Novel Payloads to Mitigate Maladaptive Inward Arterial Remodeling in Drug-Coated Balloon Therapy

Abstract

Drug-coated balloon therapy is a minimally invasive endovascular approach to treat obstructive arterial disease, with increasing utilization in the peripheral circulation due to improved outcomes as compared to alternative interventional modalities. Broader clinical use of drug-coated balloons is limited by an incomplete understanding of device- and patient-specific determinants of treatment efficacy, including late outcomes that are mediated by postinterventional maladaptive inward arterial remodeling. To address this knowledge gap, we propose a predictive mathematical model of pressure-mediated femoral artery remodeling following drug-coated balloon deployment, with account of drug-based modulation of resident vascular cell phenotype and common patient comorbidities, namely, hypertension and endothelial cell dysfunction. Our results elucidate how postinterventional arterial remodeling outcomes are altered by the delivery of a traditional anti-proliferative drug, as well as by codelivery with an anti-contractile drug. Our findings suggest that codelivery of anti-proliferative and anti-contractile drugs could improve patient outcomes following drug-coated balloon therapy, motivating further consideration of novel payloads in next-generation devices.

1 Introduction

Drug-coated balloon (DCB) therapy is a minimally invasive intravascular intervention for treatment of obstructive arterial disease, with growing popularity attributable to improved patient outcomes and reduced complications when compared to plain-old balloon angioplasty (POBA) and stenting, respectively [1–6]. During the DCB procedure, balloon inflation acutely restores lumen patency via lesion compression and facilitates local drug delivery to the arterial wall. Current DCB therapies most effectively restore and retain lumen patency in patients with peripheral artery disease, and as such this is the prototypical clinical indication for these devices [7–9].

Broader clinical use of DCBs, including coronary applications, hinges on a better understanding of how these devices work and the conditions in which they fail. Multiple determinants of DCB efficacy have been implicated in preclinical and clinical settings, including device design (i.e., balloon size, balloon compliance, coating excipient type/concentration, drug payload type/concentration), and deployment (i.e., lesion preparation, inflation pressure, inflation time) variables as well as patient-specific biological variables (i.e., lesion type/characteristics, comorbidities, hemodynamics) [10,11]. While DCB failure can manifest in multiple ways, including vessel dissection, perforation, or thrombosis [12,13], here we focus on the occurrence of restenosis due to maladaptive inward post-DCB arterial remodeling, where the proliferation and migration of vascular smooth muscle cells (SMCs), i.e., neointimal hyperplasia, play a central role in late lumen loss [14,15].

Remodeling is termed maladaptive when in response to a sustained stimulus such as persistent hypertension, the process yields a homeostatic state that at the cellular level is distinct from the initial (preremodeling) state, i.e., the baseline local mechanical environment of mechanosensitive vascular cells is not fully restored [16]. By contrast, adaptive remodeling outcomes include the restoration of baseline values of both the flow-induced shear stress at the intima and the pressure-induced medial stress, thus restoring the local mechanical environment of vascular endothelial cells (ECs) and SMCs, respectively [17,18]. There are many modes of maladaptive remodeling in response to various stimuli [19], each of which potentially alters arterial geometry as well as tissue composition and microstructure. Previous theoretical studies have proposed models of arterial remodeling in response to hypertension, some of which consider remodeling kinetics and evolution toward a new homeostatic state [17,18,20,21] and others which directly determine the homeostatic state based on conditions imposed on remodeling outcomes [22–24]. Here, we propose a model of the latter type to better understand maladaptive remodeling in a post-DCB context and evaluate the role of delivered drugs on remodeling outcomes. Specifically, we focus on pressure-induced inward remodeling in the presence of EC dysfunction, which is termed according to its effects on the apparent wall growth direction and is a particular case of post-DCB maladaptive remodeling associated with restenosis and late interventional failure. Indeed, all current DCBs deliver anti-proliferative/anti-inflammatory drug payloads, with a therapeutic goal of preserving lumen patency via limiting inward arterial remodeling.

Paclitaxel and derivative compounds are the most used DCB medications due to a proven ability to inhibit SMC proliferation for prolonged postinterventional times cf. Refs. [13], [25], and [26]. A clinical study of femoropopliteal interventions [27] found that patients treated with paclitaxel-coated DCBs had a significant reduction in neointimal hyperplasia compared to POBA, while a preclinical study found that similar DCBs effectively inhibit restenosis after coronary angioplasty with stent implantation [28]. In another study on rabbits [29], paclitaxel DCBs significantly reduced inflammation and plaque burden in aortic lesions compared to POBA or sham procedures, supporting the broader clinical use of these devices.

While these and other results are certainly encouraging, full realization of DCB potential requires identifying determinants of patient outcomes, which although superior to POBA remain highly variable across clinical settings. For example, a recent study of 95 patients with severe femoropopliteal lesions compared DCB versus POBA treatments and found that DCBs were associated with significantly reduced lumen loss at six months, but the primary patency rate at two-years was approximately 50% [30]. We seek to better understand differential patient outcomes by examining the role of common comorbidities of peripheral artery disease, namely, persistent hypertension and EC dysfunction [31–35], in the post-DCB arterial remodeling process. Experimental and clinical studies have reported that with these comorbidities, maladaptive pressure-mediated arterial remodeling outcomes include inward growth/lumen loss and elevated SMC tone [19,36–39]. We hypothesize that in the post-DCB context, instances of late lumen loss are a result of pressure-driven maladaptive inward remodeling due to EC dysfunction, which may be pre-existent and/or exacerbated by lesion preparation immediately preceding DCB deployment. Indeed, previous studies have established the potential for standard lesion preparation, namely, high-speed rotational atherectomy [40,41], to cause endothelial denudation to a degree that exacerbates postinterventional neointimal hyperplasia and inflammation [42–44]. Motivated by our recent theoretical findings on pressure-mediated muscular artery remodeling in which we associate lumen loss with EC dysfunction/elevated SMC tone [22], we posit that the inclusion of an anti-contractile drug within the DCB payload could be used to alter the balance of resident SMC phenotype in a manner that promotes lumen patency upon remodeling completion.

We propose a predictive mathematical framework to better understand the effects of delivered drugs on pressure-mediated femoral artery remodeling outcomes, with the goal of simulating a post-DCB remodeling scenario in terms of the targeted vessel (femoral artery), traditional and novel payloads (anti-proliferative and anti-proliferative + anti-contractile drugs, respectively), and typical patient comorbidities (hypertension and EC dysfunction). Our theoretical findings suggest that an anti-proliferative drug delivery alone does not mitigate maladaptive inward remodeling in this post-DCB scenario, while codelivery with an anti-contractile drug can preserve the lumen upon remodeling completion. Taken together, our findings provide insight into a potential cause of differential post-DCB outcomes and motivate the consideration of novel drug payloads in next-generation DCBs.

2 Methods

2.1 Overview.

Our study uses an experimental-theoretical approach to predict pressure-mediated arterial remodeling outcomes following DCB deployment in the peripheral vasculature, with consideration of the degree of hypertension, EC dysfunction, and the anti-proliferative and anti-contractile effects of delivered drugs on resident SMCs. We first conduct inflation–extension mechanical testing and quantitative histology on a porcine femoral artery and enable identification of a representative structure-based constitutive model of a commonly targeted vessel in DCB therapy. We then use the femoral artery constitutive model to illustrate a global growth model of post-DCB arterial remodeling [17,45], in which we formulate and solve inverse boundary value problems to predict adaptive and maladaptive pressure-mediated remodeling outcomes.

2.1.1 Active and Passive Arterial Response.

The porcine femoral artery was first isolated from the hindquarters of a freshly slaughtered adult American Yorkshire Sow (∼3 years old; ∼200 kg) between the deep femoral bifurcation and the popliteal initiation at the popliteal fossa, whereby applied tissue marking dye was used to determine a segmental vessel length first in situ and following isolation. The pig was designated for human consumption and is therefore not subject to IACUC protocols. The isolated vessel was immediately transported to the laboratory in Krebs saline solution on ice. Once there, perivascular tissues were gently removed, and the vessel was trimmed down to a straight section between branches roughly 4 cm in length. Next, the vessel was cannulated to hose barbed Luer fittings using 3-0 braided suture and mounted into our custom-built porcine vessel active/passive mechanical testing device [46,47]. Briefly, this bi-axial testing device controls pressure and axial extension while measuring outer diameter and axial force for vessels up to 20 cm in length. The mounted vessel was continuously perfused and bathed in 37 °C temperature-controlled 7.4 pH Krebs solution aerated with purified 95% oxygen and 5% carbon dioxide from a compressed gas cylinder.

Prior to data acquisition, the vessel was preconditioned to minimize viscous effects via five cycles of axial stretching and pressurization following established protocols cf. Refs. [46–49]. To characterize the vessel response under the basal SMC state, it was extended and held at a given fixed length (equal to the corresponding in situ length recorded prior to tissue harvest or ±5% of this length) and pressurized from 10 to 200 mm Hg in increments of 10 mm Hg. Here, the term “basal” reflects that SMCs are in an intermediate contractile state (between subsequently induced fully passivated and maximally contracted states) that is realized once the specimen is cannulated and acclimated within our perfusion bioreactor system. Vessel outer diameter, transmural pressure, and axial force were recorded in triplicate and averaged at each experimental state. After flushing the vessel with saline, we induced a fully contracted SMC state with an aerated bathing media containing phenylephrine (10⁻⁵ M), waited 15 min for tissue acclimation, and repeated the testing protocol [50,51]. To assess the vessel response in the passive SMC state, we again repeated the testing protocol after flushing and adding sodium nitroprusside (10⁻⁴ M) to the bathing media [50,51].

2.1.2 Arterial Wall Composition.

Upon completion of mechanical testing, the arterial sample was fixed in 4% paraformaldehyde, embedded vertically in paraffin, and cut into ten sections of 5-μm thickness using a microtome to obtain sequential ring-shaped profiles. All sections were deparaffinized and rehydrated in xylene and alcohol of decreasing concentrations before staining. Staining alternated between Direct Red (0.1% in saturated picric acid) for 90 min and mounting with Permount or Resorcin Fuchsin working solution (16 h) with Woodstain Scarlet Acid Fuchsin solution (5 min) and mounting with Poly Mount fluorescent mounting media. Both staining protocols entailed dehydration in alcohol and xylene of increasing concentrations before mounting. All sections were imaged using a Zeiss Axioskop 2 microscope with either bright-field or cross-polarized light to detect collagen birefringence. imagej software was used to quantify collagen birefringence in darkfield images (threshold: 34–255) and total tissue area in the brightfield images (threshold: 0–210) of Direct Red-stained samples. For simplicity, we assumed that the area fractions obtained from two-dimensional image thresholding and mass fractions were equivalent. Likewise, elastin content was measured as the ratio of black (threshold: 0–140) to all other tissue area in the Resorcin and Woodstain Scarlet Acid Fuchsin brightfield images. Neglecting ground substance, we assumed the remaining wall constituents were predominantly circumferentially oriented SMCs [52].

2.1.3 Experimental Data Processing.

Obtained experimental data enabled a continuum mechanics-based analysis of the arterial response with account of the SMC contractile state, e.g., Refs. [45] and [53]. The artery is modeled as a cylindrical membrane made of an elastic, orthotropic, and incompressible material. As a result of loading (transmural pressure $P$ and axial force $f$) and circumferentially oriented SMC contraction, the vessel undergoes a finite axisymmetric deformation. The reference arterial geometry was determined by measures of passivated/unloaded sample length ( $L)$, inner radius ${(R}_i)$, and wall thickness $\left(H\right)$, which were used to compute wall volume ( $V)$ as

$$V=\pi ({\left(R_i+H\right)}^2-R_i^2)L$$ (1)

The incompressibility assumption allows calculation of the vessel inner radius $r_i$ at each deformed state, namely

$$r_i=\sqrt{r_o^2-\frac{V}{\pi l}}$$ (2)

where $r_o$ and $l$ are the deformed outer radius and length, respectively.

The deformed state is described by the deformation of the midwall arterial surface in terms of the right Cauchy–Green strain tensor $\mathit{C}=\mathrm{diag}\left\{{\lambda }_1^2{,\hspace{0.17em}\lambda }_2^2\right\}$ and the change in wall thickness. The principal stretches in the axial ( ${\lambda }_1)$ and circumferential ${(\lambda }_2)$ direction and the deformed wall thickness ( $h)$ are given by

$${\lambda }_1=\frac{l}{L}\hspace{1em}{\lambda }_2=\frac{r_i+h/2}{R_i+H/2}\hspace{1em}h=\frac{H}{{\lambda }_1{\lambda }_2}$$ (3)

Equation (2) in combination with recorded experimental data enable calculation of mean principal wall stresses in the axial ( ${\sigma }_1)$ and circumferential $\left({\sigma }_2\right)$ direction at each deformed state

$${\sigma }_1=\frac{f+P\pi r_i^2}{\pi h(2r_i+h)}\hspace{1em}{\sigma }_2=\frac{P{r}_i}{h}$$ (4)

We consider the tissue as a constrained mixture of two passive load-bearing constituents (elastin and collagen) and one active constituent (SMCs), hereafter denoted by superscripts $\mathrm{el}$, $\mathrm{col}$, and $\mathrm{smc}$, respectively. The mass fractions ( $\phi )$ of each constituent are

$${\phi }^{\mathrm{el}}=\frac{M^{\mathrm{el}}}{M}\hspace{1em}{\phi }^{\mathrm{col}}=\frac{M^{\mathrm{col}}}{M}\hspace{1em}{\phi }^{\mathrm{smc}}=\frac{M^{\mathrm{smc}}}{M}$$ (5)

where $\left\{M^{\mathrm{el}},\hspace{0.17em}{M}^{\mathrm{col}},\hspace{0.17em}{M}^{\mathrm{smc}}\right\}$ are the masses of each constituent; $M$ is the total tissue mass. Consideration of only these three tissue constituents implies

$${\phi }^{\mathrm{el}}+{\phi }^{\mathrm{col}}+{\phi }^{\mathrm{smc}}=1\hspace{0.17em}\mathrm{and}\hspace{0.17em}\hspace{0.17em}{M}^{\mathrm{el}}+M^{\mathrm{col}}+M^{\mathrm{smc}}=M$$ (6)

As in Ref. [54] the stress field in the arterial wall is described as a sum of passive Cauchy stress tensor, $\hspace{0.17em}{\mathit{\sigma }}^{\mathrm{pas}}=\mathrm{diag}\left\{{\sigma }_1^{\mathrm{pas}},\hspace{0.17em}{\sigma }_2^{\mathrm{pas}}\right\},$ and an active circumferential stress ${\sigma }_2^{\mathrm{act}}$. Given the passive strain energy function $\left(W\right(\mathit{C}\left)\right)$ and a general form for ${\sigma }_2^{\mathrm{act}}$ [54], the total arterial wall stresses are

$${{\sigma }_1=\lambda }_1\frac{\partial W}{\partial {\lambda }_1},\hspace{1em}{{\sigma }_2=\lambda }_2\frac{\partial W}{\partial {\lambda }_2}+{\sigma }_2^{\mathrm{act}}={\lambda }_2\frac{\partial W}{\partial {\lambda }_2}{+\hspace{0.17em}\phi }^{\mathrm{smc}}S\hspace{0.17em}F\left({\lambda }_2\hspace{0.17em}\right)$$ (7)

As shown in the second equation and previously elaborated [22], the magnitude of ${\sigma }_2^{\mathrm{act}}$ depends on the SMC content (via ${\phi }^{\mathrm{smc}}$), activation state (via activation parameter $S$), and deformation (via normalized function $F\left({\lambda }_2\right)$).

The flow-induced shear stress at the endothelium is $\tau =4\mu Q/\pi r_i^3$, where $Q$ is the volumetric flowrate and $\mu$ is the dynamic blood viscosity.

The equation of equilibrium in the radial direction that follows from a free-body diagram of a vessel inflated by an internal pressure is ${\sigma }_2=P{r}_i/h,$ often called Laplace's law, can be expressed as

$${\lambda }_2\frac{\partial W}{\partial {\lambda }_2}+{\phi }^{\mathrm{smc}}S\hspace{0.17em}F\left({\lambda }_2\hspace{0.17em}\right)=P\hspace{0.17em}\frac{\left[{\lambda }_1{\lambda }_2^2\left(R_i+\frac{H}{2}\right)-\frac{H}{2}\right]}{H}$$ (8)

Given $W\left(\mathit{C}\right)$, initial dimensions $R_i$ and $H$, axial stretch ${\lambda }_1,$ constituent mass fractions, activation parameter $S,$ lumen pressure $P$, and the function $F\left({\lambda }_2\right)$, Eq. (8) enables calculation of the circumferential stretch ${\lambda }_2$ when the vessel is in equilibrium.

When an artery is inflated by the normotensive pressure $P^N$, extended to in situ axial stretch ${\lambda }_1=\lambda ,$ and SMCs are under a basal level of stimulation, the corresponding strain and stress values are termed as basal and are hereafter denoted by the subscript $\left(b\right)$.

2.1.4 Remodeling Scenario 1: Adaptive Pressure-Mediated Arterial Remodeling Following Traditional Drug-Coated Balloon Deployment.

We use the global growth approach to predict the outcomes of pressure-mediated arterial remodeling, wherein we formulate and solve equation systems that reflect observed/plausible characteristics of the remodeling process [22,23,45]. While this study focuses on maladaptive pressure-mediated post-DCB remodeling, our framework entails specification of adaptive remodeling outcomes under equivalent hypertensive pressures (as explained below). Thus, in analogy to our previously detailed approach [22], we first predict outcomes of adaptive pressure-mediated post-DCB remodeling to both inform our proposed model of maladaptive remodeling and provide context for our obtained results.

Upon completion of adaptive post-DCB remodeling under a hypertensive pressure $P^H$, the vessel is assumed to manifest an increase in wall thickness with no change in inner radius—as a result of these geometrical changes, remodeling restores basal values of flow-induced shear stress (assuming no change in flowrate) and circumferential wall stress. Additionally, it is assumed that constituent mechanical properties, SMC contractile state, and axial stretch are not altered by an adaptive remodeling process.

In line with these assumptions, we formulate and solve the following system of governing equations to calculate the geometrical parameters that describe apparent growth due to adaptive remodeling, i.e., $r_{i\left(a\right)}\hspace{0.17em}$ and $h_{\left(a\right)}$, with the subscript $\left(a\right)$ indicating an adaptive remodeling outcome

$$r_{i\left(a\right)}=r_{i\left(b\right)\hspace{1em}}{h}_{\left(a\right)}=h_{\left(b\right)}\frac{P^H}{P^N}$$ (9)

The first equation in System (9) enforces the restoration of flow-induced shear stress; the second equation enforces the restoration of circumferential wall stress.

System (9) equations can be combined to express the deformed cross-sectional wall area of the remodeled artery ( $a_{\left(a\right)}$) as

$$a_{\left(a\right)}=2\pi \left(r_{i\left(b\right)}+\hspace{0.17em}\frac{h_{\left(b\right)}}{2}\frac{P^H}{P^N}\right)h_{\left(b\right)}\frac{P^H}{P^N}$$ (10)

We assume that in the absence of an anti-proliferative (AP) drug, pressure-mediated adaptive remodeling results in an increase in SMC mass that is proportional to the increase in total arterial mass such that ${\phi }^{\mathrm{smc}}$ remains constant, reflecting a partial condition imposed in previous models of adaptive arterial remodeling in hypertension [45,55,56]. To model the effect of an AP drug on resident SMCs in a manner in-line with in vitro and in vivo findings [18], we introduce the following relation in which drug dosing limits SMC mass increase during the remodeling process

$$M_{\left(a\right)}^{\mathrm{smc}}=M_{\left(b\right)}^{\mathrm{smc}}\left[\frac{a_{\left(a\right)}}{a_{\left(b\right)}}+D_{\left[\mathrm{AP}\right]}\left(1-\frac{a_{\left(a\right)}}{a_{\left(b\right)}}\right)\right]$$ (11)

The normalized drug dosing parameter ( $D_{\left[\mathrm{AP}\right]}$) ranges from 0 to 1, where in these limits the increase in SMC mass in the remodeled artery is proportional to wall growth ( $D_{\left[\mathrm{AP}\right]}=0)$ or fully arrested ( $D_{\left[\mathrm{AP}\right]}=1$).

The mass of elastin is assumed to be unaltered by the remodeling process, which has been experimentally observed [57] and understood to be a consequence of the exceedingly low turn-over rate of this protein [58], but the mass fraction changes due to changes in other constituents' mass. Thus, with these assumptions and making use of Systems (5) and (6), constituent mass fractions in the remodeled artery are

$${\phi }_{\left(a\right)}^{\mathrm{el}}=\frac{M_{\left(b\right)}^{\mathrm{el}}}{M_{\left(a\right)}}\hspace{0.17em}{\phi }_{\left(a\right)}^{\mathrm{col}}=1-\hspace{0.17em}{\phi }_{\left(a\right)}^{\mathrm{el}}-\hspace{0.17em}{\phi }_{\left(a\right)}^{\mathrm{smc}}\hspace{0.17em}{\phi }_{\left(a\right)}^{\mathrm{smc}}=\frac{M_{\left(a\right)}^{\mathrm{smc}}}{M_{\left(a\right)}}$$ (12)

Finally, to calculate the geometrical parameters that describe true growth due to adaptive pressure-mediated remodeling, i.e., $R_{i\left(a\right)}$ and $H_{\left(a\right)}$, and deformation parameter ${\lambda }_{2\left(a\right)},$ we formulate and solve the following system:

$$\begin{array}{c}{\lambda }_{2\left(a\right)}\left(R_{i\left(a\right)}+\frac{H_{\left(a\right)}}{2}\right)-\frac{H_{\left(a\right)}}{2\lambda {\lambda }_{2\left(a\right)}}-r_{i\left(b\right)\hspace{0.17em}}=0\\ \frac{H_{\left(a\right)}}{\lambda {\lambda }_{2\left(a\right)}}-h_{\left(b\right)}\hspace{0.17em}\frac{P^H}{P^N}=0\hspace{0.17em}\\ {\lambda }_{2\left(a\right)}\frac{\partial W}{\partial {\lambda }_{2\left(a\right)}}+{{\phi }_{\left(b\right)}^{\mathrm{smc}}S}_{\left(b\right)}\hspace{0.17em}F\left({\lambda }_{2\left(a\right)}\right)-{\sigma }_{2\left(b\right)}=\hspace{0.17em}0\end{array}$$ (13)

The first and second equation in System (13) are analogous to System (9) but expressed in terms of the undeformed vessel dimensions, while the third equation incorporates the constitutive equation into the condition that remodeling restores the circumferential wall stress [59,60].

2.1.5 Remodeling Scenario 2: Maladaptive Pressure-Mediated Arterial Remodeling Following Traditional Drug-Coated Balloon Deployment.

Here, we consider post-DCB femoral artery remodeling in response to a sustained hypertensive pressure $P^H$ as a maladaptive process due to EC dysfunction, which compromises EC-mediated regulation of SMC contractility. Previous studies suggest that maladaptive inward remodeling in hypertension is associated with EC dysfunction and an increase in SMC tone [38,61]—the predominance of the contractile phenotype consequently diminishes the upregulation of matrix synthesis as seen in adaptive remodeling [62,63]. In addition to this tradeoff, we account for the AP drug effects on SMCs via imposed conditions on remodeling-mediated changes in both arterial tissue composition as well as total mass. We again assume that basal values of the axial stretch and flow are unaffected by remodeling.

In line with these notions, our mathematical model of post-DCB maladaptive remodeling assumes the following: (i) EC dysfunction causes a pressure-mediated elevation in SMC contraction, (ii) remodeled arterial mass is reduced as compared to the case of adaptive remodeling under equivalent hypertensive pressures, with the extent of reduction dependent on both the increase in SMC contraction (due to EC dysfunction) and the decrease in SMC proliferation (due to the AP drug), and (iii) the circumferential wall stress is restored to its basal value as in the case of adaptive remodeling. Hereafter, terms labeled with the subscript $\left(\mathrm{ma}\right)$ refer to outcomes of maladaptive post-DCB remodeling.

To calculate the geometrical parameters that describe apparent growth due to post-DCB maladaptive remodeling, i.e., $r_{i\left(\mathrm{ma}\right)}$ and $h_{\left(\mathrm{ma}\right)}$, we formulate and solve the following system of governing equations:

$$\begin{array}{c}\frac{P^H{\hspace{0.17em}r}_{i\left(\mathrm{ma}\right)}}{h_{\left(\mathrm{ma}\right)}}-{\sigma }_{2\left(b\right)}=0\\ S_{\left(\mathrm{ma}\right)}=\left\{\begin{array}{c}{S}_{\left(b\right)}+(S_{\left(\max \right)}-S_{\left(b\right)})\frac{P^H-P^N}{P^{\mathrm{cr}}-P^N}\hspace{1em}\mathrm{i}\mathrm{f}\hspace{1em}{P}^H\le P^{\mathrm{cr}}\\ \hspace{0.17em}{\hspace{0.17em}S}_{\left(\max \right)}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{i}\mathrm{f}\hspace{1em}{P}^H>P^{\mathrm{cr}}\hfill \end{array}\right.\\ 2\pi \left(r_{i\left(\mathrm{ma}\right)}+\frac{h_{\left(\mathrm{ma}\right)}}{2}\right)h_{\left(\mathrm{ma}\right)}-a_{\left(b\right)}+\left(\frac{S_{\left(\max \right)}-S_{\left(\mathrm{ma}\right)}}{S_{\left(\max \right)}-S_{\left(b\right)}}\right)(1-D_{\left[\mathrm{AP}\right]})\left(a_{\left(b\right)}-a_{\left(a\right)}\right)=\hspace{0.17em}0\end{array}$$ (14)

The first equation in System (14) reflects the restoration of the baseline circumferential stress; the second equation gives the relationship between hypertensive pressure $P^H$ and the value of the activation parameter $S\in \hspace{0.17em}(S_{\left(b\right)},S_{\left(\max \right)})$, where $S_{\left(\max \right)}$ reflects the maximal contractile capacity of SMCs and is assigned for pressures equal or higher than a certain critical value $P^{\mathrm{cr}}$ as described and rationalized in Ref. [35]; the third equation relates remodeling-mediated growth variables to SMC contractility and AP drug dosing, and insomuch reflects a tradeoff among the synthetic, contractile, and proliferative phenotypes of the resident cell population. The third equation stipulates that the deformed wall area after maladaptive remodeling under a prescribed level of hypertension is decreased relative to the adaptive response wall area (at the same level of hypertension), with the extent of decrease dependent on the degree of SMC stimulation and AP drug dosing.

Anti-proliferative drug dosing is assumed to impact wall composition in the same manner as in the adaptive scenario and is thus given by Eqs. (11) and (12) with replacement of subscript $\left(a\right)$ with $\left(\mathrm{ma}\right)$ for all terms.

Finally, as done in Sec. 2.1.4, to calculate the true growth, the first and the third equations in System (14) are rewritten in terms of the initial arterial dimensions and circumferential stretch ${\lambda }_{2\left(\mathrm{ma}\right)}$, and the expression for restoration of the circumferential stress ${\sigma }_{2\left(\mathrm{ma}\right)}$ is given as a sum of passive and active stress. The set of governing equations becomes

$$\begin{array}{c}{P}^H\frac{\left[\lambda {\lambda }_{2\left(\mathrm{ma}\right)}^2\left(R_{i\left(\mathrm{ma}\right)}+\frac{H_{\left(\mathrm{ma}\right)}}{2}\right)-\frac{H_{\left(\mathrm{ma}\right)}}{2}\right]}{H_{\left(\mathrm{ma}\right)}}\hspace{0.17em}-{\sigma }_{2\left(b\right)}=0\\ S_{\left(\mathrm{ma}\right)}=\left\{\begin{array}{c}{S}_{\left(b\right)}+(S_{\left(\max \right)}-S_{\left(b\right)})\frac{P^H-P^N}{P^{\mathrm{cr}}-P^N}\hspace{1em}\mathrm{i}\mathrm{f}\hspace{0.17em}{P}^H\le P^{\mathrm{cr}}\\ \hspace{0.17em}{\hspace{0.17em}S}_{\left(\max \right)}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.5em}\hspace{1em}\mathrm{i}\mathrm{f}\hspace{1em}{P}^H>P^{\mathrm{cr}}\hfill \end{array}\right.\\ 2\pi \left[{\lambda }_{2\left(\mathrm{ma}\right)}\left(R_{i\left(\mathrm{ma}\right)}+\frac{H_{\left(\mathrm{ma}\right)}}{2}\right)-\frac{H_{\left(\mathrm{ma}\right)}}{2\lambda {\lambda }_{2\left(\mathrm{ma}\right)}}\right]\frac{H_{\left(\mathrm{ma}\right)}}{2\lambda {\lambda }_{2\left(\mathrm{ma}\right)}}-a_{\left(b\right)}+\left(\frac{S_{\left(\max \right)}-S_{\left(\mathrm{ma}\right)}}{S_{\left(\max \right)}-S_{\left(b\right)}}\right)(1-D_{\left[\mathrm{AP}\right]})\left(a_{\left(b\right)}-a_{\left(a\right)}\right)=0\\ {\lambda }_{2\left(\mathrm{ma}\right)}\frac{\partial W}{\partial {\lambda }_{2\left(\mathrm{ma}\right)}}+{{\phi }_{\left(\mathrm{ma}\right)}^{\mathrm{smc}}S}_{\left(\mathrm{ma}\right)}\hspace{0.17em}F\left(\hspace{0.17em}{\lambda }_{2\left(\mathrm{ma}\right)}\right)-{\sigma }_{2\left(b\right)}=\hspace{0.17em}0\end{array}$$ (15)

2.1.6 Remodeling Scenario 3: Maladaptive Pressure-Mediated Arterial Remodeling Following Novel Drug-Coated Balloon Deployment.

Although current DCBs exclusively deliver AP drugs as the bio-active payload component, we extended our modeling framework to predict the effects of anti-contractile (AC) drug codelivery on maladaptive post-DCB remodeling outcomes. To account for a nonspecified AC drug, we assume that the SMC activation parameter $S_{\left(\mathrm{ma}\right)}$ remains dependent on the hypertensive pressure $P^H$, but is also modulated by the AC drug dose within the DCB payload. Like for the AP drug above, we introduce a normalized AC dosing parameter ( $D_{\left[\mathrm{AC}\right]}$) that ranges from 0 to 1, where in these limits the SMC activation parameter in the remodeled artery is as defined for the maladaptive scenario ( $D_{\left[\mathrm{AC}\right]}=0)$ or valued at zero to reflect fully passivated SMCs ( $D_{\left[\mathrm{AC}\right]}=1$). Specifically

$$S_{\left(\mathrm{ma}\right)}=\left\{\begin{array}{c}{S}_{\left(b\right)}+(S_{\left(\max \right)}-S_{\left(b\right)})\frac{P^H-P^N}{P^{\mathrm{cr}}-P^N}\}\hspace{0.17em}(1-D_{\left[\mathrm{AC}\right]})\hspace{1em}\mathrm{i}\mathrm{f}\hspace{1em}{P}^H\le P^{\mathrm{cr}}\\ {\hspace{0.17em}S}_{\left(\max \right)}(1-D_{\left[\mathrm{AC}\right]})\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.5em}\hspace{0.17em}\hspace{1em}\mathrm{i}\mathrm{f}\hspace{1em}{P}^H>P^{\mathrm{cr}}\hfill \end{array}\right.$$ (16)

After replacing the second equations in Systems (14) and (15) with Eq. (16), the resultant systems were used to both apparent and true growth upon completion of maladaptive remodeling following novel DCB deployment.

3 Results

3.1 Mechanical Response.

The femoral artery exhibited a nonlinear pressure-diameter response (at constant axial stretch) that is typical for muscular arteries [50,64], wherein biochemical induction of SMC contraction/relaxation induced a leftward/rightward shifting of the response curve with respect to the basal state (Fig. 1(a)). The axial force-pressure response (Fig. 1(b)) also showed expected trends and modulation via SMC contractile state [50,64]. At basal stimulation and axial stretch of $2.0$, the axial force-pressure response was relatively constant, and as such the in situ axial stretch $\lambda$ was assigned this value. Analogous pressure-diameter and force-pressure data obtained at ${\lambda }_1=1.9$ and ${\lambda }_1=2.1$ showed qualitatively similar trends and were used for material property identification (not shown).

Fig. 1.

Mechanical and histological data on the porcine femoral artery. Obtained mechanical response data include (a)pressure-outer diameter and (b) axial force-pressure relations when the artery is at fixed axial stretch ${(\lambda }_1=2.0)$ and under basal (■), maximally contracted (●), and fully relaxed (○) SMC states. (c) Histological preparations to assess arterial wall composition include (i) Resorcin Fuchsin with Woodstain Scarlet Acid Fuchsin counterstain, Direct Red (0.1% in saturated picric acid) using (ii) bright-field, and (iii) cross-polarized light, and (iv) a combination of Verhoeff–Masson's stain.

Histological images (Fig. 1(c)) were processed to identify constituent mass fractions for elastin, collagen, and SMCs, with obtained values ${\phi }^{\mathrm{el}}=0.20,\hspace{0.17em}{\phi }^{\mathrm{col}}=0.26,\hspace{0.17em}\mathrm{and}\hspace{0.17em}{\phi }^{\mathrm{SMC}}=0.54$ reflective of a typical muscular artery [65].

Isometric comparison between response curves under contracted (basal and maximal SMC contraction) and relaxed (passive) SMC states were used to generate total, passive, and active circumferential stretch-circumferential stress relations (Fig. 2, data points), where again responses typical of muscular arteries were observed [50,64].

Fig. 2.

Circumferential stress–stretch relations exhibited by the porcine femoral artery. The total (■), active (●), and passive (○) circumferential stress-circumferential stretch relations when the artery is at fixed axial stretch ${(\lambda }_1=2.0)$ and under (a) basal and (b) fully contracted SMC states. Points indicate experimental data; curves indicate fits with identified constitutive models.

To model the passive properties of the arterial tissue, we incorporated constituent mass fractions into a four-fiber family strain energy function $\left(W\right)$ as follows:

$$W={\phi }^{\mathrm{el}}\frac{c}{2}\left(I_1-3\right)+\sum _{k=1.4}{\phi }^{\mathrm{col},k}\frac{c_1^k}{4c_2^k}\left\{\exp \left[c_2^k{\left({\left({\lambda }^k\right)}^2-1\right)}^2\right]-1\right\}$$ (17)

where the first term accounts for the elastin-dominated isotropic matrix that is modeled by material parameter $c$; the second term (summation) accounts for collagen fiber families aligned in the axial ( $k=1)$, circumferential ( $k=2)$, and diagonal ( $k=3\hspace{0.17em}\mathrm{and}\hspace{0.17em}4)$ directions; fiber families are modeled by material parameters $c_1^k$ and $c_2^k$, with symmetric orientation and equivalent properties for diagonal fiber families; total collagen content ${\phi }^{\mathrm{col}}$ is assumed to be equally distributed among fiber families, i.e., ${\phi }^{\mathrm{col},k}=\frac{{\phi }^{\mathrm{col}}}{4}\hspace{0.17em}\mathrm{for}\hspace{0.17em}k=1.4$; $I_1$ is the first invariant of the right Cauchy–Green strain tensor; ${\lambda }^k$ is the stretch experienced by the ${k\mathrm{th}}^{}$ fiber family, and is given by ${\lambda }^k=\sqrt{{\lambda }_1^2{\text{cos}}^2{\alpha }_0^k+{\lambda }_2^2{\text{sin}}^2{\alpha }_0^k}$ where ${\alpha }_0^k$ is the angle of orientation between the ${k\mathrm{th}}^{}$ fiber family and the axial direction [46].

Passive model parameters were identified via nonlinear regression with mechanical response data obtained under the passivated SMC state, wherein the following error function was minimized:

$$\mathrm{error}=\sum _{j=1}^n\left[{\left(\frac{P^{\mathrm{mod}}-P^{\exp }}{\overline{P^{\exp }}}\right)}_j^2+{\left(\frac{F^{\mathrm{mod}}-F^{\exp }}{\overline{F^{\exp }}}\right)}_j^2\right]$$ (18)

with $n$ the total number of $j$ observations of measured transmural pressure or axial force in the dataset with an overbar denoting the mean values. The experimental data (exp) was measured directly while model (mod) values of axial force or pressure were calculated via equations given in Systems (4) and (7). The multivariate regression analysis was performed using the lsqnonlin function within MATLAB's optimization toolbox (MathWorks—Natick, MA) with the root-mean-square error (RMSE) reported.

To model the active properties, we adopted a previously used constitutive equation for the active circumferential stress [51], where

$${\sigma }_2^{\mathrm{act}}={\phi }^{\mathrm{smc}}S{e}^{{-b\left[\frac{{\lambda }_M-{\lambda }_2}{{\lambda }_M}\right]}^2}$$ (19)

The active stress is thus determined by the SMC amount/activation and a normalized function of the tissue stretch via dimensionless parameters $b$ and ${\lambda }_M$, where the latter is the circumferential stretch for which ${\sigma }_2^{\mathrm{act}}$ is maximal.

Active model parameters were identified via nonlinear regression with mechanical response data obtained under activated SMC states (basal and maximal contraction), wherein the following error function was minimized:

$$\mathrm{error}=\sum _{j=1}^n{\left(\frac{{{(\sigma }_2^{\mathrm{act}})}^{\mathrm{mod}}-{{(\sigma }_2^{\mathrm{act}})}^{\exp }}{{{<(\sigma }_2^{\mathrm{act}})}^{\exp }\rangle }\right)}_j^2$$ (20)

where $n$ is the total number of $j$ observations of active circumferential stress in basal and maximally contracted data sets and < > denotes the mean value. The experimental active stress (exp) was determined from isometric comparisons between the contracted and fully passivated response curves, while model (mod) values were calculated via Eq. (19). In our regression scheme, model parameters $b$ and ${\lambda }_M$ were held constant between contracted SMC states, while $S$ varied to yield values reflective of basal ( $S_{\left(b\right)})$ and maximal ( $S_{\left(\max \right)})$ SMC contraction. The multivariate regression analysis was performed using the lsqnonlin function within MATLAB's optimization toolbox (MathWorks—Natick, MA).

The measured vessel reference geometry, composition, identified values for passive/active model parameters, and RMSE are given in Table 1. Theoretically determined circumferential stress–stretch relations showed excellent agreement with the experimental data in both the basal and maximally contracted SMC states (Fig. 2, curves).

Table 1.

Geometry, wall composition, and identified constitutive properties of the porcine femoral artery. RMSE of theoretical versus experimental bi-axial passive and active mechanical response.

Geometry and composition
$R_i$ (mm)	2.131
$H$ (mm)	1.173
${\phi }^{\mathrm{el}}$	0.20
${\phi }^{\mathrm{col}}$	0.26
${\phi }^{\mathrm{smc}}$	0.54
Passive properties
$c$ (kPa)	56.80
$c_1^1$ (kPa)	35.84
$c_1^2\hspace{0.17em}$(kPa)	1.908
$c_1^3=c_1^4$ (kPa)	8.231
$c_2^1$	0.006
$c_2^2$	3.082
$c_2^3=c_2^4$	0.972
${\alpha }_0^3$= ${-\alpha }_0^4$ (deg)	59.26
RMSE	0.140
Active properties
$b$	19.08
${\lambda }_M$	1.545
$S_{\left(b\right)}$ (kPa)	166.4
$S_{\left(\max \right)}$ (kPa)	263.7
RMSE	0.466

3.2 Illustrative Simulations.

The commercial numerical solver Maple 12 (Maplesoft™, Waterloo, ON, Canada) was first used to solve the governing equations referring to the vessel basal state, defined by the initial wall composition, normotensive pressure $P^N=100\hspace{0.17em}\mathrm{mm}\hspace{0.17em}\mathrm{Hg}$, in situ axial stretch $\lambda =2.0$, and SMC activation parameter $S_{\left(b\right)}=166.4\hspace{0.17em}\mathrm{kPa}$, which yielded a deformed geometry $r_{i\left(b\right)\hspace{0.17em}}=3.64\hspace{0.17em}\mathrm{mm}$, $h_{\left(b\right)}=0.41\hspace{0.17em}\mathrm{mm}$, and $a_{\left(b\right)}=10.02\hspace{0.17em}{\mathrm{mm}}^2$ and circumferential wall stress ${\sigma }_{2\left(b\right)}=117.1\hspace{0.17em}\mathrm{kPa}$. Next, the solver was used to obtain numeric solutions for the governing equations in each of the post-DCB remodeling scenarios (Secs. 2.1.4–2.1.6), with consideration of fixed axial stretch $\lambda =2.0$ and $P^H$ ranging from $100\hspace{0.17em}\mathrm{mm}\hspace{0.17em}\mathrm{Hg}$ to $200\hspace{0.17em}\mathrm{mm}\hspace{0.17em}\mathrm{Hg}$ in $10\hspace{0.17em}\mathrm{mm}\hspace{0.17em}\mathrm{Hg}$ increments in all scenarios. In remodeling scenarios 1 and 2, the AP drug dosing parameter $D_{\left[\mathrm{AP}\right]}$ ranged from 0 to 1 in increments of 0.2; in remodeling scenario 3, $D_{\left[\mathrm{AP}\right]}$ was fixed at 0.5, while the AC drug dosing parameter $D_{\left[\mathrm{AC}\right]}$ ranged from 0 to 1 in increments of 0.2. In remodeling scenarios 2 and 3, the assigned critical pressure was $P^{\mathrm{cr}}=200\hspace{0.17em}\mathrm{mm}\hspace{0.17em}\mathrm{Hg}$. For all scenarios, obtained solutions for the undeformed/deformed vessel geometry and wall composition upon remodeling completion are depicted as a function of the hypertensive pressure at the specified drug dosing (Figs. 3–5).

Fig. 3.

Geometrical and compositional outcomes of adaptive pressure-mediated arterial remodeling following traditional DCB deployment. Remodeling outcomes for AP dosing parameter ( $D_{\left[\mathrm{AP}\right]}$) ranging from $0-1$ in $0.2$ increments, with the arrow indicating the dosing associated with each curve. Outcomes include (a) undeformed inner radius, (b)undeformed wall thickness, (c) undeformed wall area, (d) deformed inner radius, (e) deformed wall thickness, (f)deformed wall area, (g) elastin mass fraction, (h) collagen mass fraction, and (i) SMC mass fraction.

Fig. 5.

Geometrical and compositional outcomes of maladaptive pressure-mediated arterial remodeling following novel DCB deployment. Remodeling outcomes for a fixed AP dosing parameter ( $D_{\left[\mathrm{AP}\right]}=0.5$) with the AC dosing parameter ( $D_{\left[\mathrm{AC}\right]}$) ranging from $0-1$ in $0.2$ increments, with the arrow indicating the AC dosing associated with each curve. Outcomes include (a) undeformed inner radius, (b) undeformed wall thickness, (c) undeformed wall area, (d) deformed inner radius, (e) deformed wall thickness, (f) deformed wall area, (g) elastin mass fraction, (h) collagen mass fraction, and (i) SMC mass fraction.

4 Discussion

We first discuss the descriptive and predictive results of our study, with focus on how delivered drugs modulate post-DCB adaptive/maladaptive remodeling outcomes under various degrees of hypertension (Sec. 4.1). For complementary and detailed discussion focused solely on pressure-induced maladaptive inward remodeling (i.e., in the absence of drugs), see Ref. [22] which introduces and utilizes the same underlying mathematical framework as the current study. We then discuss the implications of our findings as they pertain to current and novel DCBs (Sec. 4.2), note study limitations that should be considered with interpretation of our results (Sec. 4.3) and provide concluding remarks on our study (Sec. 4.4).

4.1 Descriptive and Predictive Results

4.1.1 Remodeling Scenario 1: Adaptive Pressure-Mediated Arterial Remodeling Following Traditional Drug-Coated Balloon Deployment.

Predictions of true adaptive remodeling outcomes following traditional DCB deployment show that as the degree of hypertension increases, the undeformed geometry of the remodeled vessel is characterized by a monotonic decrease in inner radius, increase in wall thickness, and increase in wall area, with moderate AP drug-mediated alterations (less than 5% over the examined range) in inner radius and wall thickness (Figs. 3(a)–3(c)). Conversely, the deformed geometry of the remodeled vessel is fully prescribed in accordance with System (9) and is therefore insensitive to AP dosing, with outward hypertrophic remodeling outcomes characterized by the retention of inner radius coupled with monotonic increases in wall thickness/area such that flow-induced shear stress and circumferential wall stress are restored to baseline values (Figs. 3(d)–3(f)). Predicted changes in wall composition commensurate with this growth include a monotonic reduction in elastin mass fraction, increase in collagen mass fraction, and retention (no AP drug) or decrease in SMC mass fraction (Figs. 3(g)–3(i)). The AP drug-mediated reduction in SMC mass (per Eq. (11)) becomes relatively more significant (in comparison to total arterial mass) with increasing hypertensive pressure, thus having a greater effect on ${\phi }_{\left(a\right)}^{\mathrm{smc}}$ that culminates with an approximate 40% drug-mediated reduction at $P^H=200\hspace{0.17em}\mathrm{mm}\hspace{0.17em}\mathrm{Hg}$ ( $D_{\left[\mathrm{AP}\right]}=1\mathrm{versus}{D}_{\left[\mathrm{AP}\right]}=0$ in Fig. 3(i)). Thus, if post-DCB remodeling is inherently adaptive, the imposed constraints on constituent mass production result in drug-mediated compositional alterations (increase in collagen content, decrease in SMC content) which could compromise the contractile function of the artery.

Scenario summary: When considering traditional DCBs, in which an AP drug is the sole payload component, the model predicts that adaptive pressure-mediated post-DCB remodeling retains the outward hypertrophic character associated with adaptive remodeling under sustained hypertension, as well-established in theoretical, experimental, and clinical studies [66]; AP drug dosing induces a negligible change in true remodeling outcomes and has no effect on the apparent remodeling outcomes; increasing AP drug dosing leads to a monotonic increase of collagen content and reduction of SMC content in the remodeled vessel.

4.1.2 Remodeling Scenario 2: Maladaptive Pressure-Mediated Arterial Remodeling Following Traditional Drug-Coated Balloon Deployment.

Predictions of true maladaptive remodeling outcomes following traditional DCB deployment show that as the degree of hypertension increases, there is a monotonic reduction in the undeformed inner radius, with notable AP drug-mediated enhancement of inward growth at intermediate pressures (Fig. 4(a)). Conversely, changes in undeformed wall thickness and area are nonmonotonic as hypertensive pressure increases, but like the inner radius these outcomes exhibit most sensitivity to AP drug at intermediate hypertension (Figs. 4(b) and 4(c)). Predictions of deformed vessel geometry (Figs. 4(d)–4(f)) exhibited analogous trends with increasing hypertension and AP drug dosing, with apparent remodeling characterized by inward growth that transitions from hypertrophic to eutrophic as the hypertensive pressure approaches the assigned critical value as stipulated by System (14). Constituent mass fractions exhibit a complex response to AP drug dosing in this maladaptive scenario (Figs. 4(g)–4(i)), which is due to drug-mediated effects on both the SMC mass (per Eq. (11)) and total wall mass (per third equation in System (14)). For example, increasing $D_{\left[\mathrm{AP}\right]}$ over the range of $[0,\hspace{0.17em}0.6]$ causes a reduction in ${\phi }_{\left(\mathrm{ma}\right)}^{\mathrm{smc}}$, whereas further increases in drug concentration causes a comparative increase in ${\phi }_{\left(\mathrm{ma}\right)}^{\mathrm{smc}}$ that culminates in preservation of the baseline value when $D_{\left[\mathrm{AP}\right]}=1$. Indeed, in the limiting scenario of $D_{\left[\mathrm{AP}\right]}=1$, our model (per third equation in System (14)) enforces a full arrest of wall growth irrespective of the hypertensive pressure, and thus there is no remodeling-mediated change in tissue composition.

Fig. 4.

Geometrical and compositional outcomes of maladaptive pressure-mediated arterial remodeling following traditional DCB deployment. Remodeling outcomes for AP dosing parameter ( $D_{\left[\mathrm{AP}\right]}$) ranging from $0-1$ in $0.2$ increments, with the arrow/hash mark indicating the dosing associated with each curve. Outcomes include (a) undeformed inner radius, (b) undeformed wall thickness, (c) undeformed wall area, (d) deformed inner radius, (e) deformed wall thickness, (f) deformed wall area, (g) elastin mass fraction, (h) collagen mass fraction, and (i) SMC mass fraction.

Scenario summary: When considering traditional DCBs, in which an AP drug is the sole payload component, the model predicts that maladaptive pressure-mediated post-DCB remodeling is inward and hypertrophic for all hypertensive pressures below $P^{\mathrm{cr}}$; AP drug diminishes remodeled arterial mass at all hypertensive pressures below $P^{\mathrm{cr}}$; AP drug promotes restenosis in maladaptive inward remodeling, with the most significant drug-mediated reduction in the remodeled vessel deformed inner radius occurring at intermediate hypertension; AP drug-mediated alterations in remodeled wall composition are complex due to effects on both SMC and total mass production, but the compositional changes are overall less significant when compared to the adaptive scenario; the biphasic changes that characterize geometric remodeling outcomes under increasing degree of hypertension emerge due to pressure-dependent growth that restores the circumferential wall stress and the modeled compromise between SMC synthetic potential and tone, the latter of which is also pressure-dependent per the second equation in System (14); the biphasic nature of pressure-mediated mass fraction alterations follows from the trend in geometry coupled with the model assumption that elastin mass remains constant throughout the remodeling process.

4.1.3 Remodeling Scenario 3: Maladaptive Pressure-Mediated Arterial Remodeling Following Novel Drug-Coated Balloon Deployment.

Predictions of true maladaptive remodeling outcomes following novel DCB deployment show that with a fixed, intermediate dose of (traditional) AP drug, codelivery of an AC drug significantly alters both growth direction and extent (Figs. 5(a)–5(c)). With respect to the growth direction, the AC drug promotes increasingly inward growth over the lower range of examined hypertensive pressures ( $P^H<120\hspace{0.17em}\mathrm{mm}\hspace{0.17em}\mathrm{Hg}$), whereas at higher hypertensive pressures ( $P^H>160\hspace{0.17em}\mathrm{mm}\hspace{0.17em}\mathrm{Hg})$ inward growth is curtailed (Fig. 5(a)). In terms of growth extent, increasing $D_{\left[\mathrm{AC}\right]}$ leads to monotonic increases in wall thickness/area for all hypertensive pressures (Figs. 5(b) and 5(c)), an effect in line with the introduced tradeoff between SMC contractile/synthetic phenotypes as modeled by the third equation in System (15) along with Eq. (16). The effect of AC drug on apparent remodeling outcomes is monotonic with respect to all deformed geometrical variables, whereby increasing $D_{\left[\mathrm{AC}\right]}$ leads to increased inner radius, wall thickness, and wall area in all hypertensive states (Figs. 5(d)–5(f)). Critically, the model predicts an AC drug-mediated reversal of apparent growth direction (inward to outward) in all hypertensive states at the higher considered doses (Fig. 5(d), $D_{\left[\mathrm{AC}\right]}=[0.8,\hspace{0.17em}1]$), supporting the therapeutic potential of an AC drug to mitigate restenosis in the maladaptive post-DCB context. At lower doses of AC drug, inward growth still occurs across the examined range of hypertensive pressures, suggesting that benefit to the patient would be limited by inadequate AC dosing/efficacy throughout the remodeling process. Remodeling-mediated changes in constituents' mass fraction include a decrease in ${\phi }_{\left(\mathrm{ma}\right)}^{\mathrm{el}}$ and ${\phi }_{\left(\mathrm{ma}\right)}^{\mathrm{smc}}$ at all hypertensive pressures (except for at $D_{\left[\mathrm{AC}\right]}=0$ and ${P^H=P}^{\mathrm{cr}}$, at which the response is eutrophic); for a given $P^H$, AC drug inclusion alters the ratio of wall constituents such that ${\phi }_{\left(\mathrm{ma}\right)}^{\mathrm{el}}$ and ${\phi }_{\left(\mathrm{ma}\right)}^{\mathrm{smc}}$ are reduced while ${\phi }_{\left(\mathrm{ma}\right)}^{\mathrm{col}}$ is proportionally increased (Figs. 5(g)–5(i)).

Scenario summary: When considering DCBs in which both AP and AC drugs are included in the payload, the model predicts that maladaptive post-DCB remodeling is significantly altered by the presence of the novel AC drug component, including changes in both true and apparent remodeling outcomes; as a consequence of the imposed tradeoff between SMC contractile and synthetic phenotypes, the AC drug promotes an increase in remodeled arterial mass at all hypertensive pressures, as well as a reversal of the growth direction from inward to outward; AC drug inclusion alters remodeled arterial wall composition, whereby drug-induced changes are monotonic across the evaluated range of hypertensive pressures and characterized by relative decreases in ${\phi }_{\left(\mathrm{ma}\right)}^{\mathrm{el}}$ and ${\phi }_{\left(\mathrm{ma}\right)}^{\mathrm{smc}}$ and increase in ${\phi }_{\left(\mathrm{ma}\right)}^{\mathrm{col}}$.

4.2 Implications for Traditional and Novel Drug-Coated Balloons.

We directly compare the following cases to highlight the implications of our findings for DCB therapy: case 1—adaptive pressure-mediated arterial remodeling (no delivered drug); case 2—maladaptive pressure-mediated arterial remodeling (no delivered drug); case 3—maladaptive pressure-mediated post-DCB arterial remodeling with an intermediate AP drug dose of ${(D}_{\left[\mathrm{AP}\right]}=0.5)$; case 4—maladaptive pressure-mediated post-DCB arterial remodeling, with intermediate doses of AP and AC drugs $(D_{\left[\mathrm{AP}\right]}=0.5$ and $D_{\left[\mathrm{AC}\right]}=0.5)$. Comparison of apparent geometric outcomes of remodeling (Figs. 6(a) and 6(b)) shows that in maladaptive cases in which AP drug is delivered alone, it decreases wall growth but promotes an inward response (case 2 versus case 3). Thus, these results suggest that in clinical scenarios of DCB deployment in which EC dysfunction and hypertension present as comorbidities, an AP drug such as paclitaxel will not prevent restenosis, but instead its occurrence will be determined by the degree to which EC dysfunction impacts the post-DCB remodeling process. When DCB therapy is augmented via codelivery of an AC drug, pressure-mediated trends in maladaptive remodeling outcomes shift toward the adaptive outcomes (Figs. 6(a) and 6(b), case 4 versus case 1), supporting the concept of AC drug inclusion as a novel strategy to mitigate post-DCB restenosis in the presence of EC dysfunction. Case comparisons of the pressure-diameter response (Fig. 6(c)) of remodeled vessels due to an intermediate degree of hypertension ${(P}^H=150\hspace{0.17em}\mathrm{mm}\hspace{0.17em}\mathrm{Hg})$ show that with respect to the baseline vessel (dashed line), all remodeled vessels exhibit a decrease in distensibility that is more pronounced in maladaptive (Cases 2–4) as opposed to adaptive scenarios (case 1). However, even in adaptive remodeling (as defined in our study) and preserved tissue composition, the remodeled vessel exhibits an unfavorable alteration in structural mechanics (increased structural stiffness/reduced compliance) due to the pressure-mediated increase in wall thickness. Like the effect on geometrical outcomes of remodeling, the inclusion of an AC drug in the DCB payload shifts the pressure-diameter response after maladaptive remodeling toward the response exhibited after adaptive remodeling (Fig. 6(c), case 4 versus case 1). To establish further theoretical support for consideration of novel DCBs that codeliver AP and AC drugs, we conducted iterative AC dosing studies at a fixed, intermediate AP dosing to identify a payload that facilitates preservation of lumen area in maladaptive post-DCB remodeling. We found that when $D_{\left[\mathrm{AP}\right]}=0.5$ and $D_{\left[\mathrm{AC}\right]}=0.74,$ the deformed inner radius after completion of maladaptive post-DCB remains within 3% of the adaptive (baseline) value for the full range of considered $P^H$ (Fig. 6(d)).

Fig. 6.

Comparison of remodeling outcomes. Predictions for the (a) deformed wall area and (b) deformed inner radius of the femoral artery after completion of pressure-mediated remodeling, where Case 1 refers to adaptive remodeling, Case 2 refers to maladaptive remodeling, Case 3 refers to maladaptive post-DCB remodeling with $D_{\left[\mathrm{AP}\right]}=0.5\hspace{0.17em}$(traditional DCB with intermediate drug dose), and Case 4 refers to maladaptive post-DCB remodeling with $D_{\left[\mathrm{AP}\right]}=0.5$ and $D_{\left[\mathrm{AC}\right]}=0.5\hspace{0.17em}$(novel DCB with intermediate drug dose). (c) Predictions for the vessel pressure-outer diameter relations after completion of remodeling under an intermediate degree of hypertension ${(P}^H=150\hspace{0.17em}\mathrm{mm}\hspace{0.17em}\mathrm{Hg})$ for Cases 1–4; dashed line indicates the baseline relation. (d) Predictions for deformed inner radius of the femoral artery after completion of pressure-mediated remodeling, where Case* refers to maladaptive post-DCB remodeling with $D_{\left[\mathrm{AP}\right]}=0.5$ and $D_{\left[\mathrm{AC}\right]}=0.74\hspace{0.17em}$(novel DCB with tuned drug dose).

Implementation of the payload designs suggested by our findings would require that the normalized dosing parameters, $D_{\left[\mathrm{AP}\right]}$ and $D_{\left[\mathrm{AC}\right]}$, are registered with specific drug concentrations in novel DCBs. At a minimum, identification of these parameters for a specific drug/tissue target would require ex vivo and/or preclinical in vivo dosing studies that interrelate initial DCB formulation, resultant tissue concentrations (after local delivery via DCB), and the manifest SMC activity (indices of proliferation and contractility) over time scales relevant to arterial remodeling (i.e., weeks-to-months). While such studies present numerous experimental challenges, high-throughput bioreactor systems which promote tissue viability for extended periods potentiate initial specification of DCB design guided by the proposed modeling framework [46].

In all formulated scenarios for maladaptive post-DCB remodeling, the tensile circumferential stress is restored to the baseline value and as such is an adaptive outcome from the perspective of SMCs, but flow-induced shear stress at the endothelium is not restored due to EC dysfunction. Moreover, also due to EC dysfunction, we prescribe an elevation in SMC tone due to hypertension, with predicted maladaptive outcomes that align with theoretical, experimental, and clinical findings of inward growth and reduction in remodeled vessel deformability as shown in Fig. 6(c) [19,36–39]. Thus, although our findings support the potential for improving patient outcomes in terms of post-DCB lumen preservation via selective tuning of codelivered AP and AC drugs, other outcomes of maladaptive remodeling, namely, loss of vessel deformability, are predicted to by only partially mitigated by this approach.

4.3 Study Limitations.

Our study of post-DCB pressure-mediated arterial remodeling consists of a predictive mathematical framework that is informed by a representative constitutive model of the femoral artery. To both describe adaptive/maladaptive remodeling processes and account for the impact of AP and AC drugs, we introduce numerous simplifying assumptions within our framework. First, we assume that with a specific payload the subsequent drug-based modulation of SMC phenotype is operative and consistent throughout the remodeling process, and thus represent it by normalized time-independent parameters (i.e., $D_{\left[\mathrm{AP}\right]}$ and $D_{\left[\mathrm{AC}\right]}$). Support for or refinement of this assumption requires vessel- and drug-specific pharmacokinetic data throughout remodeling, including information on the degree to which SMC phenotype is transiently altered throughout the process. Given this limitation, it is possible that our results reflect drug-based alterations in the remodeling trajectory as opposed to outcomes, but nevertheless support the future consideration of novel DCBs with AP and AC payloads. Second, as with our initial implementation of the underlying model of maladaptive inward remodeling [22], the utilized analytical expressions that model relations between vascular tone and hypertensive pressure, as well as the tradeoffs between SMC synthetic, proliferative, and contractile activity, are assumed to be linear. Clearly, these relations may be more complex and require detailed biological data for full specification, but as implemented are in qualitative agreement with numerous studies on maladaptive remodeling that associate increased SMC contractility with sustained hypertension [19,36–39]. Third, we conducted mechanical/histological studies and constitutive modeling on a single arterial specimen, and our obtained results would obviously differ with use of other material parameters. However, the porcine femoral artery mechanical properties/composition identified for our study are in qualitative agreement with the behavior reported for muscular arteries [50,64,65], supporting the relevance of our findings for DCB applications. Finally, we employ a membrane model of the femoral artery, and assume that SMCs are circumferentially aligned within the arterial wall and thus only generate an active circumferential stress; further refinement of our model could consider wall stress gradients that result from the inflation–extension of a thick-walled cylindrical tube, and use advanced imaging to quantify the likely slight helical orientation of SMCs [67] and enable more precise account of the role of bi-axial active mechanics in arterial remodeling.

4.4 Conclusion.

We propose a theoretical framework to predict the outcomes of post-DCB femoral artery remodeling with account of patient- and device-specific variables, where the former consists of the degree of hypertension and the presence of EC dysfunction, and the latter includes locally delivered AP and AC drugs to the arterial wall. Our findings suggest that in maladaptive post-DCB remodeling scenarios, restenosis due to EC dysfunction is not prevented by traditional AP drug delivery, but that novel payloads which codeliver AP and AC drugs may effectively mitigate this maladaptive outcome. Future experimental studies are required to validate model predictions of post-DCB remodeling outcomes and further evaluate the potential for novel drug payloads to improve procedural outcomes.

Funding Data

• National Heart, Lung, and Blood Institute, National Institutes of Health (Grant No. R01-HL159620; Funder ID: 10.13039/100000050).

• National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health (Grant No. R01-DK132948; Funder ID: 10.13039/100000062).

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.