Mechanics and mechanobiology of arterial development

Abstract

Arteries serve primarily a biomechanical function. Critical insight into arterial structure, properties, and function thus derives from knowledge of mechanosensitive gene expression, associated microstructural organization, and biomechanical metrics such as compliance and vasoactive capacity. This review focuses on time-course changes in hemodynamic loads and associated changes in the transcriptional profile, mural composition, overall geometry, and mechanical properties of arteries during postnatal development, namely, from birth to a healthy adult. Although we examine the postnatal period, we allude to key findings during the prenatal period; although we draw on findings from multiple species and vessels, most data come from studies of the thoracic aorta in mice as an archetype vessel; and although we focus on normal development, we highlight four pathologic cases in which emergent homeostasis is compromised. Collectively, the data suggest that tissue-level mechanical homeostasis typically emerges following postnatal growth, with set-point values for multiple metrics dictating subsequent adaptations to changing hemodynamic loads in maturity, though with congenital defects, pathogenic variants, and disease conditions compromising homeostatic processes. Understanding the normal developmental program is essential for studying early-onset conditions, early surgical and pharmacological intervention, and ultimately aging as well as disease progression and its treatment in maturity.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1007/s10237-026-02088-0.

“If you would understand anything, observe its beginning and its development.” Aristotle.

Introduction

The primary function of the vasculature is blood-borne biotransport, especially delivery of oxygen and nutrients to and removal of carbon dioxide and waste products from tissues throughout the body, which is accomplished in part by directing blood to allied organs including the intestines, kidneys, liver, and lungs. Toward this end, appropriate pressure gradients are needed to drive the viscous blood as suggested by the simple relation $\mathrm{\Delta }P=QR$, where $\mathrm{\Delta }P$ denotes the pressure drop that drives the volumetric blood flow $Q$ against the intrinsic resistance to flow $R$, which depends on the viscosity of the blood (dictated largely by the hematocrit), the length of travel (further revealing gradients), and especially the luminal radius of the vessel. The heart generates the requisite pressures: the left ventricle pumps blood throughout most of the body (systemic circulation, with maximum normal pressures in the adult of order 120 mmHg ~ 16 kPa) and ultimately back to the right atrium while the right ventricle pumps blood through the lungs (pulmonic circulation, with maximum normal pressures in the adult of order 25 mmHg ~ 3.3 kPa) and ultimately back to the left atrium. From the large (elastic), medium-sized (muscular), and small (arterioles) arteries that carry blood from the heart to the capillaries, which enable most gas and nutrient exchanges, to the small, medium-sized, and large veins that return blood to the heart (at pressures of 3 to 5 mmHg), the vascular tree exhibits differential structure–function relationships along its course, with cell phenotype, mural composition, material properties, and geometry appearing to optimize function both locally (e.g., compliance or constriction) and globally (e.g., capacitance or conduction) while enabling the vasculature to exhibit a remarkable ability to mechano-adapt to moderate sustained changes in blood pressure and flow in maturity (Humphrey 2021).

It has long been recognized that multiple mechanical quantities tend to remain near preferred values in the healthy adult aorta (Wolinsky and Glagov 1967; Shadwick 1999; Chien 2007). Although the specific values of these regulated mechanical metrics may differ from region-to-region and from species-to-species (Greve et al. 2006; Cheng et al. 2007; Ramachandra et al. 2024), they yet appear to be well maintained locally under both normal conditions and modest perturbations (Dajnowiec and Langille 2007; Bersi et al. 2014). In this regard, note that the concept of homeostasis was introduced in the 1920s by the physiologist W.B. Cannon (1871–1945) who chose carefully the term homeo (meaning similar to), rather than homo (meaning the same as), when referring to quantities that change little over time (with stasis meaning a standing still). Within this context, mechanical homeostasis can be defined as a process that tends to maintain, within a particular tolerance, a mechanical quantity near a preferred value. There is, therefore, a need to identify the preferred values, often called set-points, as well as both the allowable ranges (or tolerances) and durations over which restorations of the regulated variable typically occur. Importantly, mechanical homeostasis exists within the vasculature across multiple length and time scales, from organ to tissue to cellular to the subcellular level (Humphrey 2008a). There are, of course, cases wherein homeostasis is compromised or lost, which are often associated with vascular aging or disease (Hanada et al. 2007; Ferruzzi et al. 2018; Galatioto et al. 2018; Zhang et al. 2025). Critical open questions include: When does mechanical homeostasis emerge during the developmental program and how is it promoted or prevented during aging and disease? Related to these questions are the yet incompletely understood relative roles of genetics and mechanics in morphogenesis, homeostasis, and pathogenesis.

Diverse animal models have proven useful in studying arterial development, including the chick, rat, and lamb. Nevertheless, mice have emerged as the preferred animal model in most modern cardiovascular research. We will draw upon lessons learned from different animal models but focus on murine data given the wealth of information now available as well as the expectation that continued research will often be based on mice. Notwithstanding the intrinsic complexity of arterial mechanics (Humphrey 2002), we will mainly use simple concepts to emphasize salient points. Moreover, although our motivation is primarily to understand postnatal development and maturation by using the murine thoracic aorta as an archetype, we begin by contrasting multiple arteries in healthy adult mice to appreciate different aspects of structure–function relations. Considering health in maturity is helpful because it represents the target state toward which the developmental program should lead.

Maturity—starting with the end in mind

Given the complex loads experienced by arteries in vivo, it is best to consider biaxial mechanical properties. Cyclic pressure-distension and axial force-extension tests are thus critical for assessing the biomechanical phenotype of a normal artery (Gleason et al. 2004; Ferruzzi et al. 2013). Given that residual stresses tend to reduce transmural gradients in wall stress, the general biomechanical phenotype of murine arteries is appreciated easily by first comparing radially-averaged values of biaxial stretch (mean circumferential ${\lambda }_{\theta }$ and axial ${\lambda }_z$), Cauchy stress (mean ${\sigma }_{\theta }$ and ${\sigma }_z$), material stiffness (mean ${\mathbb{C}}_{\theta \theta \theta \theta }$ and ${\mathbb{C}}_{\mathit{zzzz}}$), and of course elastic energy storage density ($W$, defined per unit volume in a reference configuration). Computed for in vivo levels of distending pressure and axial stretch, Table 1 lists values of these different metrics as well as composition and geometry for different arteries in healthy adult male wild-type (WT) mice: four segments of the aorta—ascending thoracic aorta (ATA), descending thoracic aorta (DTA), suprarenal abdominal aorta (SAA), and infrarenal abdominal aorta (IAA)—as well as two major branches off the aorta—common carotid artery (CCA) and superior mesenteric artery (SMA) —plus the second branch mesenteric artery (MA). The ATA, DTA, SAA, IAA, and CCA are true elastic arteries (each with multiple elastic lamellar units organized through the thickness of the wall) whereas the MA is a true muscular artery (with only internal and external elastic laminae). These segments within the higher-pressure systemic circulation can be compared further to the right branch pulmonary artery (RPA) within the lower-pressure pulmonary circulation. Comparisons amongst segments of the aorta and other thoracic vessels can also be found elsewhere (Ramachandra et al. 2024; Badal and Barocas 2026).

Table 1.

Compositional, geometric, and mechanical metrics for different arteries in the adult male mouse

	ATA	DTA	SAA	IAA	CCA	SMA	MA	RPA
BP (mmHg)	118	118	118	118	120	100	60	25
SMC (%)	35.3	26.5	23.3	20.3	18.2	17.5	33.0	21.5
Elastin (%)	34.5	31.9	32.3	20.9	23.5	30.9	20.9	24.9
Collagen (%)	29.9	38.7	40.4	46.8	50.7	50.3	44.2	50.6
GAG (%)	0.3	2.9	4.0	12.0	7.6	1.3	1.9	< 3
$a$ (μm)	899	676	643	426	276	275	118	552
$h$ (μm)	37	40	35	31	30	24	13	24
${\lambda }_z^{\mathit{iv}}$ (−)	1.81	1.53	1.60	1.74	1.69	1.65	1.74	1.49
$a/h$ (-)	24.3	16.9	18.4	13.8	9.20	11.5	9.08	23.0
${\sigma }_{\theta }$ (kPa)	381	261	293	212	187	154	76	79
${\sigma }_z$ (kPa)	381	244	284	266	229	184	113	71
${\mathbb{C}}_{\theta \theta \theta \theta }$ (MPa)	2.52	1.78	2.06	1.84	1.87	1.26	0.81	0.41
${\mathbb{C}}_{\mathit{zzzz}}$ (MPa)	2.33	3.56	2.96	3.51	3.94	2.41	1.49	0.52
$W$ (kPa)	109	64	75	57	47	43	20	23
KCl $\mathrm{\Delta }d$ (%)	− 12	− 9	− 7	− 10	NA	− 23	− 52	− 31
med:adv	80:20	70:30	60:40	50:50	38:62	66:34	62:38	36:64
med lamellae	7–6	5	5–4	4	4–3	4–3	2	3
${\sigma }_{\theta }$/layer	54.4	52.2	58.6	53.0	46.8	38.5	38.0	26.3

In most cases, values are averages across studies, which included Eberth et al. (2010), Ferruzzi et al. (2013), Bersi et al. (2017), Murtada et al. (2021), and Ramachandra et al. (2024). Thus, the genetic background includes C57BL/6 and C57BL/6;129SvEv mice, both WT and Apoe^−/− on regular diets; all mice were adult males ranging from P70–P140, $a$ = luminal radius, $h$ = wall thickness, ${\lambda }_z^{\mathit{iv}}$ = energetically preferred value of axial stretch, $\theta$ = circumferential direction and $z$ = axial direction, with $\sigma$ = stress, $\mathbb{C}$ = stiffness, and $W$ = elastic energy storage; Δd indicates the percent change in diameter following 5 min of exposure to a high potassium chloride (KCl) solution; med indicates medial layer, adv indicates adventitial layer

Most of these metrics depend strongly on blood pressure, which varies throughout the day, with different levels of activity / excitement, and of course with anesthesia. Shown are representative reported values of systolic blood pressure (BP) for the ascending thoracic aorta (ATA), descending thoracic aorta (DTA), suprarenal abdominal aorta (SAA), infrarenal abdominal aorta (IAA), common carotid artery (CCA), superior mesenteric artery (SMA), mesenteric artery (MA), and right pulmonary artery (RPA). The ATA, DTA, SAA, and IAA are elastic arteries while the MA is a muscular artery. The CCA (connecting the aorta to the muscular internal and external carotid arteries) and SMA (connecting the aorta to the branching muscular mesenteric arteries) serve as connectors of elastic and muscular arteries. The RPA appears to be closer to a systemic muscular artery than an elastic artery based on metrics of functionality

As seen in Table 1, the ratio of the thickness of the elastin-rich tunica media to the collagen-rich tunica adventitia decreases progressively down the aorta (from approximately 80:20 in the ATA to 70:30 in the DTA, 60:40 in the SAA, and 50:50 in the IAA) with nearly concurrent decreases in elastic energy storage capability (from approximately 109 to 64, 75, and 57 kPa, noting that energy storage in the DTA is likely less than that in the SAA due to its lower in vivo axial stretch). Mean circumferential wall stress ${\sigma }_{\theta }$ follows a similar decreasing trend along the aorta (Table 1), though when normalized by the number of elastic lamellar units it becomes more comparable across these four segments (52–59 kPa per layer) consistent with an observation of Wolinsky and Glagov (1967) when comparing a single aortic segment across multiple mammalian species. This measure of Cauchy stress is often used to characterize the general mechanical environment of the arterial wall due to the ease and reliability of computation via the universal relation known as Laplace (${\sigma }_{\theta }=Pa/h$, where $P$ is transmural pressure, $a$ pressurized luminal radius, and $h$ pressurized wall thickness; Humphrey 2002). By contrast, note the low elastic energy storage in the muscular MA (~ 20 kPa) commensurate with its lower percent elastin (~ 21%) though relatively high media:adventitia ratio (62:38), which is due to a higher percentage of smooth muscle (33%). Not surprisingly, the MA exhibits higher vasoconstrictive capacity (~ 50% reduction in outer diameter in response to high K⁺ depolarization of cell membranes) when compared with the aorta (~ 10% diameter reduction). Whereas characteristics of the CCA and SMA tend to fall within these ranges, the proximal pulmonary artery shows distinct characteristics. Evaluated at a systolic pressure of 25 mmHg, the often-considered elastic RPA exhibits modest elastic energy storage (23 kPa) but marked vasoconstrictive capacity (~ 31% diameter reduction) over its lower pressure range. Indeed, biaxial stress and stiffness in the RPA tend to be closer to the MA than any segment of the aorta. While the reader is encouraged to peruse Table 1 for additional insights, note that the listed values for mean circumferential wall stress and the linearized circumferential material stiffness (cf. Baek et al. 2007) appear to be preferred values in maturity, that is, homeostatic targets (Wolinsky and Glagov 1967; Shadwick 1999), thus emphasizing that such targets are vessel specific.

Although not listed in Table 1, it similarly appears that flow-induced mean wall shear stress ${\tau }_w$ tends to assume target values in the adult that also differ from vessel-to-vessel and species-to-species (Greve et al. 2006; Cheng et al. 2007). Given a simple result for mean wall shear stress in a cylindrical tube under steady laminar flow (${\tau }_w=4\mu Q/\pi a^3$, where $\mu$ is viscosity, $Q$ volumetric flow rate, and $a$ the luminal radius for a Poiseuille flow; Humphrey 2002), consider a local perturbation in flow from a normal value ($Q_o$) given by $Q=\epsilon Q_o$ where $\epsilon$ is a fold-change. It is then easy to show that a homeostatic restoration of local wall shear stress toward normal in response to a perturbation in flow requires luminal radius to change according to the rule (Humphrey 2008b):

$$\mathrm{\Delta }{\tau }_w\approx 0\to \frac{4\mu \left(\epsilon Q_o\right)}{\pi a^3}-\frac{4\mu Q_o}{\pi a_o^3}\approx 0\to a\approx {\epsilon }^{1/3}{a}_o$$ 1

where $a_o$ represents the original local radius and $a$ its current value.

Based on empirical studies across species, Wolinsky and Glagov (1967) observed further that the thickness of the thoracic aortic wall tends to scale linearly with radius in maturity. Toward this end, recall the Laplace relation, ${\sigma }_{\theta }=Pa/h$, while noting that radius and thickness change with both pressure and vasoconstriction (i.e., $a=\widehat{a}\left(P,C\right)$ and $h=\widehat{h}\left(P,C\right)$ where $C$ is a measure of vasoconstrictive strength). Whereas acute increases in pressure tend to increase radius (due to intrinsic compliance) and decrease wall thickness (due to incompressibility), acute increases in actomyosin-mediated vasoconstriction tend to restore radius via wall shear stress regulation. Additionally, if a sustained perturbation in pressure from a normal value ($P_o$) is given by $P=\gamma P_o$, where $\gamma$ is a fold-change, then it is easy to show (while still ensuring that wall shear stress is restored) that a homeostatic restoration of mean circumferential stress toward normal in response to a perturbation in pressure requires wall thickness to follow the rule (Humphrey 2008b)

$$\mathrm{\Delta }{\sigma }_{\theta }\approx 0\to \frac{\left(\gamma P_o\right)a}{h}-\frac{P_o{a}_o}{h_o}\approx 0\to h\approx \gamma {\epsilon }^{1/3}{h}_o$$ 2

where $h_o$ represents the original thickness and $h$ its current value.

Whereas these two results tacitly assume that multiple cell types (e.g., endothelial cells for flow-induced stress and both smooth muscle cells (SMCs) and fibroblasts (FBs) for pressure-induced stresses) accurately sense their local mechanical environment for the response to be homeostatic, mechanosensing need not be accurate in cases of aging, particular pathogenic variants, or disease (cf. Li et al. 2023). Rather, it proves useful to generalize the above considerations and consider possible degrees of reduced mechanosensing whereby

$$\mathrm{\Delta }{\sigma }_{\theta }=\frac{\left(1-\delta \right){\sigma }_{\theta }-{\sigma }_{\theta }^o}{{\sigma }_{\theta }^o},\mathrm{\Delta }{\tau }_w=\frac{\left(1-\xi \right){\tau }_w-{\tau }_w^o}{{\tau }_w^o},$$ 3

with parameters $\delta \in \left[0,1\right]$ and $\xi \in \left[0,1\right]$ defining how well a cell senses its local mechanical environment—parameter values of zero indicate perfect mechanosensing, as in homeostasis, whereas values of unity indicate a complete loss of mechanosensing, which would signify a loss of mechanical homeostasis that would drive disease progression (Humphrey and Schwartz 2021). That is, from the perspective of a cell, it is the sensed state of stress (not the actual state of stress) plus its sensitivity to the perceived difference in stress from a set-point value that governs its responses to changes in local pressure and flow, typically resulting in differential gene expression and associated gene products. Compromised or lost mechanical homeostasis can thus result from dysfunctional mechanosensing as well as reduced mechanosensitivity or responsiveness to a perturbation, including altered intracellular-mediated functions such as actomyosin induced pre-stretch when new extracellular matrix (ECM) is deposited within extant matrix and extracellular-mediated functions such as cross-linking of ECM. Hence, we see the importance of mechanobiology, which can be defined as the study of biological responses of cells to changes in mechanical environment. Of course, the actual state of stress is yet critical in determining possible failure – as in aneurysms, dissections, and ruptures—and stress must always satisfy the equations of mechanics such as balance of momentum and energy, hence the equal importance of the mechanics. Finally, note that dividing each difference term in Eq. (3) by a homeostatic value of stress not only non-dimensionalizes the stress differences (i.e., deviations from set-point values), it also supports the concept that cells are most sensitive to deviations in relative, not absolute, values of stress.

Albeit less well studied, changes in the axial length and thus axial stress of a mature artery can similarly induce marked remodeling responses (Jackson et al. 2002; Gleason and Humphrey 2005a). Indeed, axial adaptations appear to be among the earliest and fastest responses even in cases of altered pressure and flow (Humphrey et al. 2009), noting that changes in length can affect luminal radius and wall thickness and thus wall shear stress ${\tau }_w$ as well as mean circumferential (${\sigma }_{\theta }={\widehat{\sigma }}_{\theta }\left({\lambda }_{\theta },{\lambda }_z\right)$) and axial (${\sigma }_z={\widehat{\sigma }}_z\left({\lambda }_{\theta },{\lambda }_z\right)$) stress, which depend constitutively on circumferential (${\lambda }_{\theta }$) and axial (${\lambda }_z$) stretch (assuming ${\lambda }_r=1/{\lambda }_{\theta }{\lambda }_z$ by incompressibility). It can thus be useful to consider cases of mechanical homeostasis wherein $\mathrm{\Delta }\sigma \to 0$ with $\sigma ={\sigma }_{\theta }+{\sigma }_z$ (assuming ${\sigma }_r\ll {\sigma }_{\theta },{\sigma }_z$) the first invariant of the in-plane (2-D) Cauchy stress (Humphrey 2021). Noting that the degree of in vivo axial stretch in maturity appears to arise during somatic growth (Dobrin et al. 1975), comparisons across multiple mammalian species reveal further that the degree of axial stretch (or retraction when transected) also depends strongly on the ratio of elastin-to-collagen, which in turn appears to correlate with heart rate (Humphrey et al. 2009). That is, mammals with higher heart rates (e.g., mice which have HR ~ 600 beats per minute vs humans with HR ~ 60 bpm) tend to have higher percentages of mural elastin and higher values of in vivo axial stretch for a given elastic artery. Again, therefore, we are reminded of the importance of biaxial wall mechanics.

Given that homeostasis is a ubiquitous biological or physiological process by which key variables are regulated to remain near set-point values, this process is necessarily achieved via negative feedback (Langille 1993; Humphrey et al. 2014). Here, consider the tissue scale that is important physiologically and clinically. Although one can think of arterial homeostasis within the context of theories of mechanobiological equilibrium and mechanobiological stability (Cyron and Humphrey 2014; Latorre and Humphrey 2019), it is critical to remember that this is a “dynamic equilibrium” in that most constituents of the ECM and multiple types of cells turn over continuously, even if slowly in health and in maturity; hence the so-called stasis is achieved via a delicate balance between production (matrix deposition, cell division) and removal (matrix degradation, cell death) within an unchanging mechanical configuration (Humphrey and Rajagopal 2002). Homeostatic responses can similarly proceed in changing configurations that ultimately stabilize, often at a new geometry and with a composition that yet preserves homeostatic targets, as, for example, for flow- and pressure-induced stresses (cf. Eqs.  1 and 2).

Next consider, for conceptual not computational purposes, a theoretical approach that incorporates basic ideas of mechanical homeostasis within a framework of evolving arterial mechanics. Given that biaxial stress and material stiffness can be derived directly from a stored energy function $W$ (i.e., a scalar function that depends on deformations experienced by a material that exhibits an elastic response), it proves useful to consider a simple rule-of-mixtures formulation whereby the energy stored in the arterial wall is calculated as the sum of the energies stored in separate families of structurally significant constituents. Denoting such constituents via index $\alpha =1,2,3,\dots ,N$ (e.g., $\alpha =1$ can represent elastic fibers, $\alpha =2$ can represent fibrillar collagens, and so forth), the total energy $W\left(s\right)={\sum }_{\alpha =1}^N{W}^{\alpha }\left(s\right)$ at any growth (change in mass) and remodeling (change in microstructure) time $s$ can be computed given potentially evolving constituent-specific stored energy functions (Humphrey 2021), namely

$$\rho \left(s\right)W^{\alpha }\left(s\right)={\rho }^{\alpha }\left(0\right)Q^{\alpha }\left(s\right){\widehat{W}}^{\alpha }\left({\mathbf{C}}_{n\left(0\right)}^{\alpha }\left(s\right)\right)+{\int }_0^s{m}^{\alpha }\left(\tau \right)q^{\alpha }\left(s,\tau \right){\widehat{W}}^{\alpha }\left({\mathbf{C}}_{n\left(\tau \right)}^{\alpha }\left(s\right)\right)\text{d}\tau$$ 4

where $\rho \left(s\right)={\sum }_{\alpha =1}^N{\rho }^{\alpha }\left(s\right)$ is the overall mixture (tissue) mass density at growth and remodeling (G&R) time $s$ and ${\rho }^{\alpha }$ are constituent-specific apparent mass densities (i.e., mass of constituent $\alpha$ per mixture volume), with constituent-specific mass fractions defined by ${\varphi }^{\alpha }\left(s\right)={\rho }^{\alpha }\left(s\right)/\rho \left(s\right)$. It is often assumed that $\rho \left(s\right)=\rho \left(0\right)$ given the high level of hydration of an artery in vivo. Note that constituent-specific mass-averaged stored energy functions ${\widehat{W}}^{\alpha }$ depend on constituent-specific deformations ${\mathbf{C}}_{n\left(\tau \right)}^{\alpha }\left(s\right)$ (right Cauchy-Green tensor) at G&R time $s$ that are computed relative to the natural configuration $n\left(\tau \right)$ at which that constituent was produced and deposited within extant tissue at G&R time $\tau \in \left[0,s\right]$. As desired, Eq. (4) recovers the special case of a simple rule-of-mixtures both in the absence of a perturbation from normal and in the case of constant turnover in an unchanging configuration (Humphrey 2021).

This theoretical framework reveals the need for two additional classes of constituent-specific constitutive relations: one for rates of mass density production $m^{\alpha }\left(\tau \right)>0$ and one for survival functions $q^{\alpha }\left(s,\tau \right)\in \left[0,1\right]$ where it is often convenient to let $Q^{\alpha }\left(s\right)=q^{\alpha }\left(s,0\right)$. Survival can be used to track a constituent-specific half-life, which can depend on multiple factors including the mechanical state (e.g., degradation of collagen depends on the state of stress at the time of enzymatic insult; Bhole et al. 2009). Consistent with prior work, the following functional forms for production and survival have proven useful in describing mechano-regulated G&R in the healthy adult mouse aorta (Humphrey 2021):

$$m^{\alpha }\left(\tau \right)=m_o^{\alpha }\left(1+K_{\sigma }^{\alpha }\mathrm{\Delta }\sigma -K_{{\tau }_w}^{\alpha }\mathrm{\Delta }{\tau }_w\right),$$ 5

$$q^{\alpha }\left(s,\tau \right)=exp\left(-{\int }_{\tau }^s{k}_o^{\alpha }\left(1+\omega \mathrm{\Delta }{\sigma }^2\left(t\right)+\dots \right)dt\right)$$ 6

where $m_o^{\alpha }$ are basal mass density production rates, $K_x^{\alpha }$ and $\omega$ are gain-type mechanosensitivity parameters that account for how sensitive a cell is to a perceived deviation in stress (either $\mathrm{\Delta }\sigma$ or $\mathrm{\Delta }{\tau }_w$, or both) from target values (recall Eq. 3 above), and $k_o^{\alpha }$ are basal rate parameters that capture removal, noting that $m_o^{\alpha }={\rho }_o^{\alpha }{k}_o^{\alpha }$ for each constituent $\alpha$ that turns over in the homeostatic state (accounting for the delicate balance between rates of production and rates of removal). Studying the changing transcriptional profile provides important information on possible production rates. Early studies of the kinetics of matrix degradation suggested that first-order rate-type kinetics appears to describe such processes (Tilahun et al. 2023), which motivated the general exponential decay form in Eq. (6). Finally, note that Eqs. (5) and (6) reflect a type of “proportional controller” consistent with the concept of homeostasis, namely, that regulated quantities tend to be restored close to but not exactly to original set-points.

We conclude from this brief summary that it can be useful to calculate at least mean values of the three primary stresses that act on the wall—flow-induced wall shear stress, pressure-induced circumferential stress, and axial load-induced axial stress—and to determine region- and species-specific homeostatic values in the healthy adult, deviations from which can elicit either adaptive or maladaptive responses that can be understood within the context of negative or positive feedback, respectively, while satisfying fundamental equations for the arterial mechanics. Importantly, immune cells often play complex roles in arterial G&R (Bersi et al. 2017; Spronk et al., 2021; Latorre et al. 2021), both pro-healing and pro-inflammatory, which merit increased attention within the context of development, as discussed briefly below. We return here, however, to the fundamental question: When do homeostatic rates of cell and matrix turnover and homeostatic values of mechanical metrics emerge during the developmental program? Related to this, one might also ask: How well can a cell mechano-sense its environment, how mechanosensitive is it to perturbations from normal, and what are the bounds on possible rates of cell and ECM turnover? Let us now consider arterial development with these key points in mind.

Prenatal development

The overall morphology of the vascular tree is initiated via a plexus of endothelial tubes that arise during early prenatal development, prior to the first heartbeat and thus prior to initiation of hemodynamic loading via blood pressure and flow (Table S1). Genetic programming thus plays a fundamental role in this regard. Similarly, the functional lamellar units that characterize the medial layer of an adult elastic artery, which differ in number from species-to-species and with location along the arterial tree, are individually set during the perinatal period, before local blood pressure and flow reach mature values (Table S2), suggesting that aspects of mural structure are also genetically predetermined or preadapted in some regard (Davis 1995). The same may be true for some of the postnatal deposition of adventitial collagen (Majesky and Weiser-Evans 2022), which serves as a sheath that engages and protects the underlying media primarily under conditions of supraphysiological loads (Bellini et al. 2014) but appears to form as part of a normal developmental program (Murtada et al. 2021). Clearly, genetics plays multiple fundamental roles in establishing functional vessels from early prenatal to late postnatal periods.

Yet, early development of the vascular tree, including establishment of the final hierarchical network morphology and regional differences in luminal caliber, wall composition, and wall thickness, is also driven by developmental changes in hemodynamics, or, based on additional observations and calculations, driven by changes in flow-induced wall shear stresses and possibly pressure-induced intramural stresses (Taber 2001; Jones 2011). This observation should not be surprising because all normal primary vascular cells—endothelial cells of the intimal layer, SMCs of the medial layer, and FBs and tissue-resident macrophages (tMΦs) of the adventitial layer—are exquisitely sensitive to changes in their mechanical environment (Haga et al. 2007; Chiquet et al. 2009; Yamashiro and Yanagisawa 2020; Davis et al. 2023), often defined in terms of stresses or strains even though it is unlikely that cells actually sense these continuum quantities directly (Humphrey 2001). These fundamental mechanical metrics nevertheless remain convenient and suitable for correlating with transcriptional changes and modeling mechanobiological processes as implied above (Humphrey 2021).

It appears, therefore, that morpho-genetics and morpho-mechanics work together to establish, maintain, and, when necessary, remodel the vasculature during prenatal development (Jones et al. 2006; Culver and Dickinson 2010; Garcia and Larina 2014). As a key case in point, the earliest vascular network (capillary plexus) covers the yolk sac with nearly uniform diameter, randomly oriented, interconnected vessels. Following initiation of viscous blood flow (with erythroblasts), the characteristic branched vascular tree begins to emerge via expansion, extension, or regression of the initial vessels. This process has been thought since at least the early twentieth century (Chapman 1918) to be mediated by locally increased and decreased flows (Jones et al. 2006). A common way to test such a hypothesis is to perturb the prenatal hemodynamics and assess changes in morphology, if any. Using a clever manipulation of blood viscosity in the embryo, Lucitti et al. (2007) showed that “changes in the viscosity of blood, which alters the physical force [wall shear stress] exerted by the blood, are sufficient to induce vascular remodeling and to trigger signaling cascades within endothelial cells in the embryonic mouse yolk sac.”

Using concepts of optimization to examine effects of blood volume and flow, Murray derived multiple fundamental relationships in 1926, including $d^3=d_1^3+d_2^3$, where $d$ is luminal diameter of a parent vessel and $d_1$ and $d_2$ are luminal diameters of the daughter branches at a vascular bifurcation. A companion relation suggested that the ratio of volumetric flowrate to luminal radius cubed ($Q/a^3$) tends to remain constant within individual segments of the vasculature, which suggests mechanoregulation of mean wall shear stress (recall ${\tau }_w=\left(4\mu /\pi \right)(Q/a^3$)) as noted in Eq. (5). Murray’s basic relation holds reasonably well at many bifurcations within the adult vasculature and similarly at days 2–4 of a 21-day incubation period in the chick embryo (e.g., Taber et al. 2001), consistent with a mechano-specified or mechano-adaptive capability during prenatal development. Indeed, these authors suggested that “blood vessels follow the same basic morphogenetic rules throughout life.”

Lucitti et al. (2005) used left atrial ligation or right vitelline artery ligation in the chick embryo at ~ 3.5 days of incubation (HH stage 21) to alter hemodynamic loading and found compensatory changes in ventricular-vascular coupling over the study duration (to HH stage 27). Arterial pressure was preserved via reductions in stroke volume and cardiac output as well as via increased arterial stiffness and total peripheral resistance. A subsequent study revealed further that vitelline artery ligation at HH21 increased dorsal artery stiffness (measured via pulse wave velocity), with associated changes in smooth muscle-alpha actin (SMαA) staining as well as increased intramural collagen I and III (Lucitti et al. 2006). Hence, hemodynamic loads influence both vascular geometry and mechanical properties. A similar study by another group found altered ECM deposition in the dorsal aorta of the embryonic chick in response to altered hemodynamics—an induced decrease in flow via a right vitelline vein ligation at HH18 reduced diameter to maintain flow-induced wall shear stress at a nearly constant value, ~ 3 Pa, over the period of study from HH28 to HH36 (Espinosa et al. 2018a). Importantly, these authors reported differential gene expression (including for Et1, Klf2, Mmp9, and Tgfb2 that preceded changes in expression for Eln and Lox) that manifested as changes in ECM proteins (decreased elastin and increased collagen) while cell number appeared unaffected. They suggested that “the adaptive response to a decrease in DA [dorsal aorta] flow succeeds in temporarily regulating shear stress, but at the cost of long-term arterial stiffening and further decreases in flow.” Hence, changes in both blood pressure and blood flow can alter normal developmental patterns of gene expression and the associated vascular composition, properties, and geometry during prenatal development. Similar alterations in hemodynamics affect cardiac development, with adverse hemodynamics contributing to morphological defects that are counted among common congenital heart defects (e.g., Taber 2001; Hoog et al. 2018; Keller et al. 2020).

Responses to altered hemodynamics must be compared to normal developmental changes and, fortunately, multiple papers report changes in geometry, composition, and gene expression of the healthy prenatal thoracic aorta, often in rats but more recently in mice. Using electron microscopy, Nakamura (1988) presented revealing information on the prenatal evolution of mural composition of the DTA in the rat (Table S3). In particular, wall composition (percent elastin, collagen, and cells) was contrasted at embryonic days E12–E13, E13–E16, E17–E19, and E20–E21, noting that the normal gestational period is 21–23 days in the rat. Cells represented the highest percentage (from 78 to 64%) from E12 to E21, with elastin increasing from 0.03% to 6.4% but collagen remaining similar (< 1%) over this period. The remaining extracellular material was denoted “other” and likely represented glycosaminoglycans (GAGs), which increased from 21 to 29% during this same fetal period. In landmark studies, Mecham and colleagues (Kelleher et al. 2004; McLean et al. 2005) reported gene expression and transmission electron microscopic images of the mouse thoracic aorta at embryonic days E12, E14, E16, and E18; additional transcriptional information was similarly provided for postnatal ages (see below). Focusing on the ECM, transcripts for Bgn, Col1a1, Col3a1, Col6a1, Dcn, Eln, Fbn1, and Tnc, among others, tended to increase from E12 to E18 while that for Fbn2 tended to decrease. Notwithstanding the critical importance of prenatal development, we focus on postnatal development below.

Postnatal development and maturation

Recalling findings of Nakamura (1988) for the prenatal rat aorta, Gerrity and Cliff (1975) reported a similar 65% cellular composition in the medial layer of the rat DTA at birth, though with higher elastin (13%) and lower other constituents (19%), including particularly low collagen (3%). They reported that the percentage of elastin increases to 35% by 8 weeks of age (occupying 50% of the medial layer) while that for collagen increases to 30% of the wall with cells accounting for most of the remaining 35% though with low levels of GAGs as well (Table S4). GAGs nevertheless play important roles in both mechanobiology and mechanics in development, homeostasis, and disease (Wight 1989; Roccabianca et al. 2014; Koch et al. 2020). Elastin is critical to aortic function (Li et al. 1998), and effective elastogenesis requires finely orchestrated cell-mediated processes (Yanagisawa and Yokoyama 2021) that depend, in part, on coexpression of genes encoding elastin (Eln), fibrillin-1 (Fbn1), fibulins 4 and 5 (Efemp2 or Fbln4, Fbln5), latent TGFβ binding proteins (Ltbp1, Ltbp4), lysyl oxidase (Lox), and lysyl oxidase like 1 (Loxl1). Many different collagens contribute to the structure and function of the arterial wall (Osidak et al. 2015), including collagens I, III, and V (fibrillar), IV (network), VI (beaded filament forming), VIII (membrane), and XV and XVIII (multiplexins). Collagen fibrillogenesis (for types I, III, and V) also requires multiple partners, as, for example, assembly of collagen I fibers requires coexpression of genes for the type I alpha helices (Col1a1, Col1a2) as well as for binding partners including genes for fibronectin (Fn1), collagen V (Col5a1, Col5a2, Col5a3), biglycan (Bgn), decorin (Dcn), and lysyl oxidase (Lox).

Cell-driven deposition and organization of ECM require actomyosin activity, including RhoA signaling, as well as appropriate integrins (Li et al. 2003; Kadler et al. 2008). Whereas integrins αvβ3 and αvβ5 have strong binding affinities for elastin, elastin-associated glycoproteins, and multiplexins, integrins α1β1 and α2β1 have strong affinities for fibrillar collagens; note, too, that α5β1 has a strong affinity for fibronectin, which serves as an important scaffolding glycoprotein for the assembly of elastic and collagenous fibers (Wagenseil and Mecham 2007; Kadler et al. 2008), while SMC α8β1 has a strong affinity for fibronectin, vitronectin, tenasin, and osteopontin (Moiseeva et al., 2001). Although multiple cell types contribute to the diverse ECM that defines the arterial wall, SMCs and FBs play particularly important roles (with endothelial cells contributing to the intimal layer and tMΦ contributing to adventitial development). SMCs not only produce ECM, but their phenotype is influenced by the composition (ligand presentation) and compliance (mechanics) of the ECM, often referred to as reciprocity (Sazonova et al. 2015). Given the broad phenotypic spectrum exhibited by SMCs (including synthetic, contractile, and degradative; Li et al. 2020), it is useful to note that markers identifying SMCs change with development—from SMαA early on, to SM-22α, caldesmon, calponin, smoothlin, and finally smooth muscle myosin heavy chain (SM-MHC) in maturity (Zalewski et al., 2002).

Importantly, Gerrity and Cliff (1975) delineated elastic fibers organized within laminae and those forming interlamellar and intralamellar structures (which they called branch elastic fibers). Whereas elastic laminae form early in the aorta, mainly by 4 weeks of age in rats and mice, branch elastin begins to form 2 weeks after birth and continues to increase up to 12 weeks of age. Among other functions, intralamellar elastic fibers and microfibrils (largely fibrillin-1) serve to connect the SMCs to elastic laminae (Davis 1993a), thus allowing mechanosensing of wall stresses therein via multiple integrins (Moiseeva 2001; Rupp and Little 2001). Given that the wall of a pressurized artery experiences a compressive radial stress, the low levels of GAGs in the mature vessel wall likely provide sufficient local Gibbs-Donnan swelling to put the intralamellar connections in tension as required for mechanosensing tensile stresses in the lamellar structures (Roccabianca et al. 2014).

Gerrity and Cliff (1975) suggested that “the increase in collagen [during postnatal development] directly parallels the increase in tangential tension,” a concept consistent with that of Wolinsky and Glagov (1967) that derived from comparisons of mature aortas across species. Gerrity and Cliff further observed that wall tension, aortic geometry, and body mass tend to increase sigmoidally during postnatal development (~ P0–P84), with rapid development from birth to 4 weeks of age followed by a period of maturation from 4 to 8 weeks of age at which time values tend to reach an apparent steady state, which we assume to be homeostatic in health (Murtada et al. 2021). The near sigmoidal increase in branch elastin from 2 to 12 weeks also appears to reflect that of the temporal increase in wall tension / stress. Indeed, it has been reported that there is “a marked increase in connections of [a smooth] muscle cell to elastic lamellae in hypertension” consistent with the concept of mechanical adaptation (Bezie et al. 1998).

Davis (1993a, 1995) reported detailed microscopic findings of the elastic laminae in developing C57BL/6 mice from E15 to P120. She reported that cells recruited from the mesenchyme differentiated into the SMCs that produced both elastin and elastin-associated microfibrils. She confirmed in mice that the number of elastic laminae is determined early in development (well before wall stresses reach mature levels) and that the aorta can double its diameter after the laminae are formed completely. Based on modeling, Rego et al. (2024) suggested further that the elastic laminae become compacted during this developmental period. A complementary study showed that desmosine (indicative of elastin cross-links) increases sigmoidally from P3 through P21, with near-steady-state values thereafter in C57BL/6 mice (Cheng et al. 2013). Combined with the recognition that aortic elastic fibers have an extremely long half-life (decades; Davis 1993b), these observations suggest that fully formed elastic laminae are prestretched / prestressed beyond deposition values due to somatic growth during the latter half of postnatal development. This expectation explains, in part, the existence of residual stresses in an adult elastic artery (Cardamone et al. 2009) and is confirmed by the increase in diameter and length that is observed when an unloaded elastic artery is exposed to elastase (Ferruzzi et al. 2011). Similar to the suggestion of Gerrity and Cliff (1975) regarding stress-mediated deposition of collagen fibers, Davis (1995) suggested that “After birth, elastin accumulates rapidly in the aorta as a response to the changing hemodynamic stresses…”.

Clark and Glagov (1979) reported evolving changes in the aorta in rabbits from birth through one year of age. They observed two distinct patterns of organized intra-lamellar ECM emerging during postnatal development: first, intra-lamellar basal laminae with associated collagen fibrils that formed “continuous sleeves over cell groups and appeared to bind groups of cells together” and, second, coalescing elastic fibers that formed branching systems, as observed by Gerrity and Cliff (1975). Regarding the latter, they wrote “as medial tension increased with age and aortic diameter, and small intercellular elastic tissue islands merged to form well developed fiber systems, the growing media made a gradual transition from a predominantly diffuse, basal laminar-fibrillar mode of cohesion to a system that increasingly included tenacious, focal, dense body to elastin attachments.” Their term tenacious was motivated by the observation in hyperdistended vessels of “tears and breaks across cell projections near cell to elastic fiber junctions” without disruptions to the actual cell-to-elastic fiber attachments. Indeed, a recent report in a loss-of-function Tgfbr1r2^ismko mouse model similarly reported tenacious cell-to-elastic fiber connections in aortas that otherwise dissected—namely, some cells appeared to remain connected to the intra-lamellar elastic fibers while being pulled apart as lamellae separated (Jiang et al. 2025). Based on bulk RNA-seq, it was suggested that the dissection may have resulted in part from decreased Col15a1 and Col18a1, which are part of the pericellular matrix / cellular basal lamina.

As noted earlier, Mecham and colleagues (Kelleher et al. 2004; McLean et al. 2005) used microarray technology to quantify transcriptional changes within the mouse aorta from E12 to P180. They reported four general classes of time-courses in ECM gene expression: (i) a pattern characterized by increases in expression from E14 to ~ P7–P14 followed by decreases to lower steady state values in maturity, (ii) a pattern of consistent expression throughout the period studied, (iii) a pattern of high expression in the embryonic-fetal period followed by decreased expression, and (iv) low expression throughout development followed by high expression in maturity. In particular, production of ECM constituents such as fibrillins, elastin, and collagens fell within the first group—increasing during the late fetal period and into the early postnatal period, then peaking within the first three weeks following birth only to decrease to much lower values in maturity. More recently, Weiss et al. (2024) used bulk RNA-sequencing and extended this classification to include six patterns, including the four reported by Mecham and colleagues, with sigmoidal changes within multiple classes. Figure 1 shows a few of the results from this study, emphasizing transcripts involved in cellular proliferation and migration (Pcna and Vcan, which are high at birth and decrease monotonically thereafter), matrix synthesis and cross-linking (Eln and Lox, Col1a1 and Col3a1, typically peaking from P7 to P21), and SMC contractility (Acta2 and Myh11, increasing monotonically to steady state mature values). In agreement with the suggestion of Mecham and colleagues, it is emphasized that the primary role of SMCs in the aorta is to establish, maintain, and remodel the ECM of the media, not vasoconstrictive capacity (cf. Table 1). SMC contractile activity is yet a central component of mechanosensing and mechanoregulating (e.g., prestretching and aligning) the ECM. That the expression of both branch elastic fibers and SM-MHC (encoded by Myh11) increases after P14 may hint further to an increasing need to sense and respond to (perhaps via evolving mechanosensitivity) the sigmoidally increasing mechanical stresses within the developing aortic wall.

Fig. 1.

Illustrative time-course changes in expression of 8 select genes in the descending thoracic aorta (DTA) of male WT mice during development from postnatal day P2 to P84: Pcna (proliferating cell nuclear antigen), Vcan (versican), Eln (elastin), Lox (lysyl oxidase), Col1a1 (collagen I alpha helix 1), Col3a1 (collagen III alpha helix 1), Acta2 (smooth muscle alpha actin), and Myh11 (smooth muscle myosin heavy chain). The first column hints at early proliferation and potential for migration through a more permissive viscoelastic matrix; the second column suggests early elastic fiber formation consistent with the appearance of elastic laminae; the third column suggests that collagen fibers form in large numbers soon thereafter; the fourth column suggests increasing smooth muscle alpha-actin with delayed increases in smooth muscle myosin heavy chain as the vessel matures. Importantly, SMCs not only endow the wall with vasoconstrictive capacity, they use actomyosin activity to mechano-sense and mechano-regulate the ECM that they synthesize and deposit within the medial layer. Data are from Weiss et al. (2024), which report time-course changes in many additional transcripts

Transcription need not indicate translation, but for purposes of mathematical modeling there tends to be a good correlation between gene expression for intracellular and extracellular proteins and actual synthesis (i.e., production). By contrast, changes in proteolytic activity involved in the degradation of ECM (i.e., removal) need not track transcriptional changes for multiple reasons. First, matrix metalloproteinases (MMPs) are secreted into the extracellular space in latent pro-forms, which require subsequent activation via different mechanisms, including by other proteases (e.g., serine proteases such as plasmin) as well as changes in mechanical stress. It has been shown, however, that comparing histologically measured rates of accumulation of ECM against measured rates of synthetic transcriptional activity can help to determine appropriate removal functions that are needed for modeling (Rego et al. 2024; Schwarz et al. 2025). For example, the rate of change of a structural constituent ($\text{d}{A}^{\alpha }/ds$, where $A^{\alpha }$ is a histologically measured area occupied by constituent $\alpha$ at G&R time $s$) can be written as the difference between the rates of production (related to transcripts) and removal, the latter of which can be inferred from this simple relationship. Data for a normally developing DTA showed an exponentially decreasing rate of removal of fibrillar collagens, suggesting rapid turnover during early periods of rapid growth that slow to low basal levels in maturity (Rego et al. 2024), noting that the normal half-life of aortic collagen in maturity has been measured at 60–90 days (Humphrey 2002). Combining a similar approach with the concept of little-to-no removal of elastic fibers due to their long half-life (~ 50 years) led to the aforementioned suggestion that elastic laminae are compacted following deposition during the postnatal period (Rego et al. 2024).

To complement transcriptional and histological information, one also needs detailed information on the evolving biomechanical properties and geometry of the vessels. Although numerous studies are available in the rat aorta (e.g., Berry et al. 1972; Gerrity and Cliff 1975; Olivetti et al. 1980), considerable data are accumulating for the mouse aorta. Huang et al. (2006) compared changes in mechanical and geometric metrics for the thoracic and abdominal aorta in WT mice from P1.5 to P30. They reported a sigmoidal decrease in circumferential stretch that reached a steady state value by ~ P14 but a sigmoidal increase in circumferential stress that began to increase after ~ P14; whereas the stretches tended to be similar in the thoracic and abdominal aorta at all ages considered (which some suggest implies a homeostatic target, though such strains tend to decrease in many responses to altered loading in maturity), the stresses were similar along the aorta only until P3, after which they were higher in proximal relative to distal segments (cf. Table 1). Le et al. (2011) reported monotonic increases in unloaded outer diameter and wall thickness in the ATA following excision in C57BL/6 J WT mice at P3, P7, P14, P21, P30, and P60. They also reported monotonic changes in systolic blood pressure, from ~ 33 mmHg at P3 to 111 mmHg at P60 (cf. Table S2). In contrast to the report of Huang et al. (2006), Le and colleagues reported nonmonotonic changes in circumferential wall stretch at systolic pressure (lowest at P14–P21) though a sigmoidal increase in circumferential wall stress (values reaching ~ 150–219 kPa). These and related metrics for the thoracic aorta have been used from P3 to P30 for modeling (Wagenseil 2011) using a reduced form of a constrained mixture model (Gleason and Humphrey 2005b). Of note, flow-induced wall shear stress was suggested to peak at ~ P12, with the values at P3 and P30 nearly identical and presumably homeostatic, perhaps extending from the prenatal period.

Collecting geometric and mechanical data at E18.5, P2, P10, P21, P42, and P98, Murtada et al. (2021) reported time-course changes in histology, mechanical properties, and geometry in the DTA in male C57BL/6 J WT mice (Table S5). These time-course data were fit with continuous functions that allowed computation of ages at which rates of change were maximal or at which there were local maxima or minima. Referring to Fig. 2, mean arterial pressure, volumetric flow rate, and thorax length all increased monotonically, with maximum rates of change at P14.4, P15.2, and P14.4, respectively. Circumferential and axial wall stresses and material stiffnesses (not shown) increased nearly sigmoidally when calculated at the evolving mean arterial pressure, with maximum rates of change of biaxial stress at ~ P22–P25 (when transcriptional activity for fibrillar collagens peaked; Weiss et al. 2024) and biaxial stiffness from P15 (axial) to P29 (circumferential). Not only did the axial stress and stiffness initially increase at a higher rate, both experienced maximal values around P42 followed by slight decreases to mature values. Overall, it appeared that the DTA matured biomechanically by ~ P56. Similar to the report by Wagenseil (2011), flow-induced wall shear stress peaked early, at ~ P12.9, with values at P2 and P98 similar at ~ 5 Pa. Interestingly, the age of the peak in shear stress corresponded well with the age at which smooth muscle contractility was lowest (P12.2), with the rate of medial collagen production correlating inversely with smooth muscle contractility—that is, low synthetic activity when contractility was high and high synthetic activity when contractility was low. Recall from above that transcriptional expression of elastin peaked at ~ P11. These findings suggest a dynamic phenotypic modulation of contractile-synthetic-contractile activity by the aortic SMCs, noting that early vasoconstriction is against a low distending pressure whereas later vasoconstriction is against a higher distending pressure typically associated with mature arteries (~ 93 mmHg mean pressure in the aorta).

Fig. 2.

Time-course changes in applied loads (left), geometry (middle), and associated Cauchy stress (right) in the descending thoracic aorta (DTA) of male WT mice from embryonic day E18.5 well into maturity at P98. Note that the maximum rate of increase in the driving loads (~ P12–P15 for pressure, flow, somatic growth) occurs approximately one week before the maximum rate of increase of the intramural stresses (~ P22–P25). Data from Murtada et al. (2021). When comparing results from Figs. 1 and 2, note that the peak of elastin transcriptional activity (Eln) occurs just before the maximum rate of change in applied loads whereas the peak of collagen I and III transcriptional activity (Col1a1, Col3a1) occurs after the maximum rate of change in applied loads, closer to the age of maximal rate of change of wall stress

Finally, although our focus is primarily on mechanobiological processes, immunobiological processes also play important roles during development and maturation. Under normal conditions, ~ 90% of immune cells within the aortic wall in mice are macrophages (Weinberger et al. 2020). Whereas macrophages have long been known to be among the first responders to pathological insults and injuries, it has become evident that these cells also play critical roles in development, homeostasis, and adaptation (Ginhoux and Jung 2014; Okabe and Medzhitov 2016). Toward this end, it is useful to distinguish two types of macrophages: tissue resident macrophages (tMΦ, often denoted as LYVE-1 positive), that derive primarily from the yolk sac and fetal liver, and recruited macrophages (rMΦ, which are CCR2 positive) that derive primarily from the bone marrow. The tMΦs initially emerge from the yolk sac at ~ E8.5 in the mouse (just after the heart begins to beat) and begin to take up residence by E9 to E12 within the aortic wall, mainly in the adventitia (Weinberger et al. 2020). Additional tMΦs arise from the fetal liver after E11 (Ginhoux and Jung 2014). It has been suggested that tMΦ constitute ~ 80% of macrophages within the aortic wall in the perinatal period (P3), ~ 70% early in maturity (P56–P77), ~ 60% later in maturity (P112), and then 45 to 42% in aged mice (P315–P600). That is, tMΦs represent the majority of all macrophages in the normal aortic wall during postnatal development and early adulthood, only to yield their majority to rMΦ late in the healthy adult, noting that the total number of macrophages within the aortic wall increases ~ 3.7-fold from birth to adulthood (Weinberger et al. 2020).

Studies in mice revealed that absence of LYVE-1 positive tMΦs results in increased stiffening of the aorta during development, which was attributed to increases in Col1a1 and decreases in Eln, Mmp2, and Mmp3 in the media as well as increases in Col1a1 and Col3a1 and decreases in Mmp9 in the adventitia (Lim et al. 2018). That is, despite tMΦ residing primarily in the adventitia, and exhibiting strong paracrine interactions with the adventitial FBs (Zhou et al. 2018), these data suggest similar paracrine interactions with medial SMCs, thus extending their influence during development as well as during homeostasis in maturity. The authors suggested that normal Mmp9 expression by tMΦ serves as a negative regulator of excessive collagen accumulation in the adventitia (Lim et al. 2018). Indeed, the aortic wall has also been reported to be stiffer in both Mmp9^−/− (Flamant et al. 2007) and Mmp12^−/− (Spronck et al. 2022) mice. It is important in this regard that broad spectrum blocking of MMP activity (e.g., using doxycycline) can also have adverse effects on arterial wall remodeling by decreasing rates of collagen synthesis (Strauss et al. 1996), hence reminding us of the need to consider delicate balances between removal and production, with degradation products able to stimulate some production. Although CCR2 positive rMΦs play additional transient or chronic roles in cases of disease, injury, or pathogen invasion, we do not discuss this complex and important role of macrophages here.

Modeling development and maturation

An excellent review of vascular morpho-mechanics can be found elsewhere (Taber 2009). Consistent with a few studies (Wells et al. 1998; Taber 1998; Wagenseil 2011), Taber suggested that time-course changes in the values of key mechanical metrics can be captured during development and maturation by assuming that set-points evolve to mature values. Although such an assumption simplifies computations and can fit data, it is inconsistent with the concept of homeostasis, which necessarily focuses on responses to perturbations from an established (unchanging) state. Indeed, the developmental biologist C.D. Waddington (1905–1975) put it this way (Waddington 2022):

A developing system is, by definition, always changing in time, moving along some defined time trajectory, from an initial stage, such as a fertilized egg, through various larval stages to adulthood, and finally to senescence. The regulation that occurs in such systems is not a regulation back to an initial stable equilibrium, as in homeostasis, but to some future stretch of the time trajectory.

For this reason, Waddington introduced in 1957 the term homeorhesis, focusing on a similar flow rather than similar state. This “defined time trajectory” may be the genetic program. Regardless, it appears that homeostatic values are either preserved throughout development (e.g., mean wall shear stress) or they emerge following postnatal development (e.g., circumferential wall stress as in Fig. 2). Consistent with the latter, Gerrity and Cliff (1975) suggested that “This [observed] sigmoid type of growth curve is common to most biologic systems, and secures a rapid development of systems to form a homeostatic organism in as short a time as possible.” That is, they also recognized that tissue-level homeostatic targets do not evolve during development; rather, they emerge in maturity.

In agreement with these observations, and based on fundamental definitions, it is suggested here that there is a pressing need to couple effects of morpho-genetics and morpho-mechanics, which likely entails a feedback loop that works to establish the target composition, material properties, and geometry of the mature circulation while ensuring an efficient transition from the fetal circulation. Let us consider a few options for modeling development within the context of mathematical models of G&R. Again, it proves useful to start with the end in mind. A biomechanical theory of development should lead naturally to a theory of homeostasis, that is, general relations for development should yield those for maturity in the limit as the subject approaches adulthood (cf. Eqs.  4–6). Recall therefore that the governing equations of motion at any G&R time $s$ require that $div\mathbf{t}\cong 0$ (assuming that G&R is a slow process relative to the cardiac cycle) with the constitutive relation for the point-wise Cauchy stress tensor $\mathbf{t}$ given by $\left(det\mathbf{F}\right)\mathbf{t}=2\mathbf{F}\left(\partial W/\partial \mathbf{C}\right){\mathbf{F}}^T$ with $\mathbf{C}={\mathbf{F}}^{\mathit{T}}\mathbf{F}$ the point-wise right Cauchy-Green (deformation) tensor (Humphrey 2002). Assuming a constrained mixture, we have a point-wise stored energy density $W={\sum }_{\alpha =1}^N{W}^{\alpha }$ with tissue mass density $\rho ={\sum }_{\alpha =1}^N{\rho }^{\alpha }$, which together can account for contributions of $\alpha =1,2,\dots ,N$ individual structurally significant constituents.

Recalling the aforementioned constrained mixture approach that has proven useful for modeling adaptations and maladaptations in maturity (Humphrey 2021), which introduces constituent-specific constitutive functions for rates of mass density production ($m^{\alpha }\left(\tau \right)\ge 0$) and removal ($q^{\alpha }\left(s,\tau \right)\in \left[0,1\right]$), one could simply write Eq. (4) as the sum of Prenatal, Postnatal, and Mature periods:

$$\begin{array}{cc}\hfill \rho \left(s\right)W^{\alpha }\left(s\right)=& {\int }_{-\infty }^b{m}^{\alpha }\left(\tau \right)q^{\alpha }\left(s,\tau \right){\widehat{W}}^{\alpha }\left({\mathbf{C}}_{n\left(\tau \right)}^{\alpha }\left(s\right)\right)d\tau \hfill \\ \hfill & +{\int }_b^0{m}^{\alpha }\left(\tau \right)q^{\alpha }\left(s,\tau \right){\widehat{W}}^{\alpha }\left({\mathbf{C}}_{n\left(\tau \right)}^{\alpha }\left(s\right)\right)d\tau \hfill \\ \hfill & +{\int }_0^s{m}^{\alpha }\left(\tau \right)q^{\alpha }\left(s,\tau \right){\widehat{W}}^{\alpha }\left({\mathbf{C}}_{n\left(\tau \right)}^{\alpha }\left(s\right)\right)d\tau \hfill \end{array}$$ 7

to focus independently on the three primary phases of normal development to maturity (here we consider distant past times for the beginning of development, that the integration limit $b$ denotes time of birth, and the integration limit 0 denotes a time/age in maturity from which a perturbation from the normal baseline conditions occurs). Of course, to recover Eq. (4) for G&R within maturity, we let

$${\int }_{-\infty }^b{m}^{\alpha }\left(\tau \right)q^{\alpha }\left(s,\tau \right){\widehat{W}}^{\alpha }\left({\mathbf{C}}_{n\left(\tau \right)}^{\alpha }\left(s\right)\right)\text{d}\tau +{\int }_b^0{m}^{\alpha }\left(\tau \right)q^{\alpha }\left(s,\tau \right){\widehat{W}}^{\alpha }\left({\mathbf{C}}_{n\left(\tau \right)}^{\alpha }\left(s\right)\right)\text{d}\tau ={\rho }^{\alpha }\left(0\right)Q^{\alpha }\left(s\right){\widehat{W}}^{\alpha }\left({\mathbf{C}}_{n\left(0\right)}^{\alpha }\left(s\right)\right).$$ 8

In similar fashion, if we wish only to model postnatal development into maturity, then the partitioned equation could be written

$$\begin{array}{c}\rho \left(s\right)W^{\alpha }\left(s\right)={\rho }^{\alpha }\left(b\right)Q^{\alpha }\left(s\right){\widehat{W}}^{\alpha }\left({\mathbf{C}}_{n\left(b\right)}^{\alpha }\left(s\right)\right)+{\int }_b^0{m}^{\alpha }\left(\tau \right)q^{\alpha }\left(s,\tau \right){\widehat{W}}^{\alpha }\left({\mathbf{C}}_{n\left(\tau \right)}^{\alpha }\left(s\right)\right)\text{d}\tau \\ +{\int }_0^s{m}^{\alpha }\left(\tau \right)q^{\alpha }\left(s,\tau \right){\widehat{W}}^{\alpha }\left({\mathbf{C}}_{n\left(\tau \right)}^{\alpha }\left(s\right)\right)\text{d}\tau \\ \end{array}$$ 9

whereby one would need to measure certain key properties at birth and then focus on identifying separate constitutive relations for $m^{\alpha }\left(\tau \right)\ge 0$, $q^{\alpha }\left(s,\tau \right)\in \left[0,1\right]$, and ${\widehat{W}}^{\alpha }\left({\mathbf{C}}_{n\left(\tau \right)}^{\alpha }\left(s\right)\right)>0$ and determining values of the material parameters therein during periods of postnatal development (age b to 0) and maturity (0 to s). Critically important is the possibility that values of many of the parameters may evolve during development, reflecting changes in mechanosensing, mechanosensitivity, ECM maturation (e.g., via compaction, fibrillogenesis, cross-linking), and so forth. In summary, extensions of Eq. (4) to Eqs. (7) or (9) are natural and simply reveal the need to determine constituent-specific functions for productions, removals, and material properties during the desired periods: either for prenatal, postnatal, and maturity or for postnatal and maturity. As expected, theory tells us what to measure and why.

Transcriptional changes in genes associated with elastic fiber formation tend to correlate well with evolving changes in the ratio of systolic-to-diastolic wall stress during postnatal development while changes in genes associated with fibrillar collagen formation tend to correlate well with evolving changes in the rate of change of wall stress during this same period (Weiss et al. 2024). These findings suggest the need for new forms for $m^{\alpha }\left(\tau \right)$ and possibly $q^{\alpha }\left(s,\tau \right)$ for these structurally significant constituents during postnatal development (cf. Eqs.  5 or 6, which have only been tested in cases of adaptation or maladaptation in maturity). For example, one could include a phenomenological relationship between early elastic fiber formation and the ratio of systolic-to-diastolic wall stress ${\sigma }_{s/d}$ at early G&R times $\tau$ as

$$m_o^e\left(\tau \right)\propto K_{{\sigma }_{s/d}}^e\left(\tau \right){\sigma }_{s/d}\left(\mathrm{\tau }\right)$$ 10

where the gain-type mechanosensitivity to this “pulse stress” would tend to zero early in the postnatal period. Such a relationship would take advantage of the versatile form of the stimulus function and its ability to incorporate multiple contributors to mediate production and removal. While the form in Eq. (10) is purely illustrative, specific data-informed relationships between various biomechanical metrics (including stress, strain, and energy) and constituent turnover during the postnatal period merit further attention.

Alternatively, another approach for modeling postnatal development into maturity could simply use Eq. (4) with G&R time $s=0$ denoting birth rather than an early age in maturity. In this case, one would seek production $m^{\alpha }\left(\tau \right)$, removal $q^{\alpha }\left(s,\tau \right)$, and stored energy ${\widehat{W}}^{\alpha }\left({\mathbf{C}}_{n\left(\tau \right)}^{\alpha }\left(s\right)\right)$ functions that account for changes throughout the developmental period that asymptotically approach those in maturity. Noting that cell and ECM production and removal are each particularly high during early postnatal periods but decrease to low steady state values in maturity, one such approach could consider removal $q^{\alpha }\left(s,\tau \right)=exp\left(-{\int }_{\tau }^s{k}^{\alpha }\left(t\right)\text{d}t\right)$ where

$$k^{\alpha }\left(t\right)=\left(1+g^{\alpha }\left(t\right)\right)k_o^{\alpha }\left(1+\omega {\left(\mathrm{\Delta }\sigma \right)}^2+\dots \right)$$ 11

with

$$m^{\alpha }\left(\tau \right)=m_o^{\alpha }\left(\tau \right){\mathrm{{\rm Y}}}^{\alpha }\left(\tau \right)\text{and}{m}_o^{\alpha }\left(\tau \right)={\rho }^{\alpha }\left(\tau \right)k^{\alpha }\left(\tau \right),$$ 12

where $g^{\alpha }\left(t\right)\to 0$ as $t$ increases to mature ages is used to capture phenomenologically the high initial removal and production rates (largely determined genetically; Weiss et al. 2024) that, in the limit as age increases, reduce to homeostatic rates in maturity (e.g., $m_o^{\alpha }={\rho }_o^{\alpha }{k}_o^{\alpha }$ in maturity), where ${\mathrm{{\rm Y}}}^{\alpha }\left(\tau \right)$ is a constituent-specific chemo-mechanical stimulus function that can depend on, for example, differences in mechanical stress from homeostatic targets. In this way, the model for a developing artery can remain sensitive to external stimuli throughout the postnatal period without violating the concept of homeostasis in maturity. Example functions for $g^{\alpha }\left(t\right)$ include exponential decays (e.g., $g^{\alpha }\left(t\right)=a^{\alpha }{e}^{-b^{\alpha }t}$, where $a^{\alpha }$ and $b^{\alpha }$ are parameters) or gamma-type distributions (e.g., $g^{\alpha }\left(t\right)=t^{{\beta }^{\alpha }-1}{e}^{-t/{\theta }^{\alpha }}/\mathrm{\Gamma }\left({\beta }^{\alpha }\right){({\theta }^{\alpha })}^{\alpha }$, where $\mathrm{\Gamma }\left({\beta }^{\alpha }\right)$ is the Gamma function, with ${\beta }^{\alpha }>0$ controlling the shape of the function and ${\theta }^{\alpha }>0$ controlling the scale for each constituent $\alpha =1,2,\dots ,N$). The latter form proved useful, for example, in describing early inflammation-driven G&R in a tissue engineered vascular graft that developed in vivo into a neovessel in mice (Szafron et al. 2019).

Indeed, we recently showed that utilizing Eq. (4) where G&R time $s=0$ denotes birth with the exponential decay form of $g^{\alpha }\left(t\right)$ and including constituent-specific remodeling equations for the material parameters within the stored energy functions to account for postnatal compaction and maturation of elastic fibers and maturation of fibrillar collagens post-deposition yielded a G&R model of proximal pulmonary artery postnatal development and maturation that captured evolving changes in wall composition, material properties, and geometry as well as steady state values in maturity (Schwarz et al., 2026). Tacit to this study of pulmonary arteries was that homeostatic, or near-homeostatic, values of pressure- and flow-induced mechanical stresses held throughout postnatal development and into maturity. Knowing that this is not strictly true, the excellent fit to data using enhanced genetically-controlled productions and removals may have overshadowed possible attenuated mechanoregulation during early postnatal periods and/or exploited a lower mechanosensitivity during early postnatal development. The latter is expected based on the data from Gerrity and Cliff (1975) that reveals a delayed but increasing organization of intralamellar microfbrils / elastic fibers that are needed for mechanosensing by SMCs. While this phenomenological modeling approach may inform paths for modeling in aortic development, it is not clear if postnatal development of the aorta could be captured similarly unless multiple mechanical metrics are normalized with pressure.

Need and opportunity to study early disease progression

Notwithstanding the importance of understanding the mechanics and mechanobiology of normal arterial development, maturation, and homeostatic maintenance in maturity, there is also a pressing need to understand better both early- and late-onset disease progression. Obvious examples of early-onset conditions include congenital abnormalities such as aortic coarctation, patent ductus arteriosus, and pulmonary artery stenosis. Although it is beyond the current scope to review in detail the many related studies and future needs, we highlight four reports for illustrative purposes—one focused on ECM, one on intracellular signaling and associated gene products, one on nuclear integrity, and one on pharmacologic induction of disease-like changes. In each case, the measurements and/or manipulations appropriately included multiple ages during postnatal development; simply comparing results at juvenile versus adult ages does not provide enough information for understanding progression or for computational modeling of the G&R. Toward this end, mouse studies continue to provide significant insight given the ease of study from the postnatal period into maturity.

Competent elastin is critical both for efficient function of the aorta in maturity and for proper development (Li et al. 1998). Moreover, in laminar form, elastin can also provide a convenient computational reference in mixture models given its deposition and cross-linking by P21–P28. Elastin-null mice (Eln^−/−) are perinatal lethal, but elastin haploinsufficient mice (Eln^+/-) are viable. Cheng et al. (2013) used a fiber-based constitutive model to quantify and compare the mechanical behavior of the ascending aorta from WT and Eln^+/- mice at P3, P7, P14, P21, P30, and P60—that is, from the perinatal period to maturity. Among other differences, the aorta becomes stiffer in Eln^+/- mice relative to WT, with this increased stiffness correlating with elevated blood pressure. Among other findings, the authors emphasized the progressive transfer of pressure-induced circumferential stress from elastic fibers to collagen fibers in the developing Eln^+/- mice. See Wagenseil and Mecham (2007) and Espinosa et al. (2018b) for a more detailed discussion of the importance of elastic fibers.

Transforming growth factor-beta (TGFβ) signaling is critical for proper vascular development and homeostasis. Thus disruptions to associated ligands, receptors, or downstream signaling molecules can each cause significant arterial disease. Li et al. (2014) studied inducible smooth muscle-specific Tgfbr2 knock-out mice at multiple ages during postnatal development and maturity. They found that vulnerability to aortic dissection within 28 days of receptor disruption covaried with the age of disruption, namely, 77% dissection when disrupted at P21, 48% when disrupted at P28, 19% when disrupted at P42, 11% when disrupted at P63, and 0% when disrupted at P126. These data provide considerable insight into changes in TGFβ-driven matrix turnover at different ages among many other insights.

Hutchinson–Gilford Progeria Syndrome results from pathogenic variants in the gene (LMNA in humans, Lmna in mice) that encodes the nuclear scaffolding protein lamin-A. Among the many different manifestations of progeria, the thoracic aorta experiences premature structural stiffening (indicated by an increased pulse wave velocity) similar to that seen in extreme aging, which tends to manifest by sexual maturity in progeria mice. Murtada et al. (2023) quantified the evolving transcriptional profile and biomechanical phenotype of multiple systemic arteries in WT and Lmna^G609G/G609G progeria mice at P42 (~ age of sexual maturity, recalling that P56 is the age at which the aorta appears to be mature biomechanically; Murtada et al. 2021), P100, P120, P140, and P168 across five arterial segments, three elastic (ascending and descending thoracic aorta, common carotid artery) and two muscular (internal carotid artery and a mesenteric artery). Whereas the phenotype worsened progressively in the elastic arteries during late maturation and maturity, it did not worsen in the muscular arteries. Comparing results across ages and arterial sites suggested that the compromised nuclear envelope was unable to protect against mechanical damage to the nucleus when the mean circumferential stress exceeded ~ 80 kPa. These data are also consistent with a progressive accumulation of fibrillar collagens after ~ P14 in the normal aorta (Rego et al. 2024) to shield normal intramural cells (i.e., with a structurally normal nuclear envelope) from the sigmoidally increasing wall stresses (Murtada et al. 2021).

The lathyrogen β-aminopropionitrile (BAPN) inhibits lysyl oxidase and thus its cross-linking of newly synthesized elastic and collagenous fibers. BAPN has been used for many decades to study aortic dissection, now more relevant given the discovery that pathogenic variants in LOX (humans) / Lox (mice) predispose to aortic dissection (Lee et al. 2016). It has long been known that, for common periods of observation in mice (often 4 weeks or less), BAPN has dramatic detrimental effects on the aorta during early postnatal development but has markedly diminished effects in the mature aorta. Franklin et al. (2025) studied effects of genetic background, sex, age, and concentration of BAPN on the aortic phenotype in mice. Among other findings, they showed marked differences in percent survival when BAPN was started at P21 vs. P28, with no mortality when started at P182. These results appear consistent with the very different rates of deposition of intralamellar elastic fibers and turnover of fibrillar collagens from the early to later postnatal period to maturity (cf. Rego et al. 2024).

Again, these four examples are simply meant to be illustrative, emphasizing that disease presentation and progression can vary significantly by age when including the period of postnatal development, emphasizing again that there is a need to understand the normal developmental process in order to understand the effects of pathogenic variants, congenital defects, early-onset disease, and even early pharmacological and surgical interventions.

Conclusions

As emphasized throughout, a key open question in arterial mechanobiology and mechanics is: How do genetics and mechanics work together to establish, maintain, and remodel structure and function at different times during morphogenesis and homeostasis? Although we did not answer this question by introducing and testing new specific functional forms of the requisite constitutive relations, we hope that the discussion herein provides motivation and some guidance for future efforts to model postnatal development into maturity. Multi-scale computational models (cf. Irons et al. 2021; Schwarz et al. 2023) further promise to be particularly useful as we try better to understand progressive disease in congenital heart conditions, most of which affect the vasculature, early-onset diseases (e.g., neonatal Marfan syndrome), early surgical interventions (e.g., Glenn or Fontan procedures), and rapidly evolving vascular conditions arising from pathogenic variants (e.g., Progeria syndrome).

Although this review focused on arteries, it is suggested that these vessels represent an archetype for many load-bearing soft tissues (Cyron and Humphrey 2017); thus it is hoped that this review will similarly stimulate experimental-computational work seeking to understand the development and maturation of diverse soft tissues and organs.

Supplementary Information

Supplementary file1 (DOCX 35 KB). ^{(34.6KB, docx)}

Author contributions

JDH and ELS contributed to this Review and agree to its submission.

Data availability

All data discussed are available in the tables or figures.

Declarations

Conflict of interest

The authors declare no conflict of interest.