Attenuated Microcirculation in Small Metastatic Tumors in Murine Liver

pharmaceutics

Article Attenuated Microcirculation in Small Metastatic Tumors in Murine Liver

Arturas Ziemys 1,*, Vladimir Simic 2, Miljan Milosevic 2, Milos Kojic 1,2, Yan Ting Liu 1 and Kenji Yokoi 1

1 Houston Methodist Research Institute, Houston, TX 77030, USA; [email protected] (M.K.); [email protected] (Y.T.L.); [email protected] (K.Y.) 2 Bioengineering Research and Development Center BioIRC Kragujevac, 3400 Kragujevac, Serbia; [email protected] (V.S.); [email protected] (M.M.) * Correspondence: [email protected]

Abstract: Metastatic cancer disease is the major cause of death in cancer patients. Because those small secondary tumors are clinically hardly detectable in their early stages, little is known about drug biodistribution and permeation into those metastatic tumors potentially contributing to insufficient clinical success against metastatic disease. Our recent studies indicated that breast cancer liver metastases may have compromised perfusion of intratumoral capillaries hindering the delivery of therapeutics for yet unknown reasons. To understand the microcirculation of small liver metastases, we have utilized computational simulations to study perfusion and oxygen concentration fields in and around the metastases smaller than 700 µm in size at the locations of portal vessels, central vein, and liver lobule acinus. Despite tumor vascularization, the results show that blood flow in those tumors can be substantially reduced indicating the presence of inadequate blood pressure gradients

across tumors. A low blood pressure may contribute to the collapsed intratumoral capillary lumen limiting tumor perfusion that phenomenologically corroborates with our previously published

Citation: Ziemys, A.; Simic, V.; in vivo studies. Tumors that are smaller than the liver lobule size and originating at different lobule Milosevic, M.; Kojic, M.; Liu, Y.T.; locations may possess a different microcirculation environment and tumor perfusion. The acinus and Yokoi, K. Attenuated Microcirculation portal vessel locations in the lobule were found to be the most beneficial to tumor growth based on in Small Metastatic Tumors in Murine tumor access to blood flow and intratumoral oxygen. These findings suggest that microcirculation Liver. Pharmaceutics 2021, 13, 703. states of small metastatic tumors can potentially contribute to physiological barriers preventing https://doi.org/10.3390/pharmaceutics efficient delivery of therapeutic substances into small tumors. 13050703 Keywords: metastases; liver lobule; perfusion; diffusion; therapeutic resistance Academic Editor: Giovanni Tosi

Received: 26 March 2021 Accepted: 10 May 2021 1. Introduction Published: 12 May 2021 Despite advancements in anticancer treatments, advent of immunotherapies, and im-

Publisher’s Note: MDPI stays neutral proved diagnostics, metastatic disease remains the leading cause for 90% of cancer-related with regard to jurisdictional claims in deaths [1]. The low therapeutic efﬁcacy of anti-cancer treatments for metastatic tumors neg- published maps and institutional afﬁl- atively impacts patient survival. While many types of primary tumors can be imaged and iations. resected due to their size, it is challenging to even detect the metastases spreading from the primary site to distant organs which are made of individual circulating cancer cells (CTCs) or small CTC clusters [2,3]. The majority of CTCs are eliminated by the immune system of the host, but some can circulate in the bloodstream to reach and reside in the distant organs eventually becoming secondary tumors. Detection of such small cells is beyond Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. current imaging capabilities due to a limited resolution of the modern clinical non-invasive This article is an open access article diagnostic tools [4]. Thus these cells or cell clusters at distant organs, frequently referred to distributed under the terms and as micrometastases in clinics, can escape their detection [5]. conditions of the Creative Commons These tiny secondary tumors may only be treated therapeutically on a systemic basis Attribution (CC BY) license (https:// while also acknowledging common resistance mechanisms [6]. Drug biodistribution by the creativecommons.org/licenses/by/ cardio-vascular system and drug extravasation/permeation into tissue microenvironment 4.0/). are key factors in delivering chemotherapeutic or immunotherapeutic drugs to cancer

Pharmaceutics 2021, 13, 703. https://doi.org/10.3390/pharmaceutics13050703 https://www.mdpi.com/journal/pharmaceutics Pharmaceutics 2021, 13, 703 2 of 11

cells inside tumors. Nanoformulations were shown to be effective in exploiting Enhanced Retention and Permutation (EPR) effect in murine models. However, this effect is not widely present in humans and such nanoformulated drugs do not always reach their desired potential [7,8]. These formulations exploit the features of the capillary bed found in primary tumors; however, the small metastatic tumors may have no vasculature at times and different drug delivery strategies should be considered. Inadequate understanding of microcirculation in metastases could be one of the reasons that treatments of metastatic disease fail. Limited knowledge of drug delivery coupled with scarce literature on the circulation in micrometastases contributes to poor outcomes in surviving metastasis disease. It is likely that there is a common assumption that drugs should reach those tiny tumors without obstacles and drug delivery challenges are impulsively dismissed in research questions. However, some of our studies conducted on murine breast cancer liver metastases have undoubtedly indicated that drug permeation into metastatic tumors is fundamentally hindered [9,10]. The metastatic tumors ranging from 50 to >600 µm in size did not show doxorubicin inside the tumors; instead, most of doxorubicin was presented in liver tissue surrounding those tumors. Drug permeation was not observed at any point of time for up to several days and the treatment did not affect tumor progression: Nontreated and treated animal groups have shown the same tumor progression. The common determinant of this therapeutic outcome is the absence of drug in tumors. Even though our immunohistochemical imaging and intravital microscopy indicates the presence of vasculature, the tumor capillaries were not functioning due to compromised blood flow [9]. Some studies have indicated that establishment of micrometastases may alter hepatic perfusion (e.g., the presence of ~500 µm size metastases in rats decreased hepatic perfusion on the level of an organ by up to 25%) [11]. Other studies have also found that the presence of metastases could significantly reduce liver perfusion in rats [12]. However, these results cannot explain the perfusion patterns present in and around metastases. One study investigated the intratumoral capillary perfusion in colon cancer liver metastases as a function of tumor progression [13]. Those results indicated that small tumors start as avascular but developed vascularization and perfusion during their progression above 500 µm in tumor size. Our previous study on breast cancer liver metastases [10] did not reveal evidences of perfusion within these tumor dimensions, but the differences in tumor models should be noted. Other study using casting techniques indicated that small metastases in the liver start in the liver lobules and eventually develop arterial supply only when tumors grew above 800–1000 µm [14]. While the overall number of studies is small, we one can notice that only larger tumors develop perfusion. However, the critical size at which tumors start angiogenesis and getting perfused can be different in different animal and tumor models. Thus, the question of how drugs reach those small tumors becomes even more relevant. This study extends our focus on drug delivery challenges to liver metastases by conducting simulations of blood perfusion and oxygen permeation to metastatic tumors. The computational models inspired by our previous published in vivo results seek to understand better what physiological factors could be important in this problem. Our main goal is to understand what local microcirculation patterns are developed at different tumor locations in the liver lobule and how these patterns may influence drug delivery.

2. Material and Methods 2.1. Computational Perfusion and Diffusion Analysis Perfusion and diffusion were simulated by using our developed Composite Smeared Finite Element (CSFE) method [15,16], which employs the concept of smeared physical fields, like fluid flow, molecule transport by convection and diffusion through capillary system and tissue, or capillary density. Fluid flow within capillaries is governed by the Hagen–Poiseuille law, while in tissue it is modeled according to the Darcy pressure–velocity relationship. It is assumed that the Fickian law is applicable for diffusion. The 1D transport Pharmaceutics 2021, 13, x 3 of 11 Pharmaceutics 2021, 13, 703 3 of 11

Hagen–Poiseuille law, while in tissue it is modeled according to the Darcy pressure–ve‐ in capillarieslocity relationship. is transformed It is assumed into a continuum that the format.Fickian Thelaw materialis applicable parameters for diffusion. of the modelThe 1D includetransport fluid viscosity,in capillaries hydraulic is transformed permeability into a of continuum the capillary format. walls, The Darcy material coefficient parameters for fluidof flow the inmodel tissue, include and diffusivity fluid viscosity, in capillaries hydraulic and permeability tissue for diffusion.of the capillary walls, Darcy coefficientFinite Element for fluid (FE)-based flow in tissue, and other and Computationaldiffusivity in capillaries Fluid Dynamics and tissue (CFD) for diffusion. methods were alreadyFinite successfully Element (FE) applied‐based and to other study Computational hepatic circulation, Fluid Dynamics including (CFD) in a methods human liverwere [17– already19]. The successfully SCFE method applied simulated to study localhepatic perfusion circulation, and including diffusion in fieldsa human in liver the vicinity[17–19]. of a The small SCFE tumor method embedded simulated in local different perfusion locations and diffusion with respect fields toin the liver vicinity lobule of witha lobule small tumor side distance embedded of in 250 differentµm (representative locations with distancerespect to between liver lobule portal with vessels lobule side in liverdistance lobule hexagon). of 250 μm Each (representative model has distance common between key components: portal vessels sinusoidal in liver lobule capillaries, hexa‐ livergon). tissue, Each portal model vessels, has common and central key components: vein. Blood flowsinusoidal was pressure-driven capillaries, liver fromtissue, portal portal vesselsvessels, into the and central central vein vein. by Blood passing flow through was pressure capillaries‐driven of the from sinusoidal portal vessels space into (Figure the cen1 ).‐ The modeltral vein was by executedpassing through in 2D setup capillaries with tissueof the sinusoidal thickness setspace to 1(Figureµm. 1). The model was executedPortal and in 2D central setup vessels with tissue were thickness modeled set explicitly to 1 μm. with assigned vessel diameters of 40 andPortal 25 µ m,and and central local vessels blood were pressures modeled of explicitly 250 and 0with Pa, assigned that is a vessel driving diameters force of of local40 hemodynamics and 25 μm, and in local liver blood lobule. pressures The portal of 250 vessel and triad 0 Pa, was that simplified is a driving into force one of main local vessel.hemodynamics The pressure in differenceliver lobule. was The adjustedportal vessel to representative triad was simplified values into found one main in in vessel. vivo studiesThe [pressure20]. The difference sinusoidal was lobule adjusted domain to representative was simulated values with found the smeared in in vivo vascular studies and[20]. tissue The domains. sinusoidal The lobule sinusoidal domain capillary was simulated domain with was simulatedthe smeared with vascular the volumetric and tissue capillarydomains. fraction Ther sinusoidalV = 0.4, the capillary capillary domain diameter was of simulated 8 µm, and with the capillary the volumetric wall thickness capillary of 1 fractionµm. Blood rV = viscosity0.4, the capillary was set diameter to 0.001 of Pa 8· μs.m, The and hydraulic the capillary permeability wall thickness of capillary of 1 μm. wallsBlood was viscosity set to zero was because set to 0.001 the Pa pressure∙s. The hydraulic gradient permeability in sinusoidal of space capillary is only walls present was set alongto capillary zero because length the and pressure our previous gradient studies in sinusoidal indicated space clearly is only that present were effectivelyalong capillary no perfusionlength inside and our small previous metastatic studies tumors indicated in liver clearly [9, 10that]. were effectively no perfusion inside smallWe have metastatic built three tumors representative in liver [9,10]. perfusion models, where small metastatic tumors get initiatedWe inhave the built central three vein representative (Figure1A), portalperfusion vein models, (Figure where1B), and small acinus metastatic ( Figure tumors1C ). If theget tumor initiated domain in the overlapped central vein with (Figure portal 1A), or central portal vessels vein (Figure in liver 1B), lobules, and acinus those vessels (Figure were1C). eliminated If the tumor from domain the model. overlapped Capillaries with portal inside or tumors central werevessels modeled in liver lobules, in the same those vessels were eliminated from the model. Capillaries inside tumors were modeled in the way as in the liver domain, just different rV values were assigned as it is explained further. Bloodsame viscosity way as in in tumors the liver was domain, set to 0.003 just different Pa·s to mimic rV values vascular were assigned tortuosity as effects. it is explained further. Blood viscosity in tumors was set to 0.003 Pa∙s to mimic vascular tortuosity effects. Oxygen (O2) diffusion was simulated to understand the impact of the changes of local Oxygen (O2) diffusion was simulated to understand the impact of the changes of local microcirculation upon the presence of tumors. The diffusion coefficient of O2 was set to 1000microcirculationµm2/s, which is upon 2.5 times the presence lower from of itstumors. diffusivity The diffusion in water coefficient to reflect potential of O2 was effects set to 1000 μm2/s, which is 2.5 times lower from its diffusivity in water to reflect potential effects3 from dense tissues [21,22]. Arterial O2 concentration is 0.13 mM [23] or 0.13 amol/µm ; 3 however,from becausedense tissues it is mixed [21,22]. approximately Arterial O2 concentration at a 1:4 ratio is with 0.13 venous mM [23] blood or 0.13 in theamol/ portalμm ; however, because it is mixed approximately at a 1:4 ratio with venous3 blood in the portal structure, O2 concentration in portal vessels was set to 0.085 amol/µm .O2 consumption structure, O2 concentration in portal vessels was set to 0.085 amol/μm3. O2 consumption by tissues was simulated by introducing a sink term in tissue domains with representative by tissues was simulated by introducing a sink term in tissue domains with representative consumption rates of 0.03 in tumors and 0.05 in liver [23,24]. consumption rates of 0.03 in tumors and 0.05 in liver [23,24].

Figure 1. Schematics of three representative models of small metastatic tumors in the liver at different locations with Figure 1. Schematics of three representative models of small metastatic tumors in the liver at different locations with respect respect to liver lobule structure: (A) central vein, (B) portal vein, and (C) acinus. Portal vessels are represented by open to liver lobule structure: (A) central vein, (B) portal vein, and (C) acinus. Portal vessels are represented by open circles and circles and portal veins by blue filled circles. Red gradient illustrates the O2 gradients and red arrows represent blood flow portal veins by blue ﬁlled circles. Red gradient illustrates the O2 gradients and red arrows represent blood ﬂow direction from portal vessel toward central veins. The black circles represent tumors with different radii (50, 200, 350 µm) to illustrate how tumor size interferes with local blood microcirculation during tumor progression.

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2.2. In Vivo and Imaging Experiments The in vivo and imaging data that were used in this study for the comparison to simulations were published in [10]. Here we provide only a brief summary of those experiments for the benefit of readers. Experimental liver metastases were created by injecting 4T1 breast cancer cells (1 × 105/100 µL) into the spleen bodies of female Balb/C mice (6–8 weeks of age). Later, mice were intravenously injected with 6 mg/kg PLD (Doxoves-Liposomal Doxorubicin HCl; FormuMax Scientific Inc., Sunnyvale, CA, USA) and sacrificed 24 h later. The liver was excised and processed to image endothelial cells, nuclei, and PLD accumulation. The surgical procedures have been approved by the Institutional Animal Care and Use Committee (IACUC) of Houston Methodist Research Institute. Immunofluorescent staining of endothelial cells and nuclear staining were performed using antibodies to CD31 and DAPI, respectively. The fluorescence of doxorubicin was imaged at the excitation and emission wavelengths of 488 and 590 nm. The images were captured using a confocal laser-scanning microscope.

3. Results

We simulated blood perfusion and O2 diffusion patterns in and around small metastatic tumors in the liver seeking to understand how the establishment of a tumor in specific liver lobule locations can affects the perfusion of tumors, the microenvironment, and O2 concentration. As the liver lobules comprise characteristic locations such as the portal vein, central vein, and acinus, we simulated tumors of different sizes at those locations with different vascular fractions to mimic avascular and vascular states of tumors. Different rV values were investigated as a result of our previous findings, which elucidated that tumor capillarization can be heterogeneous despite the presence of nonperfused capillaries in the tumors [9,10]. Thus, diffusion may become the key determinant for the fundamental mass exchange mechanisms at the microenvironment level. The simulation of avascular tumors (rV = 0) in an idealized symmetric vascular configuration and vascularized tumors (rV = 0.05), in both an idealized symmetric avascular and vascular configuration, were performed by imposing 20% randomized shift in x- and y-coordinates of portal and central vessels. To model tumor progression effect on perfusion and diffusion patterns, we simulated tumors of different radii (R) in the range 50–350 µm. Central vein location: Tumors established at the central vein location obstruct the drainage of blood from the six surrounding portal vessels and further immobilize the function of the central vein (Figure2A). This situation implies that the blood flow is compromised inside the lobule where the source of O2 and nutrients delivery to the tumors are solely dependent on diffusion mechanisms. The perfusion of a tumor was estimated by calculating the mean flow velocity in the tumor domain; results are plotted in Figure2B . While blood flow velocities in the liver were at 50–100 µm/s, blood flow velocities in tumors were effectively absent for small tumors with R < 150 µm. Only when the tumor radius approached 200 µm and the tumor became comparable in size with the liver lobule, the average tumor perfusion velocity increased to 6 µm/s. The perfusion of larger tumors that engulfed the nearest portal vessels is lost. The average O2 concentration profile in tumors was different to the flow velocity profile. Tumors with R = 50–200 µm had about ~50% of the O2 concentration that was provided by portal vessels, but the O2 concentration substantially dropped when the tumor exceeded the lobule size (Figure2C ). The O2 concentration profiles in the tumors are plotted in Figure2D, showing that O 2 concentration is almost same for tumors with smaller than the lobule. However, once the nearest portal vessels are eliminated as the tumor grows, hypoxic conditions are generated due to the lack of nutrient supply from its surrounding non-functional portal veins. The flow and O2 concentration fields are shown in Figure2E to show a poorly perfused tumor with low O 2 concertation fields surrounding or inside the tumor during its progression. Interestingly, a non-ideal position of portal and central vessels contributes to better perfusion patterns when compared to ab idealized lobule structure. However, there is little effect on the O2 field inside the tumor. Pharmaceutics 2021, 13, x 5 of 11

Pharmaceutics 2021, 13, 703 a non‐ideal position of portal and central vessels contributes to better perfusion patterns5 of 11 when compared to ab idealized lobule structure. However, there is little effect on the O2 field inside the tumor.

FigureFigure 2.2. SimulatedSimulated perfusionperfusion andand diffusiondiffusion patternspatterns forfor thethe metastaticmetastatic tumortumor establishedestablished atat thethe locationlocation ofof thethe centralcentral vein.vein. (A)) The general schematic schematic of of tumor tumor location location (see (see Figure Figure 1).1). (B ()B Average) Average tumor tumor perfusion perfusion velocity velocity as a as function a function of the of tumor size for different tumor cases: avascular tumors with idealized vessel configurations, vascularized (rV = 0.05) tumors the tumor size for different tumor cases: avascular tumors with idealized vessel configurations, vascularized (rV = 0.05) tumorsin idealized in idealized vascular vascular configuration, configuration, and vascularized and vascularized tumors tumors in non in‐idealized non-idealized (asymmetric) (asymmetric) vascular vascular configuration. configuration. (C) Average O2 concentration as a function of tumor size. (D) O2 concentration profiles inside the tumor. (E) Flow velocity and (C) Average O2 concentration as a function of tumor size. (D)O2 concentration profiles inside the tumor. (E) Flow velocity O2 concentration fields at specific tumor sizes with asymmetric portal and central vein locations (open circle—portal ves‐ and O concentration fields at specific tumor sizes with asymmetric portal and central vein locations (open circle—portal sels, dark2 circles—central veins). vessels, dark circles—central veins). Portal vein location: Tumors established at the portal vessel location hinder the func‐ Portal vein location: Tumors established at the portal vessel location hinder the tion of the portal vein and obstruct the blood supply of the vessels (Figure 3A). In contrary function of the portal vein and obstruct the blood supply of the vessels (Figure3A). Into the contrary location to of the the location central vein, of the the central tumors vein, surrounded the tumors by portal surrounded and central by portal vessels and are centralable to maintain vessels are the able perfusion to maintain and nutrient the perfusion supply and outside nutrient the tumor. supply The outside calculated the tumor. flow Thevelocities calculated in tumors flow velocitiesare close into tumorszero for are tumors close with to zero R = for 50 tumors μm but with increases R = 50 toµm 15–20 but increasesμm/s for tumors to 15–20 approachingµm/s for tumors the size approaching of the liver the lobule. size ofSimilar the liver to the lobule. tumors Similar in the to cen the‐ tumorstral vein in location, the central flow vein drops location, once tumor flow drops size gets once larger tumor than size the gets lobule larger (R than > 250 the μm) lobule and further eliminates its surrounding lobule vessels. The O2 concentration is present inside (R > 250 µm) and further eliminates its surrounding lobule vessels. The O2 concentration isthe present tumors inside with theR < tumors250 μm; with however, R < 250 it dropsµm; however, to zero for it drops larger to tumors zero for (Figure larger 3C). tumors The O2 concentration profiles show that the O2 level gradually changes inside a tumor as its (Figure3C). The O 2 concentration profiles show that the O2 level gradually changes inside ahypoxic tumor ascondition its hypoxic arises; condition especially arises; when especially the size when exceeds the size the exceeds lobule radius. the lobule Perfusion radius. 2 Perfusionand centration and centrationfields (Figure fields 3E) (Figurereveal deficiencies3E) reveal deficiencies in flow velocities in flow and velocities O concentration and O 2 concentrationcompared to the compared tumor surroundings. to the tumor surroundings.

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FigureFigure 3.3. SimulatedSimulated perfusionperfusion andand diffusiondiffusion patternspatterns forfor thethe metastaticmetastatic tumortumor established at the location of portal vessels. ((AA)) TheThe general schematic schematic of of tumor tumor location location (see (see Figure Figure 1).1 ).(B) ( AverageB) Average tumor tumor perfusion perfusion velocity velocity as a function as a function of the oftumor the size for different tumor cases: avascular tumors with idealized vessel configurations, vascularized (rV = 0.05) tumors in tumor size for different tumor cases: avascular tumors with idealized vessel configurations, vascularized (rV = 0.05) tumorsidealized in idealizedvascular configuration, vascular configuration, and vascularized and vascularized tumors in tumors non‐idealized in non-idealized (asymmetric) (asymmetric) vascular vascular configuration. configuration. (C) Av‐ erage O2 concentration as a function of tumor size. (D) O2 concentration profiles inside the tumor. (E) Flow velocity and (C) Average O2 concentration as a function of tumor size. (D)O2 concentration profiles inside the tumor. (E) Flow velocity O2 concentration fields at specific tumor sizes with asymmetric portal and central vein locations (open circle—portal ves‐ and O concentration fields at specific tumor sizes with asymmetric portal and central vein locations (open circle—portal sels, dark2 circles—central veins). vessels, dark circles—central veins). Acinus location: This location is different from portal or central vessels because it Acinus location: This location is different from portal or central vessels because it does does not occlude the lobule vessels, as the smaller tumor sizes did not change the perfu‐ not occlude the lobule vessels, as the smaller tumor sizes did not change the perfusion sion patterns surrounding the tumor (Figure 4A). This location is also characterized by a patterns surrounding the tumor (Figure4A). This location is also characterized by a lower flowlower velocity flow velocity in the liverin the lobule. liver lobule. The largest The largest tumor tumor perfusion perfusion of 20 µofm/s 20 μ wasm/s calculatedwas calcu‐ forlated the for tumor the tumor with a with radius a radius of 100 ofµm 100 (Figure μm (Figure4B). However, 4B). However, flow velocities flow velocities of 100 µofm/s 100 wereμm/s calculated were calculated for the for most the of most the tumors.of the tumors. The heterogeneity The heterogeneity of spatial of spatial positions positions of lobule of vesselslobule vessels did not did affect not perfusion affect perfusion as significantly as significantly as in the locationsas in the locations of central of or central portal vessels.or por‐ tal vessels.Tumors with R < 100 µm were well oxygenated and showed monotonic reduction of Tumors with R < 100 μm were well oxygenated and showed monotonic reduction of O2 concentration with an increase in size (Figure4C). Substantial hypoxia was developed O2 concentration with an increase in size (Figure 4C). Substantial hypoxia was developed for the tumors with R > 200 µm (Figure4D). The flow velocity and O 2 concentration for the tumors with R > 200 μm (Figure 4D). The flow velocity and O2 concentration fields fields that are depicted in Figure4E showing that small tumors are embedded well in O 2 that are depicted in Figure 4E showing that small tumors are embedded well in O2 con‐ concentration field; however, larger tumors with R > 250 µm develop O2-deprived tissues insidecentration and aroundfield; however, the tumor. larger tumors with R > 250 μm develop O2‐deprived tissues inside and around the tumor.

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FigureFigure 4. 4.Simulated Simulated perfusion perfusion and and diffusion diffusion patterns patterns for for the the metastatic metastatic tumor tumor established established at the at acinus the acinus location. location. (A) The (A) gen- The eralgeneral schematic schematic of tumor of tumor location location (see (see Figure Figure1). ( B1).) Average(B) Average tumor tumor perfusion perfusion velocity velocity as a as function a function of the of tumorthe tumor size size for for different tumor cases: avascular tumors with idealized vessel configurations, vascularized (rV = 0.05) tumors in ideal‐ different tumor cases: avascular tumors with idealized vessel configurations, vascularized (rV = 0.05) tumors in idealized ized vascular configuration, and vascularized tumors in non‐idealized (asymmetric) vascular configuration. (C) Average vascular configuration, and vascularized tumors in non-idealized (asymmetric) vascular configuration. (C) Average O2 O2 concentration as a function of tumor size. (D) O2 concentration profiles inside the tumor. (E) Flow velocity and O2 concentration as a function of tumor size. (D)O concentration profiles inside the tumor. (E) Flow velocity and O concentration fields at specific tumor sizes with asymmetric2 portal and central vein locations (open circle—portal vessels,2 concentration fields at specific tumor sizes with asymmetric portal and central vein locations (open circle—portal vessels, dark circles—central veins). dark circles—central veins). Comparison of simulated perfusion and drug extravasation patterns. Figure 5 shows Comparison of simulated perfusion and drug extravasation patterns. Figure5 shows some tumor and fluorescent therapeutic extravasation patterns in murine liver from our some tumor and fluorescent therapeutic extravasation patterns in murine liver from our previous study, where experimental breast cancer liver metastasis were employed by us‐ previous study, where experimental breast cancer liver metastasis were employed by using theing 4T1the 4T1 cell cell line line in the in the Balb/c Balb/c murine murine animal animal model model [10 [10].]. The The study study investigated investigated the the pegylatedpegylated liposomal liposomal doxorubicin doxorubicin (PLD) (PLD) biodistribution biodistribution in in the the liver liver and and in in small small metastatic metastatic tumorstumors duringduring cancercancer progression.progression. In-depthIn‐depth quantitativequantitative immunofluorescentimmunofluorescent imagingimaging analysisanalysis found high high heterogeneity heterogeneity of of transport transport properties properties of tumors, of tumors, including including tumor tumor vas‐ vascularizationcularization and and a lack a lack of of doxorubicin doxorubicin inside inside tumors. tumors. The The absence absence of of drug in tumortumor waswas observedobserved despite despite the the presence presence of of intratumoral intratumoral capillaries. capillaries. Our Our other other study study using using intravital intravital imagingimaging foundfound nono perfusionperfusion inin liverliver metastases, metastases, although although capillaries capillaries werewere present present based based onon immunofluorescentimmunofluorescent imaging [9]. [9]. Both Both studies studies led led to to the the question question about about the the origins origins of offailing failing tumor tumor perfusion. perfusion. Red Red fluorescent fluorescent drug drug doxorubicin doxorubicin (Figure (Figure 5) can5) serve can serve as a surro as a ‐ 2 surrogategate marker marker to be to compared be compared with with simulated simulated patterns patterns of perfusion of perfusion and andO centration O2 centration (Fig‐ (uresFigures 2–4).2– 4While). While this this correlation correlation is circumstantial, is circumstantial, the the comparison comparison establishes establishes contextual contex- tualrelation relation allowing allowing to judge to judge if there if there are commonalities are commonalities between between what what we simulate we simulate and what and whatwe observe. we observe. FigureFigure5 A5A shows shows a a small small tumor tumor with with doxorubicin doxorubicin fluorescence fluorescence present present around around the the tumortumor butbut notnot inside,inside, whichwhich couldcould bebe similarsimilar toto thethe tumorstumors establishedestablished atat thethe acinusacinus oror portal vessel locations. Figure 5B shows many tumors in proximity, which makes it

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portal vessel locations. Figure5B shows many tumors in proximity, which makes it difficult todifficult differentiate to differentiate the tumor the type tumor based type on based the location. on the location. However, However, there is there a tumor is a tumor (#1 in the(#1 in Figure the Figure5B) that 5B) we that could we identify could identify the peripheral the peripheral ring with ring the with absence the absence of doxorubicin of doxo‐ fluorescence,rubicin fluorescence, which can which be classifiedcan be classified as the tumors as the tumors originating originating in the area in the of thearea central of the veincentral (Figure vein (Figure2). Our 2). visual Our visual inspection inspection of immunohistochemical of immunohistochemical images images could could identify iden‐ onlytify only few few instances instances of suchof such tumors, tumors, which which further further confirmed confirmed our our assumptions assumptions forfor thethe less CTC-arrestingCTC‐arresting central vein location when compared to other investigated locations. Figure 55CC shows shows a a large large metastatic metastatic tumor, tumor, which which could could be be expected expected to to be be vascularized vascularized and perfused because of its size; however, it does not show any drug inside the tumor. Similarly, thethe tumors tumors displayed displayed in in Figure Figure5A,B 5A,B have have endothelial endothelial cells presentcells present in all ofin them.all of The few instances we could observe drug perfusion and extravasation happened in large them. The few instances we could observe drug perfusion and extravasation happened in tumors only if they had large vessels developed (Figure5D). large tumors only if they had large vessels developed (Figure 5D).

Figure 5. Chemotherapeutic drug doxorubicin extravasation patterns in murine liver tissues with 4T1 breast cancer me‐ Figure 5. Chemotherapeutic drug doxorubicin extravasation patterns in murine liver tissues with 4T1 breast cancer tastases (blue—cell nuclei stained with DAPI, red—doxorubicin, green—vasculature stained in CD31. Characteristic drug metastases (blue—cell nuclei stained with DAPI, red—doxorubicin, green—vasculature stained in CD31. Characteristic extravasation patterns could be correlated to the perfusion patterns around tumors established at different locations of druglobule extravasation (see text). A patterns–tumors couldcould be be correlated similar to to the the tumors perfusion established patterns at around the acinus tumors or established portal vessel at differentlocations; locations B–tumors of lobuleoriginating (see text). in the(A area)–tumors of the could central be similarvein; C to–large the tumors metastatic established tumor at without the acinus drug or portalextravasation; vessel locations D–drug (scale perfusion = 200 µ andm); (extravasationB)–tumors originating observed in in the large area tumors of the central only if veinthey (scale had large = 200 vesselsµm); (C developed)–large metastatic tumor without drug extravasation (scale = 500 µm); (D)–drug perfusion and extravasation observed in large tumors only if they had large vessels developed (scale = 500 µm). 4. Discussion

4. DiscussionThe results of our study suggested that microcirculation patterns in tumors and their surrounding microenvironment can be drastically altered even by the smallest tumors. The results of our study suggested that microcirculation patterns in tumors and their We have explored three representative locations of metastases. The locations of portal and surrounding microenvironment can be drastically altered even by the smallest tumors. central vessels correspond to the boundary region between larger vessels and sinusoid We have explored three representative locations of metastases. The locations of portal and capillaries, where vessel lumen changes from larger to small (portal vessels) and from central vessels correspond to the boundary region between larger vessels and sinusoid small to larger (central vein). The acinus location is different due to its position in between capillaries, where vessel lumen changes from larger to small (portal vessels) and from the two portal and central vessels where local pressure gradients and flow velocities are small to larger (central vein). The acinus location is different due to its position in between lower with a possibility of CTC accumulation. Comparing all three locations, we expect the two portal and central vessels where local pressure gradients and ﬂow velocities are the tendency of arrested CTC would diminish in the following order: portal vessels, aci‐ lower with a possibility of CTC accumulation. Comparing all three locations, we expect nus, central vein. the tendency of arrested CTC would diminish in the following order: portal vessels, acinus, The microcirculation patterns inside tumors have one similarity: Blood flow is re‐ central vein. ducedThe inside microcirculation tumors compared patterns to insidethe surrounding tumors have in onethe similarity:liver. Whereas Blood the ﬂow liver is is reduced a very insideporous tumors organ comparedwith a high to volumetric the surrounding capillary in the fraction, liver. Whereas compared the to liver tumors, is a very leading porous to organhigher with flow arate high outside volumetric tumors. capillary Furthermore, fraction, after compared tumors to are tumors, established, leading their to highersize is smaller than the liver lobule and these tiny tumors remain relatively far away from feed‐ ing vessels (e.g., portal vessels). At the same time, tumor establishment blocks the flow

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flow rate outside tumors. Furthermore, after tumors are established, their size is smaller than the liver lobule and these tiny tumors remain relatively far away from feeding vessels (e.g., portal vessels). At the same time, tumor establishment blocks the flow and creates a partially hypoxic environment inside and outside of the liver lobules. In the early phase of tumor growth, a small tumor does not depend on vessels for nutrient supply because diffusion can serve them well. It is possible that despite the developed hypoxia, which trig- gers angiogenesis, the interior of tumors may not have enough of a pressure gradient to provide efficient flow and mechanically stimulate vessel development. Even if vessels were developed by angiogenesis induced by hypoxia and biological signaling, the blood pressure inside capillary lumen of tumors may be insufficient to counteract the mechanical pressure inside tumor leading to collapse of capillary lumen which corroborates with other studies indicating that pressure is key in hepatic microcirculation [17]. We have already shown by using immunohistochemistry, intravital imaging, and fluorescent therapeutic perfusion that capillaries are present in small metastatic tumors, whereas blood flow is absent [9]. Heterogeneity of pure physical origin and its effect on biology is little studied, while biological heterogeneity is widely researched [25]. Our analysis shows an interesting mani- festation of physical heterogeneity that could potentially alter the perfusion in metastatic tumor. We have investigated idealized configurations of portal and central vessel and configurations of vessels that were slightly randomized to mimic biological reality. Non-ideal or slightly asymmetric configurations led to slightly larger flow velocities inside tumors, most probably because of the development of larger local pressure gradients. However, it had no effect on the O2 concentration field inside and around the tumors. Furthermore, our analysis shows that the physical location can be a factor in determining the interaction between the tumors and its microenvironment. The microcirculation differences are due to distinct tumor locations with respect to the levels of functioning blood vessels which can result in different progression patterns; potentially instigating different biological cues, including therapeutic resistance. Micrometastatic tumor circulation is still being investigated, while circulation in primary tumors has been under investigation for decades [26]; especially in the context of anti-angiogenic treatments [27]. Antivascular treatments prevent tumors from obtaining nutrient supply because primary tumors at the time of their detection are well established and most of them are well vascularized tissues. However, the metastatic tumors are found to be at least two to three orders of magnitude smaller than the primary tumor in size and can be avascular. Many anti-vascular strategies and theories were developed for primary tumors, like the well-known ‘normalization’ theory [28], which can be difficult to apply to the micrometastases due to their differences from the primary tumors. The key difference is the lack of circulation, at least in the current example of the 4T1 breast cancer metastases in this study. In order to facilitate the delivery of drugs to these small tumors, the development of vasculature could be a crucial condition and all anti-vascular strategies could make the treatment of early metastatic disease worse.

5. Conclusions The microcirculation simulation results have revealed that newly established small metastatic tumors in the liver may alter local microcirculation around them in the vicinity of the nearest liver lobules. Those changes also lead to poor perfusion of tumors. We have investigated a few anatomically distinct locations of tumors with respect to lobule main vessels and have found microphysiological differences among them in term of their perfusion and access to O2. Tumors established at acinus do not disrupt local microcirculation; therefore, they are well perfused with high O2 concentrations. Consid- ering that the metastatic process potentially seeds many metastatic tumors, it is possible that local microcirculation patterns eventually transcend their heterogeneity into tumor biology eventually. These results conﬁrmed our previous ﬁndings that tiny metastatic tumors are not perfused despite the presence of endothelial cells and vasculature, offering some clues that biophysics of microcirculation can be at least partially responsible for that. Pharmaceutics 2021, 13, 703 10 of 11

Our findings indicate that the local microenvironment of small metastases does not possess sufficient blood pressure gradients to perfuse tumors effectively. We speculate this may potentially lead to tumor capillary collapse as a result of insufficient pressure gradients in the local microcirculation to overcome tumor mechanical pressure. These findings have important implications in the treatment of metastatic disease, as it demonstrates that poor microcirculation in and around micron-size metastases may cause one more physiological barrier to the delivery of therapeutics, which is widely unacknowledged. While this study was performed on murine liver, future analysis on human tissues are needed in order to determine the physiological barriers and parameters in metastatic disease.

Author Contributions: Conceptualization, A.Z.; methodology, A.Z.; software, M.K., V.S., M.M.; formal analysis, A.Z.; Y.T.L.; investigation, A.Z., Y.T.L.; resources, A.Z., K.Y.; writing—original draft preparation, A.Z.; writing—review and editing, A.Z., M.K., Y.T.L., K.Y.; visualization, A.Z.; supervision, A.Z.; project administration, A.Z. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by NIH, grant number U54CA210181. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: Support is acknowledged through the NIH/NCI center grant U54CA210181. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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