SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION DOI: /NNANO Normalization of tumour blood vessels improves the delivery of nanomedicines in a size-dependent manner Vikash P. Chauhan, Triantafyllos Stylianopoulos, John D. Martin, Zoran Popović, Ou Chen, Walid S. Kamoun, Moungi G. Bawendi, Dai Fukumura, and Rakesh K. Jain Mathematical model Equations and assumptions: We represent the tumour vasculature as a percolation network at the percolation threshold, with one inlet and one outlet as shown in Fig. 3a in the main text. These network structures have been found to represent tumour vasculature in animal models well 1-2, though real angiography images could be used to represent additional heterogeneity present in unusual vascular networks. We assume that blood flow ( ) is axial and follows Poiseuille's law 3-4,, where d is the vessel diameter, p v is the vascular pressure, and μ is the blood viscosity. Fluid exchange across the vessel wall ( ) follows Starling's law with no osmotic pressure difference 3, 5,, where L p is the hydraulic conductivity of the vessel wall, S is the surface area of the vessel, and p i is the interstitial fluid pressure. The effects of decreased interstitial oncotic pressure, which occurs with vascular normalization 6 and can reduce convection, were not considered due to their relatively small effects compared to fluid pressure changes based on previous studies 7. Interstitial fluid transport ( ) follows Darcy's law,, where K is the hydraulic conductivity of the interstitial space and A c is the tissue cross-sectional area. The tissue cross-sectional area can be related to the vascular density, Sv, and the diameter of the NATURE NANOTECHNOLOGY 1

2 vessel, d, by 3. The inlet microvascular pressure is assumed to be invariable, as has been measured with DC101 therapy 6. Inside vessels, transport is assumed to be dominated by convection and is governed by, where c v is the intravascular concentration of the nanoparticle. In the interstitial space, transport can be both diffusive and convective such that, where c i is the concentration of the nanoparticle in the interstitial space, D is the diffusion coefficient, and v is the interstitial fluid velocity given by Darcy's law. Neither binding of nanoparticles to cancer cells or extracellular matrix components, nor uptake by cells, is considered, as the effects of these processes on transvascular flux are assumed negligible on short time scales. The hindrance to diffusion from transport around and through cells is taken into account through the use of SFA-FRAP diffusion data, which measures the hindrance from both cells and matrix components due to its length scale 8. The mass flux, φ, at the interface between vascular and interstitial space is given by Starling's approximation as 1 1, with = 1, where Pe is the Péclet number across the vessel wall, and P is the vascular permeability of the nanoparticle through the pores of the wall. We assume the pores of the vessel walls to be cylindrical and have a unimodal distribution of sizes. We calculate the hydraulic conductivity L p, vascular permeability P, and reflection coefficient σ, by the size and the surface area of the pores of the vessel walls and the size of the spherical nanoparticles as 9,,, where γ is the fraction of wall surface area occupied by pores, r o is the pore radius, L is the thickness of the vessel wall, D o is the diffusion coefficient of the particle in free solution at 37 o C given by the Stokes-Einstein relationship, and the diffusive, H, and convective, W, hindrance factors are given in Bungay and Brenner 10. These hindrance factors depend on the relative size of the particles to the pores (Fig. 4b) 2

3 Solution strategy: For the solution strategy we employ a two-dimensional percolation network with one inlet and one outlet to represent the structure of the tumour vasculature 1-2 (Fig. 3a), and follow a procedure similar to that employed by Baish et al 3. We discretize the intravascular and interstitial space with computational nodes as shown in Supplementary Fig. S4. For the vascular space we assign a different pore size to each of the computational nodes taken by a unimodal distribution with given mean and standard deviation. Therefore each of these nodes has its own values of L p, P, and σ. We first solve the coupled steady state fluid problem to calculate the vascular and interstitial fluid pressures, assuming that the fluid flow entering each computational node equals the fluid flow exiting the node, i.e., for each node i. For boundary conditions, we specify the vascular pressure at the inlet and outlet of the network. The boundaries of the interstitial space, are assumed to be surrounded by lymphatic vessels and specify the pressure there to be zero. Subsequently, we solve the transient nanoparticle transport problem with a finite difference method using central differencing for diffusion, upwind differencing for convection and an explicit Euler time integration scheme. We model a bolus injection of the nanoparticles according to the experimental procedure. The dimensionless concentration of the particles at the inlet is one and it is decaying exponentially based on our experimental measurements of the blood-half-life of the particles. The concentration at the outlet and at the boundary of the interstitial space is set to zero. Calculation of effective vascular permeability: To use the model in order to calculate the effective vascular permeability, P eff, we follow the same methodology as is being done in the experiment. We define a region at the centre of the interstitial space surrounding the blood vessels and record the average concentration of nanoparticles through time. The effective permeability should satisfy the equation: 3

4 , where C is the average concentration in the interstitial space, S v the vascular density, and C v the concentration of nanoparticles in the blood given by. C vo is the initial concentration, t the time, and K d is the blood half-life. Combining the two equations we get:. We fit the above equation to the model calculations of the average concentrations through time and derive the value of the effective vascular permeability. Values of model parameters: The values of the model parameters are summarized in Supplementary Table S3. The blood half-lives of these nanoparticles were measured in a previous study 11, while the interstitial diffusion coefficient of the particles were obtained by published experimental measurements of macromolecules with similar hydrodynamic diameter as the diameter of the nanoparticles employed in the current study 12 (Supplementary Table S4). Fluid pressure calculations: Typical fluid pressure calculations for vessels with small and large pores are shown in the following Supplementary Figs. S5 and S6. For small pores (Supplementary Fig. S5), the IFP is low and a transvascular pressure difference is established across the vessel wall. For large pores (Supplementary Fig. S6), the IFP at the centre of the tumour increases and becomes comparable to the microvascular pressure. As a result, the transvascular pressure difference across the vessel wall is no longer maintained. Moreover, according to our simulations it is likely for large pores the IFP to locally exceed the microvascular pressure. 4

5 Supplementary Tables Supplementary Table S1 Studies reporting the impact of anti-vegf pathway normalization strategies on the delivery of therapeutic compounds/systemically administered molecules into tumours. Adapted from Goel et al 13. Systemically administered molecule Anti-angiogenic therapy Tumour model(s) Effect on delivery Conventional cytotoxics Irinotecan A4.6.1 Colon carcinoma 14 Topotecan, etoposide Bevacizumab Neuroblastoma 15 Temozolomide Sunitinib Glioma * Antibodies Non-specific IgG, anti-e-cadherin Ab Axitinib Lung carcinoma, pancreatic tumour (per vessel) 18 Other molecules BSA DC101 Breast carcinoma, colon carcinoma 19 FDG Bevacizumab Rectal carcinoma (per vessel) ** *Increased delivery of temozolomide noted with sunitinib 20mg/kg, but not at 60mg/kg **Study performed in human subjects [Abbreviations: BSA, bovine serum albumin; FDG, fluorodeoxyglucose] 5

6 Supplementary Table S2 Studies reporting anti-vegf and downstream pathway inhibition-induced improvements in tumour oxygenation. Adapted from Goel et al 13. Anti-angiogenic therapy Tumour model Effect on oxygenation Time window of improved oxygenation Antibody therapy Bevacizumab Melanoma, breast carcinoma, ovarian carcinoma 2-4 days after start of therapy 22 Bevacizumab GBM Up to 5 days 23 DC101 GBM 2-8 days after start of therapy 24 Anti-PlGF Ab Pancreatic carcinoma No change N/A 25 TKI therapy Sunitinib Squamous carcinoma Semaxanib Melanoma O 2 measured 4 days after start of therapy 26 O 2 measured 3 days after start of therapy 27 PI-103 (PI3K inhibitor) Fibrosarcoma, squamous carcinoma O 2 measured 10 days after start of therapy 28 Other therapies FTIs (Ras inhibitors) Prostate carcinoma, bladder carcinoma, glioma, fibrosarcoma, squamous carcinoma O 2 increased up to 7-10 days Nelfinavir (AKT inhibitor) Fibrosarcoma, squamous carcinoma O 2 measured 10 days after start of therapy 28 PLX4720 (BRAF inhibitor) Melanoma, colorectal carcinoma O 2 measured 14 days after start of therapy 31 Genetic models VEGF -/- (myeloid cells) nnos -/- (tumour cells) Lung carcinoma N/A 32 Glioblastoma N/A 33 v 3/ v 5 integrin- FAK-Rho knockdown (tumour cells) Glioblastoma N/A 34 [Abbreviations: FAK, Focal Adhesion Kinase; GBM, glioblastoma multiforme; nnos, neuronal Nitric Oxide synthase; PI3K, Phosphoinostide-3-kinase; PlGF, Placental Growth Factor; TKI, tyrosine kinase inhibitor; VEGF, Vascular Endothelial Growth Factor] 6

7 Supplementary Table S3 Physiological values of the model parameters. Model parameters Value Reference Size of the domain Blood viscosity Vascular pressure at the inlet Vascular pressure at the outlet 1 cm 3x10-5 (mmhg-sec) 25 mmhg 5 mmhg Vascular density 200 cm Vessel wall thickness Vessel diameter Interstitial Space Conductivity 5 μm 15 μm 8x10-7 cm 2 /mmhg-sec

8 Supplementary Table S4 Diffusion coefficients 12 and blood half-life data 11 used in the mathematical model. Particle size 1 nm 12 nm 60 nm 125 nm 250 nm Diffusion coefficient (cm 2 /s) 2x10-6 2x10-7 5x10-8 6x10-9 1x10-9 Blood Half-life (min) 1550* 1480± ±97 582±48 500* * extrapolation from experimental data 8

9 Supplementary Figures Supplementary Figure S1 Structural vascular normalization window based on tumour vessel diameter. We imaged blood vessel networks in SCID mice bearing orthotopic E0771 mammary tumours in mammary fat pad windows, and we treated these mice with either 5mg/kg DC101 therapy or non-specific rat IgG (control) every three days starting on day 0. Treatment with DC101 resulted in a reduction in mean vessel diameter on day 2 (p=0.03, Student s t-test), with no difference by day 8, indicating the presence of a normalization window. Animal number n=4-6 for all groups. 9

10 Supplementary Figure S2 Nanoparticle penetration versus particle size in orthotopic E0771 mammary tumours in response to normalizing therapy with DC101. Intensities are relative to initial intravascular levels, with vessels in black. Normalization on day 2 after 5mg/kg DC101 improves 12nm particle penetration while not affecting 125nm penetration. Scale 100μm. 10

11 Supplementary Figure S3 Effect of a higher DC101 dose on nanoparticle delivery. A 10mg/kg dose of DC101 does not improve transvascular flux for any size of nanoparticle in orthotopic E0771 mammary tumours. Animal number n=4-5 for all groups. 11

12 Supplementary Figure S4 Local connectivity of the network. The arrows show the directions of possible fluid flow. 12

13 Supplementary Figure S5 Predicted fluid pressure for small pores. Dimensionless IFP (top) and transvascular pressure difference (bottom) for a unimodal pore size distribution with mean: 40nm and standard deviation: 20nm. The pressure values are dimensionless by division with the vascular pressure at the inlet. 13

14 Supplementary Figure S6 Predicted fluid pressure for large pores. Dimensionless IFP (top) and transvascular pressure difference (bottom) for a unimodal pore size distribution with mean: 400nm and standard deviation: 200nm. The pressure values are dimensionless by division with the vascular pressure at the inlet. 14

15 Supplementary Figure S7 Size of Abraxane nanomedicine upon dilution. We measured the hydrodynamic diameter of Abraxane upon dilution in PBS using dynamic light scattering. We found that Abraxane had an initial size of 130.7nm before dilution, but immediately decreased in size to 8.8nm upon dilution. We also characterized an intermediate size of 24.4nm. Furthermore, we found that Abraxane similarly breaks down in bovine serum albumin solution a simulated plasma indicating that it reaches a ~10nm size in vivo. 15

16 Supplementary Figure S8 Fits of the model predictions to the experimental data. The lines represent the predictions, while the points show the experimental data. For 4T1 tumours, 10mg/kg DC101 seems to reduce the mean pore size from 400nm to 140nm while maintaining the pore size standard deviation at 60nm. For E0771 tumours, 5mg/kg DC101 appears to reduce the mean pore size from 400nm to 100nm and the pore size standard deviation from 60nm to 20nm. These data suggest that normalizing therapy may reduce both mean pore sizes and pore size heterogeneity to achieve reductions in IFP. 16

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