The effect of interstitial pressure on therapeutic agent transport: coupling with the tumor blood and lymphatic vascular systems

Abstract

Vascularized tumor growth is characterized by both abnormal interstitial fluid flow and the associated interstitial fluid pressure (IFP). Here, we study the effect that these conditions have on the transport of therapeutic agents during chemotherapy. We apply our recently developed vascular tumor growth model which couples a continuous growth component with a discrete angiogenesis model to show that hypertensive IFP is a physical barrier that may hinder vascular extravasation of agents through transvascular fluid flux convection, which drives the agents away from the tumor. This result is consistent with previous work using simpler models without blood flow or lymphatic drainage. We consider the vascular/interstitial/lymphatic fluid dynamics to show that tumors with larger lymphatic resistance increase the agent concentration more rapidly while also experiencing faster washout. In contrast, tumors with smaller lymphatic resistance accumulate less agents but are able to retain them for a longer time. The agent availability (area-under-the curve, or AUC) increases for less permeable agents as lymphatic resistance increases, and correspondingly decreases for more permeable agents. We also investigate the effect of vascular pathologies on agent transport. We show that elevated vascular hydraulic conductivity contributes to the highest AUC when the agent is less permeable, but to lower AUC when the agent is more permeable. We find that elevated interstitial hydraulic conductivity contributes to low AUC in general regardless of the transvascular agent transport capability. We also couple the agent transport with the tumor dynamics to simulate chemotherapy with the same vascularized tumor under different vascular pathologies. We show that tumors with an elevated interstitial hydraulic conductivity alone require the strongest dosage to shrink. We further show that tumors with elevated vascular hydraulic conductivity are more hypoxic during therapy and that the response slows down as the tumor shrinks due to the heterogeneity and low concentration of agents in the tumor interior compared with the cases where other pathological effects may combine to flatten the IFP and thus reduce the heterogeneity. We conclude that dual normalizations of the micronevironment - both the vasculature and the interstitium - are needed to maximize the effects of chemotherapy, while normalization of only one of these may be insufficient to overcome the physical resistance and may thus lead to sub-optimal outcomes.

Keywords: Cancer simulation; Chemotherapy; Interstitial fluid pressure; Tumor lymphatics; Tumor vasculature.

Figure 1

Agent distribution in the tumor tissue arising from constant injection at early times. Tissue is shown in a 2×2mm area: tumor with viable tissue in red, hypoxic in blue, and necrotic in brown, with the pre-existing vasculature (brown rectangular gridlines) as well as the neovasculature (irregular brown lines) originating in response to the net release of pro-angiogenic factors from the tumor hypoxic regions. The left column shows the concentration in the blood, the middle shows the transcapillary concentration flux, and the right shows the concentration in the tissue. Row 1 corresponds to t = 0.17 min, row 2 corresponds to t = 1 min and row 3 corresponds to t = 2.5 min. With only transcapillary convection (k_T = k_D = 0), the agent extravasation is small due to the hypertension in the tissue which impedes TFF.

Figure 2

Agent distribution in the tumor tissue at later times. The left column shows the concentration in the blood, the middle shows the transcapillary concentration flux, and the right shows the concentration in the tissue. Row 1 corresponds to t = 4.17 min, row 2 corresponds to t = 16.7 min, and row 3 corresponds to t = 100 min. At t = 4.17 min, the agent concentration distribution in the blood reaches a homogeneous state which persists through t = 100 min. In row 3, the distribution of agent in the tissue shows a decrease in the tumor interior due to the lack of TFF.

Figure 3

Concentration of agent with k_T = k_D = 0 in the tissue (cross section from the center) at t = 100 min. reveals a peak in the tumor region (blue curve) compared with the case when k_T = k_D > 0 (red curve).

Figure 4

Average agent concentration (scaled by injection concentration) in the tumor vs. time (min.) shown in each subplot with lymphatic resistance KL_max = 1 in red, KL_max = 2 in green and KL_max = 3 in blue under bolus/constant (column 1/column 2) injection with/without (row 1/row 2) elevated vascular hydraulic conductivity. In all cases, a larger lymphatic resistance (i.e., KLmax = 3, blue curves) contributes to more rapid delivery to the tissue, which also contributes to a more rapid washout in the bolus injection case (column 1). For a lower lymphatic resistance (i.e., KLmax = 1, red curves), there is more drug in the tumor at later stages (t > 50 min) due to the inability of the drug to leave the tissue through either the vasculature or the lymphatics. The contrast between the two behaviors is accentuated with elevated vascular hydraulic conductivity (row 2 compared with row 1).

Figure 5

Agent availability in tumor tissue over time (area under the curve, AUC) after bolus injection with elevated vascular/interstitial hydraulic conductivity (black/cyan) compared with control (magenta) as a function of KL_max (x-axis). The left plot corresponds to convective transport of drug from the vasculature (k_D = k_T = 0) while the right plot considers other transport mechanisms (k_D = k_T > 0). In the convection only case (left), the AUC increases as KL_max for all cases while elevated vascular hydraulic conductivity contributes to a higher AUC. In addition, an elevated interstitial hydraulic conductivity contributes to lower AUC compared to the control. With additional transport (right), the AUC increases to a higher level in all cases but decreases as KL_max increases. The cases with elevated vascular/interstitial hydraulic conductivities exhibit lower AUC compared with the control. With an elevated interstitial hydraulic conductivity, the AUC is low with and without additional transport, which represents a transport impairment in general (cyan curve lies below the magenta and black curves). On the other hand, an elevated vascular hydraulic conductivity contributes to a higher AUC (black curve lies above the magenta curve) when the agent transport depends solely on convection. When there is elevated vasculature hydraulic conductivity, additional transcapillary transport, contributes to a lower AUC (black curve lies below the magenta curve).

Figure 6

Tumor vasculature, IFP and the distribution of drugs before the tumor response at day 18.07. The tumor with elevated tumor interstitial hydraulic conductivity has a broad base plateau profile of IFP (Column 2, Row 2) whereas the IFP with elevated tumor vascular hydraulic conductivity (Column 3) is more hypertensive compared to the control (Column 1) due to excessive fluid extravasation. The broad base plateau profile contributes to a larger elevated IFP area and fluid flow away from the tumor [Wu et al., 2013]. This decreases the drug concentration in and near the tumor (Column 2) while the plateau profile itself makes the drug distribution more uniform inside the tumor compared to the control (Column 2). Excessive fluid extravasation by an elevated tumor vascular hydraulic conductivity contributes to higher drug extravasation, thus increasing the concentration in the interstitium (Column 3), but the distribution is heterogeneous and the concentration in the tumor remains low (though higher than the base case).

Figure 7

Tumor tissue, vasculature, and pressure with elevated vascular/interstitial hydraulic conductivities during treament with poorly-permeable (k_D = k_T = 0) drugs at high doses (λ_effect = 1) for day 18.23 until the end of the treatment at day 23.10. Although all the treated tumors have negative pressures due to cell death, those with elevated interstitial hydraulic conductivity maintain a higher pressure due to insufficient drug extravasation (Column 2 in Fig. 6). Tumors with elevated vascular hydraulic conductivity have the most negative pressure and shrink the most by day 23.10 due to higher agent concentration resulting from excessive fluid extravasation.

Figure 8

Tumor radius after ≈ 5 days of treatment by varying drug strength λ_effect from 0 to 1 (0 corresponds to an untreated tumor), with elevated vascular/interstitial hydraulic conductivity (green and blue, respectively), their combination (cyan curve), and their further combination with an attenuated transvascular osmotic pressure difference (magenta curve), compared to the control (red curve). The black horizontal line corresponds to the tumor radius before therapy. Tumors with elevated interstitial hydraulic conductivity (blue curve) do not shrink until the drug concentration increases to ~ 0.9, which is a slightly slower effect than the control (~ 0.85), due to the excessive fluid flow from the tumor into the surrounding tissue. Tumors with elevated vascular hydraulic conductivity (green curve) begin to shrink when the drug strength increases to ~ 0.45. However, with elevated vascular hydraulic conductivity alone, the shrinkage seems to saturate (green line) (note the transition between the green curve and the cyan or magenta curves), due to the heterogeneity and low drug concentration in the tumor interior. The tumor shrinkage slows down once the tumor radius ≲ 0.35 mm.