Sr represents released drug in the interstitial fluid: Slp=Flp−Fll, (21) where Flp is the liposome encapsulated doxorubicin gained from the capillaries in

tumour and normal tissues, and Fll is the loss of liposome encapsulated doxorubicin through the lymphatic vessels per unit volume of tissue. Using the pore model for transcapillary exchange, Flp and Fll can be expressed as Flp=Fv(1−σl)Clp+PlSV(Clp−Cle)PelePel−1,Fll=FlyCle, Inhibitors,research,lifescience,medical (22) where Clp is the concentration of liposome in blood plasma, σl is the osmotic reflection coefficient for the liposome particles, and Pl is the permeability of vasculature wall to liposome. Pel is the transcapillary Peclet number defined as Pel=Fv(1−σl)Pl(S/V). (23) The amount of released liposome encapsulated drug in the Inhibitors,research,lifescience,medical interstitial fluid, Sr, is given by Sr=krel⁡Cle, (24) where krel is the release rate of liposome. 2.3.2. Free Doxorubicin Concentration in Blood Plasma (Cfp) This is described by ∂Cfp∂t=Sr−VTVBFfp−CLfpCfpVD−(kaCfp−kdCbp), (25) where Ffp represents the free doxorubicin crossing the capillary wall into the interstitial fluid. VT is tumour volume, VB is plasma volume, and VD is the volume of distribution,

which Inhibitors,research,lifescience,medical is a pharmacological theoretical volume that a drug would have to occupy to provide the same concentration as it is currently in blood plasma. CLfp is the plasma clearance of drug. ka and kd are the association and disassociation rates with proteins. 2.3.3. Bound Doxorubicin Inhibitors,research,lifescience,medical Concentration in Blood Plasma (Cbp) This is described by ∂Cbp∂t=(kaCfp−kdCbp)−VTVBFbe−CLbpCbpVD, (26) where CLbp is the plasma clearance of bound doxorubicin. 2.3.4. Free Doxorubicin Concentration

in Interstitial Fluid (Cfe) This is described by ∂Cfe∂t+∇·(Cfev)=Dfe∇2Cfe+Sf. (27) The source term Sf is the net rate Inhibitors,research,lifescience,medical of doxorubicin gained from the surrounding environment, which is given by Sf=Sv+Sb+Su+Sr. (28) Expressions for the terms on the right hand side have been given previously (see (11)–(14) and (24)). 2.4. Pharmacodynamics Model During anticancer treatment, tumour cell density may change due to cell killing as a result of drug effect, tumour cell proliferation, and physiological degradation. This can be described by a pharmacodynamics whatever model as given below: dDcdt=−fmax⁡CiEC50+CiDc+kpDc−kgDc2. (29) The first term on the right hand side represents the effect of anticancer drug, where fmax is the cell-kill rate constant and EC50 is the drug concentration producing 50% of fmax . kp and kg are cell proliferation rate constant and physiologic degradation rate, respectively. In this study, cell proliferation and physiologic degradation are assumed to reach equilibrium at the beginning of each treatment. 2.5. Model Geometry A 2D R428 chemical structure idealized model with a realistic tumour size (Figure 1) is used in this study. The tumour is located at the centre, which is surrounded by a layer of normal tissue. The diameter of the tumour is 50mm, and the thickness of the normal tissue is 10mm.