exp (- m_{2} t) \\ - f_{o u t} A_{F}^{(1)} \exp {- (k_{F} + k_{p}^{P S ρ}) t} - B_{o u t}^{(1)} \exp {- k_{o u t} t} \end{array}

\begin{array}{c} C_{p} (t) = A_{m 1}^{(2)} \exp {- m_{1} (t - τ_{i n f})} + A_{m 2}^{(2)} \exp {- m_{2} (t - τ_{i n f})} \\ - A_{F}^{(2)} \exp {- (k_{F} + k_{p}^{P S ρ}) (t - τ_{i n f})} \end{array}

\begin{array}{l} C_{e} (t) = - B_{m 1}^{(2)} \exp {- m_{1} (t - τ_{i n f})} - B_{m 2}^{(2)} \exp {- m_{2} (t - τ_{i n f})} \\ + f_{o u t} A_{F}^{(2)} \exp {- (k_{F} + k_{p}^{P S ρ}) (t - τ_{i n f})} + B_{o u t}^{(2)} \exp {- k_{o u t} (t - τ_{i n f})} \end{array}

parameter		value
m ₁ (min⁻¹ )	arterial blood	0.179 *
m ₂ (min⁻¹ )	arterial blood	0.0104 *
A ₁ (µM)	arterial blood	41 **
A ₂ (µM)	arterial blood	0
τ_inf (min)	arterial blood	25
S_inf (µMmin⁻¹ )	arterial blood	1.64 **
F_pρ (min⁻¹ )	all tissues	0.05
PSρ (min⁻¹ )	fatty tissue parenchyma carcinoma	0.67∙10⁻⁴ 1.0∙10⁻⁴ 2.0∙10⁻⁴
k_out (min⁻¹ )	all tissues	1.67∙10⁻³
v_p	fatty tissue parenchyma carcinoma	0.02 * 0.04 * 0.04 ***

Coefficients
infusion period $0 \leq t \leq τ_{i n f}$		wash-out period $t \geq τ_{i n f}$
$A_{0} = \frac{S_{\inf}}{k_{e \lim}} \frac{k_{F}}{k_{F} + k_{p}^{P S ρ}}$
$A_{m 1}^{(1)} = \frac{S_{\inf}}{k_{e l i m}} \frac{k_{F} q}{k_{F} + k_{p}^{P S ρ} - m_{1}}$		$A_{m 1}^{(2)} = A_{m 1}^{(1)} {1 - \exp (- m_{1} τ_{i n f})}$
$A_{m 2}^{(1)} = \frac{S_{\inf}}{k_{e l i m}} \frac{k_{F} (1 - q)}{k_{F} + k_{p}^{P S ρ} - m_{2}}$		$A_{m 2}^{(2)} = A_{m 2}^{(1)} {1 - \exp (- m_{2} τ_{i n f})}$
$A_{F}^{(1)} = A_{m 1}^{(1)} + A_{m 2}^{(1)} - A_{0}$		$A_{F}^{(2)} = A_{m 1}^{(2)} + A_{m 2}^{(2)} - C_{p} (τ_{i n f})$
$B_{0} = A_{0} \frac{k_{e}^{P S ρ}}{k_{o u t}}$

$B_{m 1}^{(i)} = \frac{k_{e}^{P S ρ}}{m_{1} - k_{o u t}} A_{m 1}^{(i)}$ (i = 1, 2) $B_{m 2}^{(i)} = \frac{k_{e}^{P S ρ}}{m_{2} - k_{o u t}} A_{m 2}^{(i)}$ (i = 1, 2)

$B_{o u t}^{(1)} = B_{0} + B_{m 1}^{(1)} + B_{m 2}^{(1)} - f_{o u t} A_{F}^{(1)}$		$B_{o u t}^{(2)} = C_{e} (τ_{i n f}) + B_{m 1}^{(2)} + B_{m 2}^{(2)} - f_{o u t} A_{F}^{(2)}$
Abbreviations
$q = \frac{A_{1} m_{2}}{A_{1} m_{2} + A_{2} m_{1}}$ $k_{e l i m} = \frac{(A_{1} + A_{2}) m_{1} m_{2}}{A_{1} m_{2} + A_{2} m_{1}}$ $f_{o u t} = \frac{k_{e}^{P S ρ}}{k_{F} + k_{p}^{P S ρ} - k_{o u t}}$

parameter		value
m ₁ (min⁻¹ )	arterial blood	0.179 *
m ₂ (min⁻¹ )	arterial blood	0.0104 *
A ₁ (µM)	arterial blood	41 **
A ₂ (µM)	arterial blood	0
τ_inf (min)	arterial blood	25
S_inf (µMmin⁻¹ )	arterial blood	1.64 **
F_pρ (min⁻¹ )	all tissues	0.05
PSρ (min⁻¹ )	fatty tissue parenchyma carcinoma	0.67∙10⁻⁴ 1.0∙10⁻⁴ 2.0∙10⁻⁴
k_out (min⁻¹ )	all tissues	1.67∙10⁻³
v_p	fatty tissue parenchyma carcinoma	0.02 * 0.04 * 0.04 ***

Coefficients
infusion period $0 \leq t \leq τ_{i n f}$		wash-out period $t \geq τ_{i n f}$
$A_{0} = \frac{S_{\inf}}{k_{e \lim}} \frac{k_{F}}{k_{F} + k_{p}^{P S ρ}}$
$A_{m 1}^{(1)} = \frac{S_{\inf}}{k_{e l i m}} \frac{k_{F} q}{k_{F} + k_{p}^{P S ρ} - m_{1}}$		$A_{m 1}^{(2)} = A_{m 1}^{(1)} {1 - \exp (- m_{1} τ_{i n f})}$
$A_{m 2}^{(1)} = \frac{S_{\inf}}{k_{e l i m}} \frac{k_{F} (1 - q)}{k_{F} + k_{p}^{P S ρ} - m_{2}}$		$A_{m 2}^{(2)} = A_{m 2}^{(1)} {1 - \exp (- m_{2} τ_{i n f})}$
$A_{F}^{(1)} = A_{m 1}^{(1)} + A_{m 2}^{(1)} - A_{0}$		$A_{F}^{(2)} = A_{m 1}^{(2)} + A_{m 2}^{(2)} - C_{p} (τ_{i n f})$
$B_{0} = A_{0} \frac{k_{e}^{P S ρ}}{k_{o u t}}$

$B_{m 1}^{(i)} = \frac{k_{e}^{P S ρ}}{m_{1} - k_{o u t}} A_{m 1}^{(i)}$ (i = 1, 2) $B_{m 2}^{(i)} = \frac{k_{e}^{P S ρ}}{m_{2} - k_{o u t}} A_{m 2}^{(i)}$ (i = 1, 2)

$B_{o u t}^{(1)} = B_{0} + B_{m 1}^{(1)} + B_{m 2}^{(1)} - f_{o u t} A_{F}^{(1)}$		$B_{o u t}^{(2)} = C_{e} (τ_{i n f}) + B_{m 1}^{(2)} + B_{m 2}^{(2)} - f_{o u t} A_{F}^{(2)}$
Abbreviations
$q = \frac{A_{1} m_{2}}{A_{1} m_{2} + A_{2} m_{1}}$ $k_{e l i m} = \frac{(A_{1} + A_{2}) m_{1} m_{2}}{A_{1} m_{2} + A_{2} m_{1}}$ $f_{o u t} = \frac{k_{e}^{P S ρ}}{k_{F} + k_{p}^{P S ρ} - k_{o u t}}$