Targeted cell deposition for lung re-endothelialization

Abstract

We created computational fluid dynamic models of murine lung vasculature to assess the quantity and quality of cell deposition for lung re-endothelialization under three cell seeding protocols. These protocols include the standard direct injection seeding, negative pressure seeding, and a novel dual boundary condition seeding protocol. Our results indicate that cell seeding efficiencies are similar between the direct injection and negative pressure seeding protocols. The dual boundary condition protocol, which utilizes the direct injection of cell media with the addition of a prescribed pressure boundary condition at the parenchyma, exhibited increased cell deposition efficiencies of up to 14% compared to the direct injection and negative pressure cases, as well as the ability to target cell deposition in specific (i.e., proximal and distal) regions of the lung vasculature. This novel dual boundary condition protocol has the potential to increase cell seeding efficiencies during scaffold recellularization, addressing a significant challenge in the field of lung bioengineering.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1007/s10237-026-02129-8.

Introduction

End-stage lung disease causes approximately 3.9 million deaths annually worldwide (Labaki and Han 2020), and the only definitive treatment for this condition is lung transplantation. Unfortunately, this treatment remains imperfect due to the limited availability of donor lungs as well as post-transplant complications, including the immunological response to the donor organ (Liao et al. 2023; Swaminathan et al. 2021; Van Herck et al. 2019; Verleden et al. 2020; Young & Dilling 2019), which results in a median survival rate of only 5.8 years post-transplantation (Thabut & Mal 2017). Generation of non-immunogenic bioengineered lungs is an exciting field of research with the potential of decreasing the shortage of donor lungs as well as the post-transplant complications. Lung decellularization and recellularization is an emerging approach in lung bioengineering which aims to reduce the immunological complications via repopulation of acellular scaffolds with non-immunogenic universal cell lines or recipient-derived autologous cells (Han et al. 2019; Ott et al. 2010; Petersen et al. 2010; Simpson et al. 2023). Lung decellularization consists of removing cells and DNA components from the donor organ via detergent-based protocols while preserving the extracellular matrix with intact vascular and airway architecture (Tebyanian et al. 2017; Uhl et al. 2017; Urbano et al. 2017). The lung is then recellularized via deposition of recipient-specific cells, thus reducing the likelihood of an autoimmune response (Doi et al. 2017). These two processes still require optimization, but recellularization in particular remains the biggest challenge in producing functional bioengineered lungs for clinical application (Ohata and Ott 2020).

One key criterion for the successful recellularization of lungs is the complete repopulation of endothelial cells (re-endothelialization), which is necessary for reproducing functional vascular networks that are essential for gas exchange, barrier function, nutrient supply, and waste management in lungs (Calle et al. 2014; Scarritt et al. 2018). Cell delivery strategies for re-endothelialization have taken a variety of forms, including direct perfusion using pumps at various flow rates (Calle et al. 2011; Petersen et al. 2010; Scarritt et al. 2018; Stabler et al. 2016) and the use of gravity-driven pressure heads (Ren et al. 2015; Scarritt et al. 2018). However, these methods have resulted in heterogeneous and incomplete distribution of cells, especially in the distal regions of the lung. In recent studies, we showed the use of negative gauge pressures to draw in the cell suspension at high flow rates (5–20 ml/min) for recellularization (Ahmadipour et al. 2021b). Specifically, we compared cell seeding using a gravity pressure head and a negative pressure head and showed that the negative pressure cases resulted in higher cell media flow rates and improved cell seeding compared to the gravity case (Ahmadipour et al. 2021a). However, we did not determine whether it was the negative pressure itself or the higher flow rates that contributed to the improved cell seeding. Thus, the hydrodynamic environment during recellularization must be assessed to determine the necessary parameters for optimal cell distribution.

Furthermore, the native human lung contains 58 cell types that each contribute to successful respiration, and many of these are specific to certain regions of the lung (Travaglini et al. 2020). Current recellularization strategies have yet to successfully allow region-specific delivery, which is vital for lung bioengineering efforts (Calle et al. 2014). A consequence of non-targeted random cell delivery is interstitial edema (swelling due to fluid retention) of recellularized lungs following transplant (Herrero et al. 2018; Mowery et al. 2020; Ofori-Acquah et al. 2008; Ott et al. 2010). Interstitial edema is known to be caused by abnormally high permeability of the alveolar epithelial barrier, signifying an insufficient repopulation of microvascular endothelial cells in the capillaries (Herrero et al. 2018; Mowery et al. 2020; Ofori-Acquah et al. 2008). This example highlights the need for recellularization strategies for targeting cell delivery to specific regions of the lung. In summary, the optimization of recellularization protocols is necessary to improve the functionality of bioengineered lungs. Progress in this area has been challenging, as many studies to date have relied on experimental trial-and-error investigations which are costly and time-consuming (Wendt et al. 2009).

Computational fluid dynamics (CFD) methods have been used to gain fundamental understandings of flow-dependent processes in bioengineering protocols and thus circumvent the need for trial-and-error investigations. For instance, Campos Marín et al. used a CFD model to identify the optimal flow rate for seeding cells in a commercial porous scaffold which consisted of layers of cylindrical fibers (Campos Marín et al. 2018). They also found that gravity and secondary flows helped to direct the cells toward the scaffold substrate and increase cell seeding. In another study, Lee et al. created a CFD model for the recellularization of a tracheal scaffold in a rotating bioreactor (Lee et al. 2021). They used their model to guide the design of a new bioreactor and ultimately enhanced the cell deposition uniformity in the scaffold. One caveat of these two examples is that they did not account for cell–scaffold interactions and instead assumed that all cells adhered to the scaffold upon contact. Recently, we developed a CFD model coupled with a probabilistic algorithm for cell deposition in lung scaffolds (Chan et al. 2022). This model accounted for the inertia of the cell upon contact with the vessel wall, and the deposition algorithm was found to be more accurate compared to the deposition-upon-contact algorithm upon experimental validation.

In this work, we used our CFD model (Chan et al. 2022) to compare cell deposition between various lung re-endothelialization protocols. These protocols included direct perfusion seeding and negative pressure seeding at two flow rates, as well as a novel dual pressure boundary condition. Specifically, cell seeding efficiency and uniformity was analyzed for each case, and more interestingly, the ability to target cell delivery was explored. This analysis was carried out for three lung geometries to account for variability in lung vasculature. The work herein aims to provide much needed insight to optimize lung recellularization strategies.

Materials and methods

Model generation

Three simplified lung models, A, B, and C, were generated for this study to determine whether deposition trends would remain consistent regardless of geometric differences. The models were created by following the same procedure of Chan et al. (Chan et al. 2022). In summary, three intact 12-week-old adult C57BL/6 mouse lungs were extracted and cannulated, followed by injection of liquid contrast agent (Microfil, Flow Tech Inc., USA) into their vasculature. Sets of three-dimensional images of these lungs were acquired using an X-ray micro-computed tomography system (SkyScan 1172, Bruker Corp.) at a voxel resolution of 4.97 µm. Lung A was generated from micro-computed tomography (μCT) images of only the lower lobe of a mouse lung, whereas Lungs B and C were generated from μCT images of entire mouse lungs (hence, Lungs B and C appear larger than Lung A). The images were then processed to distinguish the vasculature from the void space in the images. Next, the binarized images were imported into an open-source medical image visualization software (3D slicer (Fedorov et al. 2012)) for volume rendering of the vasculature. The largest portions of connected vessels were labeled as the vasculature domain for flow analysis. The remaining unconnected vessels were agglomerated into a single porous body and were labeled as the parenchyma domain. The geometries of the three lung models are shown in Fig. 1. Finally, the geometries were imported into ANSYS (Pennsylvania, USA) software to produce fluid meshes and perform transient modeling with laminar flow (maximum Re = 157). Element counts of 564,731, 564,113, and 617,100 were used for Lungs A, B, and C, respectively. Mesh sensitivity analyses were performed for each lung to ensure that further mesh refinement was not necessary (see Supplementary Fig. 1).

Fig. 1.

CFD models of the three lung geometries used in this study. The vasculature domain is surrounded by a porous parenchyma domain. Three boundary conditions are specified for each model: artery flow rate inlet, vein pressure outlet, and parenchyma pressure outlet

Fluid domain and boundary conditions

The incompressible Navier–Stokes equations were implemented to govern the flow of cell media within the vasculature. The Navier–Stokes equations are as follows:

$$\frac{\partial \overrightarrow{u}}{\partial t}+\overrightarrow{u}\mathrm{\nabla }·\overrightarrow{u}=-\frac{1}{\rho }\mathrm{\nabla }p+\frac{\mu }{\rho }{\mathrm{\nabla }}^2\overrightarrow{u}$$

$$\mathrm{\nabla }·\overrightarrow{u}=0$$

where $\overrightarrow{u}$ is the cell media velocity [m/s], $t$ is the time [s], $\mathrm{\nabla }$ is the vector differential operator, $\rho$ is the cell media density [kg/m³], $p$ is the pressure [Pa], and $\mu$ is the dynamic viscosity of the cell media [Pa·s].

Flow through the parenchyma domain was modeled as laminar flow through a uniform porous material using Darcy’s law:

$$\mathrm{\nabla }p=-\frac{\mu }{\alpha }\overrightarrow{u}$$

where $\alpha$ is the permeability of the parenchyma [m²]. The properties of the cell media and parenchyma permeability are shown in Table 1.

Table 1.

Properties of cell media and parenchyma permeability used for the models

Property	Value
Parenchyma permeability (Chan et al. 2022)	$8.9\times {10}^{-13}{\text{m}}^2$
Cell media density (Hinderliter et al. 2010)	$1000\text{kg}/{\text{m}}^3$
Cell media dynamic viscosity (Fröhlich et al. 2013)	$9.4\times {10}^{-4}\text{Pa}·\text{s}$

A porous jump condition was applied on the vessel wall to represent the porous nature of the acellular vasculature surfaces. This condition was used to model a thin membrane onto which the cells could deposit, while allowing the cell media to perfuse through. The permeability of this membrane was set to match the permeability of the parenchyma.

For each lung, the pulmonary artery was designated as the inlet, and the pulmonary vein and the outer surface of the parenchyma were designated as the outlets. Three cases of boundary conditions were studied for each lung. The specific boundary condition values for each case are listed in Table 2, with the corresponding boundaries (pulmonary artery, pulmonary vein, parenchyma) for each lung shown in Fig. 1. All pressures are reported as gauge pressure.

Table 2.

Boundary conditions used for each case. Artery inlet flow rates and parenchyma outlet pressures were prescribed for the baseline and dual boundary condition cases, whereas vein outlet pressure was calculated and prescribed to the model to establish realistic flow resistance throughout the vasculature. *Artery inlet flow rates were not prescribed in the negative pressure case; rather, a pressure of 0 Pa was applied at the artery inlet, and flow rates of 5 ml/min and 10 ml/min were the result of the applied vein and parenchyma outlet pressures

Lung	Case	Artery Inlet Flow Rate [ml/min]	Vein Outlet Pressure [Pa]	Parenchyma Outlet Pressure [Pa]
A	Baseline	5	720	0
		10	1604	0
	Negative Pressure	5* (0 Pa)	−127	−847
		10* (0 Pa)	−322	−1927
	Dual boundary condition	5	720	−200 to +200
		10	1604	−300 to +300
B	Baseline	5	456	0
		10	1016	0
	Negative pressure	5* (0 Pa)	−52	−508
		10* (0 Pa)	−116	−1132
	Dual boundary condition	5	456	−200 to +200
		10	1016	−300 to +300
C	Baseline	5	436	0
		10	969	0
	Negative pressure	5* (0 Pa)	−24	−462
		10* (0 Pa)	−52	−1021
	Dual boundary condition	5	436	−200 to +200
		10	969	−300 to +300

The first case utilized a flow rate inlet condition at the artery boundary to represent direct injection of cell media and a constant pressure condition at the vein boundary to represent resistance caused by frictional losses and vessel wall compliance (Chan et al. 2022; Engler et al. 2019; Lawence-Brown et al. 2011). Flow rates of 5 ml/min and 10 ml/min were studied, which are comparable to what is seen throughout literature (Ahmadipour et al. 2021b; Petersen et al. 2010; Scarritt et al. 2018). This case is herein referred to as the baseline case.

The second case involved a set of boundary conditions with a negative gauge pressure applied to the vein and parenchyma of the lung, while the artery inlet was left at atmospheric pressure. The pressure differential produced causes the cell media to be drawn into the lung through the artery, as described in (Ahmadipour et al. 2021b). The pressures in this case were tuned so that the resulting flow rates were 5 ml/min and 10 ml/min. This case is referred to as the negative pressure case.

The third case of conditions utilized the same flow rate inlet and vein pressure outlet conditions as the baseline case. In addition, this third case also involved a surrounding parenchymal pressure, $P_{\text{parenchyma}}$, outlet condition. For the flow rate of 5 ml/min, the parenchymal pressure was varied from − 200 to +200 Pa in increments of 50 Pa. For 10 ml/min, parenchymal pressure ranged from − 300 to +300 Pa. From preliminary simulation trials, parenchymal pressures less than these lower limits produced severe backflow at the vein and thus were not considered. Parenchymal pressures higher than these upper limits resulted in significantly reduced cell seeding and thus were also disregarded. This set of conditions is referred to as the dual boundary condition case. Note that when $P_{\text{parenchyma}}=0$, the boundary conditions are equivalent to that of the baseline case.

Cell modeling and deposition probability

Discrete phase particles of size 15 µm in diameter and a density of 1050 kg/m³ (Bryan et al. 2013), at a concentration of 250,000 cells per ml, were used to model endothelial cells that are commonly used for re-endothelialization, such as mouse C166 (Chan et al. 2022) and HUVECs (Jiménez et al. 2013; Ott et al. 2010; Scarritt et al. 2018). The Lagrangian formulation was used to predict the motion of the suspended particles caused by the drag force exerted by the surrounding fluid, gravity, and buoyancy. The equation of the involved forces is written as:

$$m_{\text{p}}\frac{\text{d}{u}_{\text{p}}}{\text{d}t}=m_{\text{p}}\frac{\left(u,-,u_{\text{p}}\right)}{{\tau }_{\text{r}}}+m_{\text{p}}\frac{g({\rho }_{\text{p}}-\rho )}{{\rho }_{\text{p}}}$$

where $m_{\text{p}}$ is the particle mass [kg], $u$ and $u_{\text{p}}$ are the fluid and particle velocities [m s⁻¹], respectively, $\rho$ and ${\rho }_{\text{p}}$ are the fluid and particle densities [kg m⁻³], respectively, $g$ is the gravitational constant [m s⁻²], and ${\tau }_{\text{r}}$ is the particle relaxation time [s]. ${\tau }_{\text{r}}$ represents the time required for the particle to reach the velocity of the surrounding fluid (Gosman and loannides 1983) and is given by:

$${\tau }_{\text{r}}=\frac{{\rho }_{\text{p}}{d}_{\text{p}}^2}{18\mu }\frac{24}{C_{\text{d}}Re}$$

where $d_{\text{p}}$ is the diameter of the particle [m], $C_{\text{d}}$ is the drag coefficient, and $\mathit{Re}$ is the Reynolds number. This characterization of relaxation time assumes that the fluid is incompressible and in the laminar flow regime, and that the particle is spherical and rigid. Thus, the trajectory of the cell can be rewritten as:

$$m_{\text{p}}\frac{\text{d}{u}_{\text{p}}}{\text{d}t}=m_{\text{p}}\frac{18\mu }{{\rho }_{\text{p}}{d}_{\text{p}}^2}\frac{C_{\text{d}}Re}{24}\left(u,-,u_{\text{p}}\right)+m_{\text{p}}\frac{g({\rho }_{\text{p}}-\rho )}{{\rho }_{\text{p}}}$$

where the first term on the right-hand side represents drag force, and the second term represents buoyancy and gravity.

The Stokes cell deposition algorithm, which was formulated by Chan et al. (Chan et al. 2022), was used to define the probability of a cell depositing on the vessel wall surface upon contact. This algorithm accounts for the inertia of the cell relative to the fluid flow, which is characterized by the Stokes number:

$$\text{Stk}=\frac{{\rho }_{\text{p}}{d}_{\text{p}}^{2}u}{18\mu d}$$

where ${\rho }_{\text{p}}$ and $d_{\text{p}}$ are the particle density and diameter, respectively, $u$ and $\mu$ are the mean velocity and dynamic viscosity of the fluid, respectively, and $d$ is the characteristic length equal to the diameter of the vessel. Then, the probability of cell deposition is defined as:

$$P=\text{exp}\left(-,\frac{1}{\text{Stk}·C}\right)$$

where $C$ is an empirically adjusted inertia coefficient that accounts for the effect of Stokes number on deposition, as well as biochemical interactions and the truncated geometry of the vasculature. This study used a value of $C=300$, which resulted in deposition rates that most closely matched the experimental results of (Chan et al. 2022).

Quantification of regional cell deposition

One criterion of successful lung scaffold repopulation is the uniformity of deposited cells. To quantify the uniformity, the number of cells that were deposited on each facet of the vessel wall surface mesh was counted. Then, the variability of these counts was quantified using a statistical parameter known as the coefficient of variation:

$$\text{Coefficient}\text{of}\text{Variation}=\frac{\sigma }{\mu }=\frac{\sqrt{\frac{\sum _{i=1}^n{\left(x_i-\mu \right)}^2}{n}}}{\mu }$$

where $\sigma$ is the standard deviation of cell deposition, $x_i$ is the number of cells deposited on each facet of the vessel wall surface mesh, $\mu$ is the mean of cells deposited per facet, and $n$ is the total number of facets on the vessel wall surface mesh. A lower value of coefficient of variation demonstrates a more uniform distribution of deposited cells.

In addition, the ability to target cell deposition is vital to the successful repopulation of region-specific cells. Thus, this study also investigated the relative deposition of cells in the arterial, distal, and venous regions. The criteria for defining these three regions are based on work done by Jiang et al., where it was found that the mean diameter ratio of successive orders of rat pulmonary arterial vasculature was 1.58 (Jiang et al. 1994). In this work, the arterial region was defined as the section from the inlet to the first junction where the two subsequent branches both had an average diameter that was less than 1.58 times the diameter of the preceding branch. The venous region was defined in a similar manner but started from the outlet. The rest of the vasculature was defined as distal vasculature. The proportion of cells deposited in each region of the lung was defined as:

$$\text{Proportion}\text{of}\text{deposited}{\text{cells}}_{\text{region}}\left[\%\right]=\frac{\text{Deposited}\text{cells}\text{in}\text{region}}{\text{Total}\text{number}\text{of}\text{deposited}\text{cells}}\times 100\%$$

This calculation is especially pertinent to assess the effectiveness of utilizing a surrounding parenchymal pressure in the dual boundary condition case to manipulate cell deposition in each region.

Results

Cell trajectory and deposition is directly influenced by the motion of the surrounding cell media. Herein, the cell media flow fields of the three lung models are first presented. The differences in the fluid flow fields between the geometries help to explicate the subsequently presented differences in cell deposition. Next, the results of cell seeding using the three different boundary condition cases are compared to examine their effects on cell seeding efficiency and uniformity. Finally, the dual boundary condition case is further examined to determine whether the additional modulation of parenchymal pressure can augment cell seeding efficiency and effectively target cell seeding in the various regions of vasculature.

Cell media flow

Suspended cells were carried through the mouse lung vasculature by the cell media. Differences in vasculature geometry between the three lung models influenced fluid motion and therefore cell trajectory and deposition. The flow field of the cell media can be visualized using streamlines, which demonstrate the path of the cell media originating from the inlet during steady-state flow. The streamlines of the 10 ml/min baseline case for each lung geometry are shown in Fig. 2. Although the same 10 ml/min inlet condition was applied to all three lungs, the velocities in Lung A were much higher than that of Lungs B and C. The higher velocities can be explained by the principle of mass conservation: since the vessels of Lung A are smaller in diameter, higher velocities are necessary to preserve continuity. For all three lungs, most streamlines preferentially flowed out of the pulmonary vein, while fewer streamlines permeated through the porous vessel walls and slowly perfused throughout the parenchyma. The relative amount of media egressing the vessel via the pulmonary vein compared to the vessel walls is discussed in Sect. 3.3. Furthermore, the streamlines which permeated through the walls of vasculature and into the parenchyma generally did so in regions of high tortuosity, such as the distal vasculature. These trends shown in Fig. 2 are also representative of the other flow condition cases.

Fig. 2.

Velocity streamlines throughout vasculature at steady state for the 10 ml/min baseline case for the three lung geometries. Most streamlines flowed out of the pulmonary vein, while fewer streamlines permeated through vessel walls and slowly perfused throughout the parenchyma (blue streamlines)

Images of cell media flow at selected time points for each lung were also attained from CFD modeling to further visualize how the cell media perfuses through the lung. Figure 3 shows the flow for the three lungs under the 10 ml/min baseline set of boundary conditions (the trends shown here are representative of the other flow conditions). In all geometries, the media is seen flowing into the lung through the pulmonary artery and into portions of the distal vasculature before flowing out of the lung through the pulmonary vein. It is also noted that the media egressed through the pulmonary vein before all distal regions of vasculature were saturated. Cell media fully perfused throughout the vasculature for Lung A in less time than for Lungs B and C because of its smaller size. For all simulated flow conditions, as time progressed, the cell media permeated through the vessel walls of each geometry and into the surrounding parenchyma. Permeation through the vessel wall was expected, since the decellularized lung is porous.

Fig. 3.

Perfusion of cell media throughout the vasculature of the three lungs for the 10 ml/min baseline case. Cell media fully perfused throughout the vasculature in approximately 0.10 s for Lung A and 0.40 s for Lungs B and C. Cell media can be seen permeating through the vessel walls, as shown by the darker patches of red

Cell deposition on the vessel wall

The locations of seeded cells for the three lungs under the boundary condition cases of 5 ml/min baseline, 10 ml/min baseline, 10 ml/min negative pressure, and 10 ml/min dual boundary condition with $P_{\text{parenchyma}}=-300\text{Pa}$ are shown in Fig. 4. For all cases, cells can be seen in the arterial, distal, and venous regions of the lung. Certain boundary conditions better facilitated the deposition of cells within the lung vasculature. For all three lungs, cell seeding was improved by using a higher flow rate, as shown by the increased density of cells between the 5 ml/min baseline and 10 ml/min baseline cases in the figure. Minor differences were noted between the 10 ml/min baseline and 10 ml/min negative pressure cases; however, utilizing the 10 ml/min dual boundary condition case with $P_{\text{parenchyma}}=-300\text{Pa}$ resulted in a significant increase in seeded cells.

Fig. 4.

Locations of deposited cells for each lung under the boundary condition cases of 5 ml/min baseline, 10 ml/min baseline, 10 ml/min negative pressure, and 10 ml/min dual boundary condition. The dual boundary condition case is with $P_{\text{parenchyma}}=-300\text{Pa}$. Cells are colored based on their deposition location

Comparison of cell seeding efficiency

For each lung and boundary condition case, the results of cell retention within the vasculature were characterized using the cell seeding efficiency parameter. Cell seeding efficiencies for the three lungs under the baseline, negative pressure, and dual boundary condition cases at 5 ml/min and 10 ml/min are shown in Fig. 5. The 5 ml/min dual boundary condition case shown is with $P_{\text{parenchyma}}=-200\text{Pa}$, whereas the 10 ml/min dual boundary condition case shown is with $P_{\text{parenchyma}}=-300\text{Pa}$. These values of $P_{\text{parenchyma}}$ resulted in the most cells seeded (cell seeding with other values of $P_{\text{parenchyma}}$ are explored in Sect. 3.3). Cell seeding in Lung A was consistently higher than in Lungs B and C. This phenomenon can be explained by the fact that the flow velocities in Lung A were higher than the other two lungs (Fig. 2), which contributed to the particle inertia needed for increased cell seeding. Nevertheless, the cell seeding trends, described next, were consistent for each lung.

Fig. 5.

Cell seeding efficiency for Lungs A, B, and C as a function of the three boundary condition cases at 5 ml/min and 10 ml/min. The 5 ml/min dual boundary condition case shown is with $P_{\text{parenchyma}}=-200\text{Pa}$. The 10 ml/min dual boundary condition case shown is with $P_{\text{parenchyma}}=-300\text{Pa}$

For the 5 ml/min baseline case, the cell seeding efficiencies were 55.8%, 37.2%, and 37.5% for Lungs A, B, and C respectively. Seeding efficiencies remained approximately the same when utilizing the negative pressure case at 5 ml/min: efficiency decreased to 52.8% for Lung A, increased to 40.6% for Lung B, and increased to 43.6% for Lung C. However, under the dual boundary condition case, more cell media permeated through the vessel wall, carrying along cells to impact the surface (this idea is further expanded upon in Sect. 3.3). Because of more cells impacting the vessel wall under the dual boundary condition case, seeding efficiency was improved to 64.8%, 48.5%, and 48.2% for Lungs A, B, and C respectively.

The trends between boundary condition cases were the same for cell seeding at 10 ml/min. For 10 ml/min baseline, cell seeding efficiencies were 67.8%, 55.4%, and 55.8% for the three lungs. Seeding efficiencies changed by less than 4% for each lung when the negative pressure boundary condition was used, compared to the baseline. When the dual boundary condition case was used, seeding efficiencies increased to 77.4%, 68.3%, and 69.9%.

Cell seeding distribution and uniformity

Cell distribution contour maps on the vessel walls of the three lungs are compared to assess the uniformity of cell seeding in Fig. 6. In general, large populations of cells were seen near the pulmonary artery inlet and regions of high tortuosity. These regions had streamlines that rapidly changed direction (see Fig. 2) and therefore the particles were more likely to contact the vessel wall. Conversely, regions with wide, long, and straight segments exhibited less cell deposition.

Fig. 6.

Cell distribution contours for each lung under the boundary condition cases of 5 ml/min baseline, 10 ml/min baseline, 10 ml/min negative pressure, and 10 ml/min dual boundary condition. The dual boundary condition case is with $P_{\text{parenchyma}}=-300\text{Pa}$. The black arrows on each lung indicate a region of poor cell distribution in the 5 ml/min case that is improved in the 10 ml/min case. The cell distribution in the same region then slightly decreases in the 10 ml/min negative pressure case

The uniformity of seeded cells improved with increasing flow rate, exhibited by a more homogeneous color distribution in the 10 ml/min baseline cases compared to the 5 ml/min baseline cases. To illustrate this further, a region of relatively poor cell distribution is marked with a black arrow in Fig. 6 for each lung under the 5 ml/min baseline case. Cell seeding distribution improved for each lung in these same regions under the 10 ml/min baseline case. When the 10 ml/min negative pressure conditions were utilized, the distribution in the same regions slightly decreased compared to the 10 ml/min baseline case. The cell distribution contours for the 10 ml/min dual boundary condition cases were comparable to the 10 ml/min baseline cases.

These trends of cell distribution were characterized with the coefficient of variation of deposited cells, as shown in Fig. 7. For each lung, the variation of deposited cell location decreased with flow rate (5 ml/min baseline versus 10 ml/min baseline), demonstrating that uniformity increased. When comparing the 10 ml/min baseline case to the 10 ml/min negative pressure case, variation was slightly higher (i.e., more heterogeneous) with the negative pressure conditions. The coefficient of variation for the 10 ml/min dual boundary condition cases was similar to the 10 ml/min baseline cases, signifying that the dual boundary condition case improves cell seeding efficiency without hindering cell seeding uniformity.

Fig. 7.

Variance quantification of cell distribution uniformity for each lung under the boundary condition cases of 5 ml/min baseline, 10 ml/min baseline, 10 ml/min negative pressure, and 10 ml/min dual boundary condition with $P_{\text{parenchyma}}=-300\text{Pa}$. Cell distribution variation decreased when seeding at 10 ml/min compared to 5 ml/min

Improved and targeted cell delivery using the dual boundary condition case

The dual boundary conditions were applied to the lung models to study the effect of utilizing a surrounding parenchymal pressure, $P_{\text{parenchyma}}$, at the same time as applying a direct perfusion flow rate on cell seeding. The effect that this condition had on cell media perfusion is shown in Fig. 8. For negative parenchymal pressures, more cell media was drawn toward the vessel wall. For example, media permeation through the vessel wall for Lung A at 10 ml/min increased from 76.0 to 84.3% as $P_{\text{parenchyma}}$ decreased from 0 to − 200 Pa.

Fig. 8.

Cell media flux through the vein outlet and through the vessel wall as a function of $P_{\text{parenchyma}}$ for Lungs A, B, and C at (a) 5 ml/min and (b) 10 ml/min. More media perfuses through the vessel wall, and thus less media exits through the vein, as $P_{\text{parenchyma}}$ decreases

The increased flow toward the vessel wall using negative parenchymal pressures carried more cells toward the wall, leading to increased cell deposition. The general increase in cell deposition due to negative pressure for the dual boundary condition case is seen in Fig. 9. For instance, cell seeding efficiency for Lung A at 10 ml/min increased from 67.8 to 77.4% as $P_{\text{parenchyma}}$ decreased from 0 to − 300 Pa.

Fig. 9.

Cell seeding efficiency for Lungs A, B, and C as a function of $P_{\text{parenchyma}}$ for the dual boundary condition case at (a) 5 ml/min and (b) 10 ml/min

The relationship between $P_{\text{parenchyma}}$ and cell distribution was examined next. Specifically, cell deposition in the arterial, distal, and venous regions of the lungs as a proportion of the total number of deposited cells was investigated (Fig. 10). Negative values of $P_{\text{parenchyma}}$ resulted in a greater proportion of cell deposition in the arterial region. Because of the increased deposition in the artery, fewer cells were available for deposition in the distal regions of the lung, as shown by the decreased proportion of distal cells seeded as pressure decreased. For instance, the proportion of cells deposited in the artery for the 5 ml/min case with $P_{\text{parenchyma}}=0$ Pa was 31.4% on average across the three lungs and increased to 35.1% when $P_{\text{parenchyma}}=-100$ Pa was applied. Under the same conditions, proportional seeding in the distal vasculature decreased from 54.2 to 50.0%.

Fig. 10.

Proportion of deposited cells in the artery, distal vasculature, and vein as a function of $P_{\text{parenchyma}}$ for the dual boundary condition case at (a) 5 ml/min and (b) 10 ml/min, averaged across the three lungs geometries. The error bars indicate the standard deviation. The solid line represents a linear fit for each region, with the equation of the line and coefficient of determination indicated. The solid bands represent the 95% confidence band

Conversely, positive values of $P_{\text{parenchyma}}$ imposed a flow resistance against media permeating through the vessel wall. Referring back to Fig. 8, cell media perfusion through the vessel wall was reduced as parenchymal pressure increased. As an example, cell media flow through the vessel wall in Lung A at 10 ml/min decreased from 76.0 to 67.8% as $P_{\text{parenchyma}}$ increased from 0 to 200 Pa. Since less cell media flowed toward the vessel wall at positive parenchymal pressures, fewer cells contacted the vessel wall surface, resulting in fewer instances of cell seeding. The trend of decreased cell seeding as $P_{\text{parenchyma}}$ increased is seen in Fig. 9. For instance, the cell seeding efficiency in Lung A at 10 ml/min decreased from 67.8 to 60.4% as $P_{\text{parenchyma}}$ increased from 0 to 300 Pa. Interestingly, the reduction of arterial seeding caused a higher presence and proportional availability of cells to be deposited in the distal region (Fig. 10). For example, the proportion of cells deposited in the arterial region for the 5 ml/min case with $P_{\text{parenchyma}}=0$ Pa was 31.4% on average across the three lungs and decreased to 24.1% when $P_{\text{parenchyma}}=150$ Pa was applied. Since more cells remained suspended in media when they reached the distal vasculature with $P_{\text{parenchyma}}=150\text{Pa}$, proportional seeding in the distal vasculature increased from 54.2 to 64.1%.

A linear fit was calculated for each cell seeding condition to quantify the trends in regional proportional cell seeding (Fig. 10). The proportion of deposited cells in each region was more sensitive to pressure in the 5 ml/min case, as shown by the larger values of slope. The proportion of cells seeded in the vein remained relatively unchanged for various values of parenchymal pressure. A 95% confidence band was calculated as well to represent a likely range of values that the proportion of cell deposition in each region will fall within.

Discussion

Computational fluid dynamics models of three mouse lung vasculatures were used to assess the impacts of various boundary conditions on cell seeding efficiency and distribution. Specifically, a negative pressure boundary condition case and a novel dual boundary condition case were compared to a direct perfusion baseline case at flow rates of 5 ml/min and 10 ml/min to determine whether cell seeding could be improved or targeted. It was shown that cell seeding efficiency between the baseline and negative pressure cases at the same flow rate did not differ significantly, as the maximum change in cell seeding efficiency between the two cases was only 6%. However, the negative pressure case performed slightly worse in terms of cell deposition uniformity. Even though the same inlet flow rate was used for both cases, the slight differences in cell seeding between these two cases can be explained by the difference between a flow rate inlet and a pressure inlet: a flow rate inlet produces a non-uniform pressure profile, whereas a pressure inlet produces a non-uniform velocity profile. For example, Supplementary Fig. 2 shows the velocity profiles along the inlet region for Lung C and the three different boundary conditions at 5 ml/min. Since a uniform flow rate inlet condition was applied for the baseline case (and dual boundary case), the velocity profiles change along the entrance length, thus indicating a developing flow. For the negative pressure case, the velocity profiles remain the same along the entrance, thus indicating a developed flow at the inlet region. If the same inlet velocity profile were to be applied for the baseline and negative pressure conditions, it is expected that the cell deposition results from the model would be identical. To improve the accuracy of the model, future studies should incorporate the inlet artery cannula into the model, as the cannula would provide an entrance length for the flow profile to develop before entering the vasculature.

In our previous work in (Ahmadipour et al. 2021a), negative pressure seeding resulted in improved cell deposition compared to gravity-based seeding. However, the cell media flow rates for the negative pressure cases were 7–10 ml/min, whereas the flow rate for the gravity-based seeding was 1 ml/min. In conjunction with our results here, we are now able to provide the following new insight—that the improved re-endothelialization via negative pressure seeding observed in Ahmadipour et al. can be attributed to the higher flow rates produced instead of the negative pressure.

The novel dual boundary condition case improved cell deposition and enabled targeted cell delivery. By controlling the perfusion of cell media through the vessel wall with $P_{\text{parenchyma}}$, the contact between cells and the vessel wall, and thus cell deposition could also be manipulated. Negative values of $P_{\text{parenchyma}}$ led to increased overall cell deposition and in particular arterial deposition. Furthermore, the 10 ml/min case resulted in improved uniformity of cells compared to the 5 ml/min case. Therefore, applying the dual boundary condition with $P_{\text{parenchyma}}<0$ with a higher flow rate can be useful for increasing the general seeding of pluripotent stem cells, which can then differentiate into various cell types native to the lung (Kotton 2012).

Conversely, positive values of $P_{\text{parenchyma}}$ decreased overall cell deposition but increased the proportion of cells deposited in the distal region. Thus, the dual boundary condition with $P_{\text{parenchyma}}>0$ can be vital for increasing region-specific cell delivery to distal regions of the lung, such as microvascular cells for the capillaries. Although the overall cell deposition efficiency is low using these boundary conditions, cells which flow through the lung without depositing can be re-perfused by using a circulation loop as done by Petersen et al. (Petersen et al. 2010). Furthermore, it was seen in the simulation results that the 5 ml/min dual boundary condition case allowed for the most control of targeting cell delivery, as shown by the larger values of slope in Fig. 10. This may be attributed to the fact that the cell media and cells traveling at 5 ml/min have less momentum than at 10 ml/min and so can be more readily influenced by the parenchymal pressure. It is therefore recommended that a slower flow rate be used for dual boundary condition targeted delivery of region-specific cells.

This study also compared the effects of the various boundary conditions on models of different geometries. The smaller geometry of Lung A resulted in higher velocities at the same flow rate than compared to Lungs B and C. This led to increased cell seeding, since deposition is a function of particle inertia (Chan et al. 2022). Differences in geometry between Lungs B and C caused slight variations in cell seeding, but the variations were not to the extent of that with Lung A. Nevertheless, the trends in cell seeding efficiency, uniformity, and distribution for the various boundary conditions were the same across all three geometries. It is important to acknowledge that the models were created with truncated vasculatures due to computational costs (as per Sect. 2.1). The omission of vasculature could affect the model’s total and regional cell seeding efficiency, as the occurrence of cells contacting the vessel wall increases with the surface area of the wall and therefore cells have more opportunities to deposit. Since the morphology of lung vasculature varies throughout the lung and between lung samples, the effect of incorporating more vessels into the model and using more samples of lung geometries should be investigated in future works.

Although good agreement was found between the deposition algorithm and experimental cell seeding in our earlier work (Chan et al. 2022), the model consists of a few limitations that should be addressed for improved accuracy. The first limitation is that the cells are modeled as uniform spherical particles. Cells of different sizes and shapes will be affected differently by the drag imposed by the surrounding media, thus changing the cell trajectory throughout the vasculature. The current cell seeding model also does not incorporate mechanical effects such as shear stress (Baptista et al. 2016; Tang et al. 2012) or biochemical interactions with the scaffold (Ojha et al. 2024). To improve the model, a detailed exploration of the mechanical and biochemical effects on cell seeding should be performed with microfluidic techniques, which allow for complex and controllable environments that mimic decellularized lung vasculature (Siddique et al. 2021).

This study has demonstrated the potential of using a novel dual boundary condition cell seeding method to improve and target lung recellularization. However, the effectiveness of the dual boundary condition needs to be demonstrated in clinical applications. In practice, this method would require the cannulation of the pulmonary artery as the inlet and pulmonary vein as an outlet. The artery cannula would be connected to a syringe pump, where the cell media is injected, and the vein cannula would be exposed to atmospheric pressure. The lung would then be placed in a sealed chamber, where the parenchymal pressure would be modulated by a vacuum pump (for negative pressure) and compressor (for positive pressure). A schematic of this setup is shown in Supplementary Fig. 3. It should be noted that the range of parenchymal pressure values used in this computational study was derived for truncated lung vasculatures, and structural changes in the lung vasculature as a result of the applied pressures were not considered. Therefore, a detailed clinical investigation on the range of parenchymal pressure values is warranted. The effect of parenchymal pressure values on total and regional cell seeding, as well as vessel rupture and dilation, can be evaluated via histological image analysis (Paciocco et al. 2025, 2026) or 3D light sheet ultramicroscopy (Epah et al. 2018).

Conclusion

In this study, CFD modeling was used for three distinct lung geometries to assess the effects of various boundary conditions on cell deposition. It was found that negative pressure cell seeding performed similar to direct perfusion cell seeding. Most importantly, our novel method of prescribing both a flow rate and a surrounding parenchymal pressure (dual boundary condition case) improved overall cell seeding and enabled targeted cell delivery. With the dual boundary condition case, cell seeding efficiency increased by up to 14% compared to the baseline. Furthermore, control of the parenchymal pressure altered the proportional arterial and distal seeding by up to 14% and 10%, respectively.

Recommendations of flow rates and parenchymal pressures were made for the scenarios of improving general seeding of pluripotent cells versus targeted delivery of region-specific cells. Notably, the novel dual boundary condition protocol has the potential to address the significant challenge of seeding cells in distal capillary regions, which is necessary for proper barrier permeability in bioengineered lungs.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contribution

JC, DT, MA, TW, GK, and AB contributed to conception and design of the study. EA performed the micro-CT imaging and image processing of the lungs used in this study. TS performed the decellularization procedures for the imaged lungs. All authors contributed to manuscript revision, read, and approved the submitted version.

Funding

Canada First Research Excellence Fund,Medicine by Design Program,Medicine by Design Program,Canadian Institutes of Health Research,Grant,NSERC Collaborative Health Research Projects,Grant,Natural Sciences and Engineering Research Council of Canada,Discovery Grant,Canada Research Chairs Program,Clean Energy

Data availability

Data sets generated during the current study are available from the corresponding author upon reasonable request.