Effects of age on the physiological and mechanical characteristics of human femoropopliteal arteries

Acta Biomaterialia 11 (2015) 304–313

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Effects of age on the physiological and mechanical characteristics of human femoropopliteal arteries Alexey V. Kamenskiy a,⇑, Iraklis I. Pipinos b,a, Yuris A. Dzenis c, Nicholas Y. Phillips a, Anastasia S. Desyatova c, Justin Kitson a, Robert Bowen d,e, Jason N. MacTaggart a,⇑ a

Department of Surgery, University of Nebraska Medical Center, Omaha, NE, USA Department of Surgery and VA Research Service, VA Nebraska-Western Iowa Health Care System, Omaha, NE, USA Department of Mechanical & Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE, USA d Physicians Laboratory Services, Omaha, NE, USA e Forensic Science with UNL’s Forensic Science Degree Program, Lincoln, NE, USA b c

a r t i c l e

i n f o

Article history: Received 13 May 2014 Received in revised form 23 August 2014 Accepted 29 September 2014 Available online 6 October 2014 Keywords: Human femoropopliteal artery Biaxial mechanical properties Peripheral artery disease Axial pre-stretch Aging

a b s t r a c t Surgical and interventional therapies for peripheral artery disease (PAD) are notorious for high rates of failure. Interactions between the artery and repair materials play an important role, but comprehensive data describing the physiological and mechanical characteristics of human femoropopliteal arteries are not available. Fresh femoropopliteal arteries were obtained from 70 human subjects (13–79 years old), and in situ vs. excised arterial lengths were measured. Circumferential and longitudinal opening angles were determined for proximal superficial femoral, proximal popliteal and distal popliteal arteries. Mechanical properties were assessed by multi-ratio planar biaxial extension, and experimental data were used to calculate physiological stresses and stretches, in situ axial force and anisotropy. Verhoeff–Van Gieson-stained axial and transverse arterial sections were used for histological analysis. Most specimens demonstrated nonlinear deformations and were more compliant longitudinally than circumferentially. In situ axial pre-stretch decreased 0.088 per decade of life. In situ axial force and axial stress also decreased with age, but circumferential physiological stress remained constant. Physiological circumferential stretch decreased 55–75% after 45 years of age. Histology demonstrated a thickened external elastic lamina with longitudinally oriented elastin that was denser in smaller, younger arteries. Axial elastin likely regulates axial pre-stretch to help accommodate the complex deformations required of the artery wall during locomotion. Degradation and fragmentation of elastin as a consequence of age, cyclic mechanical stress and atherosclerotic arterial disease may contribute to decreased in situ axial pre-stretch, predisposing to more severe kinking of the artery during limb flexion and loss of energy-efficient arterial function. Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

1. Introduction Peripheral artery disease (PAD) often refers to atherosclerotic obstruction of the femoropopliteal artery that reduces blood flow to the lower limb. PAD is a major contributor to overall public health burden and is associated with high morbidity, mortality and impairment in quality of life [1]. The femoropopliteal artery begins as the common femoral artery beneath the inguinal ligament (Fig. 1) and continues as the superficial femoral artery (SFA) into the upper thigh. It becomes the popliteal artery (PA)

⇑ Corresponding authors. Tel.: +1 (402) 559 5100. E-mail addresses: [email protected] (A.V. Kamenskiy), JMacTaggart@ unmc.edu (J.N. MacTaggart). http://dx.doi.org/10.1016/j.actbio.2014.09.050 1742-7061/Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

as it traverses the adductor hiatus, a gap between the adductor magnus muscle and the femur, where it passes from the anterior thigh posteriorly into the popliteal fossa behind the knee. Clinically, the two principal sites of femoropopliteal artery occlusions are the distal SFA at the adductor hiatus and the PA below the knee [2] (Fig. 1). The total annual costs spent on hospitalization of PAD patients exceed $21 billion, and per-patient costs of PAD are higher than those for coronary artery disease and cerebrovascular disease [3]. The high costs of PAD are mostly attributed to the high number of peripheral vascular operations and interventions that fail, resulting in poor clinical outcomes and a frequent need for repeat interventions [4–7]. Specifically, restenosis within 3 years after femoropopliteal bypass occurs in 27% of patients [8]. Results of minimally invasive angioplasty and stenting are even worse, with

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>45% of patients developing hemodynamically significant restenosis within just 2 years after treatment [7], leading to expensive reinterventions in 37–54% of patients [7]. These mediocre results leave significant room for improvement in the management of femoropopliteal artery occlusive disease. Interestingly, femoropopliteal artery interventions fail significantly more often than those in the carotid, renal or iliac arteries, even though the systemic risk factors for restenosis in these locations are the same. This suggests that local factors unique to the SFA and PA strongly influence reconstruction failure. The large deformations experienced by the SFA and PA during movement of the lower limbs is a major difference between the femoropopliteal artery and these other arterial segments [9]. These deformations are hypothesized to contribute to higher rates of stent fracture and restenosis in the femoropopliteal artery [10]. The mechanical properties of the femoropopliteal artery wall greatly influence its deformability and a sound knowledge of the artery’s physiological and mechanical characteristics will promote a better understanding of how this unique artery interacts with textile bypass grafts and metallic stents. Surprisingly, little detailed knowledge of physiological and mechanical characteristics of the SFA and PA exists in the literature [11]. These characteristics include in situ axial pre-stretch, residual stresses, and physiological stresses and stretches. Although ‘‘physiological’’ implies in vivo assessment, most of these characteristics cannot be measured in vivo. Some characteristics, such as mechanical stress, cannot be directly measured at all, and must be calculated based on mechanical property analysis of excised arterial wall tissue. Thus for an accurate, comprehensive mechanical analysis of the femoropopliteal artery, both in situ and ex vivo analyses of fresh arteries are required. The purpose of this study was to characterize the structural, physiological and mechanical characteristics of human femoropopliteal arteries in relation to age. In situ axial pre-stretch, circumferential and longitudinal opening angles, and biaxial mechanical properties of fresh femoropopliteal

305

arteries were determined from 70 human donors 13–79 years old. These experimental data were then used to calculate physiological stresses and stretches in the SFA and PA to determine how these mechanical characteristics are affected by age. 2. Methods 2.1. Materials Fresh femoropopliteal arteries from 70 human tissue donors were obtained under IRB protocol from the Nebraska Organ Recovery System (NORS) within 24 h of the subject’s death. Donors were 13–79 years old (average age 50 ± 16 years), 15 female and 55 male. The majority of subjects (66%) were >45 years old. All subjects except four were Caucasian, and detailed demographics are summarized in Table 1. Most arterial segments began in the common femoral artery prior to the take-off of the profunda femoris artery excised in continuity to the tibioperoneal trunk (Fig. 1). Some specimens were slightly shorter, resulting in a total of 70 proximal SFA specimens taken 1 cm distal to the takeoff of the profunda femoris artery, 52 proximal popliteal artery (pPA) specimens taken at the adductor hiatus, and 42 distal popliteal artery (dPA) specimens taken 1 cm proximal to the tibioperoneal trunk (Fig. 1). 2.2. In situ pre-stretch and mechanical testing Prior to excision from the body, the in situ length of the femoropopliteal artery segment was measured using an umbilical tape. The tape was placed between the locations at which the artery was transected representing the true in situ length of the arterial segment. The artery and the tape were then cut together, and while the umbilical tape maintained its length, the artery typically shortened due to in situ axial pre-stretch. The axial pre-stretch was then

Fig. 1. Anatomy of the femoropopliteal artery segment and an excised longitudinally opened vessel demonstrating severe PAD in the distal SFA and PA.

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Table 1 Subject demographics. Risk factors

645 years old, %

>45 years old, %

Diabetes Hypertension Dyslipidemia Coronary artery disease Ever smoker Alcohol abuse Drug abuse

13 29 13 0 54 17 17

39 61 24 13 50 28 13

defined as the ratio of the in situ arterial length (umbilical tape length) to the excised artery length. After excision from the body, each segment of the femoropopliteal artery was further separated into 5 mm rings that were used for measurement of the circumferential opening angle, and two 13 mm long segments that were used for the longitudinal opening angle measurements and assessment of biaxial mechanical properties. In addition, sections of each artery immediately adjacent to the two 13 mm long segments were used for histological evaluation. The circumferential opening angle a was measured by cutting a 5 mm long arterial ring radially to release the circumferential residual stress, and measuring the angle between the lines drawn from the center of the sector to its outer tips [12,13] (Fig. 2). Note that this definition of the opening angle follows Sommer and Holzapfel [12], and is different from the one in which a is calculated as an angle between two lines drawn from the midpoint of the arc of the inner vessel wall to the outer tips of the open sector [14]. This angle can easily be obtained from our measurements as a2. Although some dispute is present in the literature as to whether one radial cut is sufficient to release all circumferential residual stress in the tissue [14–16], this question merits a separate investigation and was beyond the scope of the current study. The longitudinal opening angle b was measured by opening the 13 mm arterial segment, cutting a 13 mm  2 mm axial strip, and measuring the sector that resulted from curving of the axial strip intima outward. Schematics of both the circumferential and longitudinal opening angle measurements are presented in the left panel of Fig. 2 and representative examples are demonstrated in the right panel of the same figure.

Biaxial mechanical testing was performed using square specimens that when possible were 13 mm  13 mm in size and free from gross pathology. Square specimens were cut maintaining the longitudinal and circumferential orientations parallel with the specimen’s square edges. Some specimens opened to initially curved configurations which flattened out either under their own weight, or after application of the 0.01 N tare pre-load. Although such flattening does introduce additional stresses to the specimen, these stresses are likely small compared to those occurring in the sample during testing. Arterial wall thickness was measured and averaged at six different locations with a Starrett 1010 Z caliper ensuring that the caliper’s lips touched the specimen, but were not compressing it. Caliper measurements were consistent with optical assessments of wall thickness using photographs of the arterial rings used for the opening angle measurements (Fig. 2, right panel). Flat arterial sheets were attached to the biaxial device using stainless steel hooks and loops of thick, rigid nylon surgical suture [11,17,18]. Hooks attaching the specimen were placed as close as possible to the edges to minimize the influence of edge effects on strain measurements. Four graphite markers were attached to the arterial intima to track specimen deformation. During testing, specimens were completely immersed in 0.9% NaCl physiological saline solution at 37 °C maintained by a Fisher Scientific Isotemp Refrigerated Circulator 9000. The entire setup was placed on a vibration isolation tabletop to minimize noise caused by stage movements. All samples were tested in the longitudinal and circumferential directions using a custom-made soft-tissue biaxial device. A more detailed device description is given in Sacks [19], Vande-Geest et al. [20,21] and our recent works [11,18,22]. The design of the custom-made planar biaxial testing device contains a specially designed pulley apparatus that allows applied forces to be equally distributed between each suture line holding the specimen, allowing the specimen to shear freely. The deformation gradient was measured by video tracking the movements of four graphite markers attached to the intima of the artery [14,17]. In-plane stretches and shear angle were calculated in real time from marker displacements using a four-node finite-element technique [14,17]. The applied loads in the circumferential and longitudinal directions were measured with a pair of

Fig. 2. (Left panel) Kinematics of the arterial wall demonstrating an artery in the reference (stress-free configuration) XR where the circumferential stress is released by the radial cut resulting in opening of the arterial ring into a sector with angle a. Curving of the axial strip into a sector with an angle b releases axial residual stress. Note that typically the femoropopliteal artery axial strip curves intima outward (see right panel), meaning that Rzi is the outer radius, and Rzo the inner radius of the axial strip sector. The artery is then transferred to the unloaded configuration via FR–U, i.e. by closing the sector circumferentially and flattening the axial strip. In the unloaded configuration XU, the artery contains circumferential and longitudinal residual stresses but has no internal pressure or axial force. Finally, the unloaded arterial segment is loaded with an internal pressure pi and an axial force Fz, resulting in the transformation FU–C to the current (loaded) configuration XC. Note that the dimensions of the arterial segment in all three configurations are different. (Right panel) Intact arterial ring (A) and circumferential (B) and longitudinal (C) opening angle measurements for the SFA of 17 and 60 year old subjects demonstrating larger diameters, a and b, for the older subject. Note that the axial strip (C) curves intima (I) outward. Measurements are performed in normal 0.9% NaCl physiological saline.

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tension/compression ‘‘250 g’’ (max load 2.5 N) load cells (Honeywell Sensotec) calibrated prior to each testing session [23]. Load cells were selected to cover the estimated physiological loads in tested arteries as will be described below. Cauchy stresses were then calculated from the biaxial loads as:

rzz ¼ kz

Pz ; HLh

rhh ¼ kh

Ph ; HLz

ð1Þ

where H is the undeformed thickness, Li are the undeformed lengths over which the applied loads Pi act (i = h, z), and kz and kh are inplane stretches. Although loads were applied perpendicular to the edges, the Cauchy stress shear components rzh and rhz are non-zero if shear deformation is present. Shear was assessed in all specimens by calculating shear angle / as:

  2Ezh 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; / ¼ sin 1 þ 2Ez 1 þ 2Eh

motivated by the underlying arterial wall structure and considers axial, circumferential and two symmetrically diagonal families of collagen fibers. The use of invariants for model formulation ensures convexity and precludes undesirable material instabilities [26]. Viscoelastic effects were not taken into account because after preconditioning most arteries demonstrated relatively narrow hysteresis. Although passive contributions to the mechanical properties of the arterial wall by smooth muscle were absorbed by the constitutive model [27], a specific assessment of smooth muscle cell contractile state and its effect on wall mechanical properties requires additional experiments that were not performed. A detailed framework for this constitutive model is given elsewhere [11,25,27,28], and considers the strain energy function in the form:

WðC; Mi Þ ¼

ð2Þ

where Ez, Eh and Ezh are components of the Green strain tensor E ¼ 12 ðFT F  IÞ and F is the deformation gradient. In the vast majority of samples shear was small (average 2.2°, standard error = 0.3°), which allowed significant simplification of the constitutive framework presented below. All artery specimens were tested whole, without separating the layers. Layer separation is challenging in younger healthier arteries and significantly increases the overall testing time, which is not compatible with the requirement of keeping the tissues fresh and unfrozen. Therefore, Eq. (1) represents average stresses in the longitudinal and circumferential directions for the artery wall thickness as a whole. To ensure consistency from sample to sample, all loading cycles were initiated at a tare load of 0.01 N and all stretch data were referenced to this tare configuration. Prior to collecting data, all specimens were preconditioned with 10 cycles of equibiaxial load at 1.5 N. All tests were load-controlled, therefore the strain rate for each specimen was tuned such that tissue reached 1.5 N load within a set time. Although in vivo arteries are loaded dynamically, in our previous study of diseased femoropopliteal arteries [11] we found that varying the loading time did not significantly affect the resulting stress–stretch curves, and therefore cycle lengths of 15 s for loading and 15 s for unloading were used as in our previous experimental protocols [11,18,22], allowing utilization of the quasistatic framework. For most specimens highly repeatable responses were observed starting from the fourth cycle. After preconditioning, each artery was subjected to nine different testing protocols to cover the wide range of strain space and to acquire sufficient data density for constitutive modeling [24]. The nine protocols included testing with constant load ratios applied in the longitudinal and circumferential directions, namely 1:1, 1:2, 1:4, 1:10, 1:1 (stability check), 2:1, 4:1, 10:1, 1:1 (stability check). The maximum load was set at 1.5 N for most arteries. Equibiaxial stability checks were performed twice: in the middle of the testing sequence and at the end to ensure that the specimen did not accumulate any damage as it went through the battery of tests. 2.3. Constitutive modeling The constitutive model selected for this study is a four-fiber family model proposed by Baek et al. [25] because this model has previously been used to accurately portray the behavior of human femoropopliteal arteries [11]. The arterial wall is assumed to be incompressible (see discussion of incompressibility assumption in Humphrey [14]), consisting primarily of a mixture of elastin-dominated amorphous matrix and families of locally parallel collagen fibers [11,25]. The model is phenomenological, but it is

4 h i o X 2 c0 ci1 n ðIC  3Þ þ exp ci2 ðIi4  1Þ  1 ; i 2 4c2 i¼1

ð3Þ

where c0 ; ci1 and ci2 are material parameters, IC = tr C is the first invariant of the right Cauchy–Green tensor. Unit vectors Mi define the fiber directions in the reference configuration that make angles ci with the axial direction. With axial and circumferential fibers fixed at c1 = 0 and c2 = p/2, and diagonal fibers located at c3 = c4 = c, the square of the stretch of the ith fiber family Ii4 ¼ Mi  CMi takes the form:

I14 ¼ k2z ;

I24 ¼ k2h ;

2

2 2 2 I3;4 4 ¼ kz cos c þ kh sin c:

ð4Þ

Assuming further mechanical equivalence of the diagonal fibers, c31 ¼ c41 ¼ c3;4 and c32 ¼ c42 ¼ c3;4 1 2 . Therefore, formulation (3) is a function of eight constitutive parameters ðc0 ; c11 ; c12 ; c21 ; c22 ; c3;4 1 ; c3;4 2 ; cÞ that need to be non-negative in order to be physically realistic. In addition 0 6 c 6 p2 due to the symmetry of the diagonal fibers. For homogeneous biaxial deformation in the absence of shear, the deformation gradient takes a diagonal form. Principal Cauchy stresses can then be found from:

rii ¼ ki

@W ; @ki

i ¼ r; h; z;

ð5Þ

where the stress in Eq. (5) is the isochoric Cauchy stress, i.e.

rii ¼ p þ rii , where p is the Lagrange multiplier. Incompressibility yields:

kr ¼ 1=ðkz kh Þ:

ð6Þ

Assuming that during biaxial testing the tissue is subject to plane stress (i.e. rrr ¼ 0), the non-zero Cauchy stress components (5) for the strain energy function (3) take the form:

rzz ¼ c0 k2z 

rhh

1 k2h k2z

!

  1 2 2 þ c11 k2z  1 ec2 ðkz 1Þ k2z

  3;4 3;4 2 c2 ðI4 1Þ 2 þ 2c3;4 I3;4 kz cos2 c 4 1 e 1 !   2 2 2 1 ¼ c0 k2h  2 2 þ c21 k2h  1 ec2 ðkh 1Þ k2h kh kz   3;4 3;4 2 2 3;4 3;4 þ 2c1 I4  1 ec2 ðI4 1Þ k2h sin c:

ð7Þ

The two Cauchy stress components in Eq. (7) are functions of the two principal stretches kh and kz , and the eight constitutive 3;4 parameters ðc0 ; c11 ; c12 ; c21 ; c22 ; c3;4 1 ; c2 ; cÞ that determine the material behavior. These eight parameters can be found by fitting Eq. (7) to the experimental data [11,18,27]. 2.4. Assessment of physiological characteristics and arterial anisotropy In situ axial pre-stretch, measurements of arterial wall thickness, diameter and opening angles, and constitutive model

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parameters determined from the biaxial experimental data, were used to determine the physiological characteristics using the framework described in Fig. 2. This framework considered the artery going through three configurations: (i) reference (stressfree), where the residual stresses are released, resulting in opening of the arterial ring into a sector with angle a and curving of the axial strip into a sector with an angle b; (ii) unloaded, which results from closing the sector and straightening of the strip; and (iii) current (loaded) configuration containing the residual stresses, internal pressure pi, and axial force Fz. Details of this framework are described in Sommer and Holzapfel [12], and here we will summarize the results necessary for the rest of the presentation. Equilibrium in the absence of body forces provides the relation for the internal pressure pi and axial force Fz in the current (loaded) configuration:

pi ¼

Z

ro

ðrhh  rrr Þ

ri

Fz ¼ p

Z

dr r

ð8Þ

ro

ð2rzz  rhh  rrr Þrdr:

ð9Þ

ri

Here the inner and outer radii are given by:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2  R2i and r o ¼ qo kh ; r i ¼ ðqo kh Þ2  o kkz;res kz

ð10Þ

where k ¼ 2p2pa is a measure of the circumferential opening angle a in the reference configuration, kz;res ¼ 2R2Rzi H is the axial residual zi stretch, qo is arterial outer radius in the unloaded configuration, Ro, Ri are outer and inner radii in the reference configuration. Since the artery is no longer subject to plane stress as was assumed during the biaxial tensile testing, its radial stress for constitutive model (3) can be expressed as rrr ¼ kr @W ¼ k2c0k2 , although @kr h z rrr was not used to find c0 in Eq. (7). Therefore, in addition to the eight constitutive model parame3;4 ters ðc0 ; c11 ; c12 ; c21 ; c22 ; c3;4 1 ; c 2 ; cÞ for the strain-energy function (3), one also needs to measure five morphometric characteristics: one in the unloaded configuration: qo (the outer radius); and four in the reference (stress-free) configuration: Ro, Ri (the outer and inner radii that define the wall thickness H = Ro  Ri), a (the circumferential opening angle) and Rzi (the outer radius of the axial strip sector). situ After subjecting the artery to in situ axial pre-stretch kz ¼ kin , z the described framework portrays the physiological behavior of the femoropopliteal artery, and this can be used for the calculation of the in situ axial force, and the circumferential, longitudinal and radial stresses and stretches at various internal pressures. Here we will calculate physiological characteristics at normal systolic (120 mmHg) and diastolic (80 mmHg) blood pressures using Eq. (8). In addition to determining the physiological conditions of the artery, we assessed arterial anisotropy by considering the equibiaxial tensile tests and comparing the circumferential and longitudinal stretches at 25 kPa (A25) and 50 kPa (A50) stress levels. Although equibiaxial loading conditions are likely not physiological, such comparison allowed characterization of arterial properties as they relate to the internal structure of the arterial wall. Anisotropy is defined as the difference in longitudinal and circum  kz kh ferential stretches divided by their average value 0:5ðk [18,22]. z þkh Þ This definition was chosen over the simple ratio of stretches due to its symmetry, which is important when describing materials that may demonstrate a switch in anisotropy [18,22]. Note that when anisotropy values are negative, the circumferential direction is more compliant than the longitudinal direction.

2.5. Histological evaluation A ring 5 mm in length and an axial strip 13 mm long  2 mm wide were cut from each artery immediately adjacent to a segment that was biaxially tested. Both the ring and the strip were fixed in 10% neutral-buffered formalin, embedded in paraffin and sliced 5 lm thick. Standard Verhoeff–Van Gieson (VVG) staining was used to assess elastin orientation in the circumferential and longitudinal directions. Images of the stained arteries were captured under 40 bright-field magnification. 2.6. Statistical analysis Curve fitting and statistical analyses were performed in OriginPro 9 (OriginLab Co.). Fitting to determine constitutive model parameters from the experimental biaxial tests was performed with the Levenberg–Marquardt algorithm using the multi-data global fit mode and constraining the parameters to be non-negative. The traditional coefficient of determination R2 e [0, 1] was used as a measure of goodness of fit. In our experience, values R2 P 0:9 typically represent a good fit to the experimental data [11,18]. Linear regression analysis was utilized to evaluate the relationship between age and each of the variables: in situ axial pre-stretch, morphometric and physiological characteristics and arterial anisotropy. Spearman’s rank correlation coefficient rs was calculated to assess the strength of relationship between age and each of the variables. Values of rs closer to ±1 indicate stronger relation. Comparison of subjects younger and older than 45 years of age was performed using Student’s two-sample t-test, and P < 0.05 was considered statistically significant. 3. Results 3.1. In situ axial pre-stretch In situ axial pre-stretch of the femoropopliteal artery vs. the subject’s age, and linear fit [29] are presented in Fig. 3 and Table 2. There was a strong decrease in the in situ axial pre-stretch with advancing age (rs = 0.77). At approximately 70 years of age, in situ and excised arterial lengths became equal, indicating that

Fig. 3. Measurements of the femoropopliteal artery in situ axial pre-stretch in subjects of different ages and a linear fit [29] (slope 0.009 [standard error = 0.008], intercept: 1.646 [standard error = 0.431]). Note that in situ and excised lengths are almost equal at the age of 70 years. After 70 years the artery becomes tortuous and could become longer after excision.

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A.V. Kamenskiy et al. / Acta Biomaterialia 11 (2015) 304–313 Table 2 Morphometric characteristics of the superficial femoral artery (SFA), proximal popliteal artery (pPA) and distal popliteal artery (dPA) in subjects situ is in situ axial pre-stretch, qo is the outer radius in younger and older than 45 years. Values are provided as average ± standard error. Here kin z the unloaded configuration, Ro, H are the outer radius and wall thickness in the reference configuration, and a, b circumferential and longitudinal opening angles measured in the reference configuration. 645 years old SFA situ kin z qo, mm Ro, mm H, mm a, ° b, °

>45 years old pPA

dPA

SFA

1.26 ± 0.01 3.12 ± 0.08 4.92 ± 0.31 1.33 ± 0.06 133 ± 10 125 ± 10

pPA

dPA

3.50 ± 0.10 6.62 ± 0.52 1.46 ± 0.09 168 ± 10 235 ± 9

3.17 ± 0.11 5.88 ± 0.45 1.40 ± 0.08 171 ± 10 246 ± 8

1.09 ± 0.01 2.81 ± 0.11 5.42 ± 0.58 1.36 ± 0.09 160 ± 14 164 ± 12

2.85 ± 0.12 5.22 ± 0.43 1.29 ± 0.09 150 ± 13 170 ± 12

in situ axial pre-stretch vanished yet the artery remained straight. After 70 years, the artery developed tortuosity, sometimes becoming longer after excision. 3.2. Morphometry and opening angles Morphometric characteristics including outer radii in the unloaded (qo) and stress-free (Ro) configurations, wall thickness (H), and circumferential (a) and longitudinal (b) opening angles are summarized in Table 2 for subjects younger and older than 45 years of age. Our data demonstrate that arterial radius qo increased with age (SFA: rs = 0.43, pPA: rs = 0.44, dPA: rs = 0.27) and decreased with more distal location (P < 0.01). Wall thickness H did not correlate with age (rs < 0.25), and was not statistically significantly different in the SFA and in the dPA (P = 0.47). The circumferential opening angle a increased with age insignificantly (SFA: rs = 0.30, pPA: rs = 0.21, dPA: rs = 0.32, P = 0.07, 0.32, 0.11), and was smaller in the SFA than in the pPA or dPA (P = 0.03). Longitudinal arterial strips curved intima outward (note Rzo and Rzi in Fig. 2) and the longitudinal opening angle b was wider distally than proximally (P = 0.02). Angle b also strongly correlated with age (SFA: rs = 0.65, pPA: rs = 0.66, dPA: rs = 0.64), demonstrating wider angles in senior arteries (P < 0.01). The dependence of b on age is illustrated in Fig. 4 and larger values of b indicate a more flat axial strip (an example is presented in Fig. 2). 3.3. Physiological stretches, stresses and assessment of anisotropy The representative constitutive model fits for the SFAs of different ages are presented in Fig. 5. Substantial nonlinearity and anisotropy were observed for most arteries. Multiple biaxial loading protocols were accurately portrayed by the constitutive model for all age groups (average R2 = 0.98, standard error <0.01).

3.76 ± 0.11 6.81 ± 0.46 1.46 ± 0.06 152 ± 8 230 ± 10

In all three segments of the femoropopliteal artery, physiological circumferential stretch kh , axial force Fz, and axial stress rzz all decreased. Circumferential stress rhh did not change and radial stress rrr increased with age (P < 0.01) (Fig. 6). During equibiaxial loading, all three segments of the femoropopliteal artery were more compliant longitudinally than circumferentially (A > 0, P < 0.01). Correlation of circumferential stretch kh with age was strong, demonstrating rs = 0.48 (SFA), rs = 0.34 (pPA) and rs = 0.54 (dPA). Average kh in subjects older than 45 years were 55–75% smaller than in subjects younger than 45 years. Decreases in both the circumferential and the longitudinal stretches with age (i.e. arterial stiffening) are illustrated in Fig. 5. Although kh demonstrated a tendency to decrease with more distal arterial location, this was not statistically significant (P = 0.25). Correlation of axial force Fz with age was also strong (rs = 0.44 [SFA], rs = 0.65 [pPA] and rs = 0.47 [dPA]). In younger subjects the force was tensile (P < 0.01) and demonstrated a tendency to decrease from diastole to systole (P = 0.12). In older subjects Fz was mostly compressive (P = 0.12 diastole, P < 0.01 systole) and tended to increase in absolute value from diastole to systole (P = 0.12). Axial force in the SFA tended to be larger than in the more distal dPA, but this was not statistically significant (P = 0.13). Correlation of axial stress rzz with age was strong (rs = 0.52 [SFA], rs = 0.61 [pPA] and rs = 0.58 [dPA]) and axial stress decreased in more distal arterial locations (P < 0.01). In older subjects rzz was on average 1.7- to 2.3-fold smaller than in younger subjects, with the largest difference observed for the pPA. Circumferential stress rhh did not vary with age and remained between 39 and 67 kPa. However, rhh did decrease with more distal arterial location (P = 0.02). No correlation was observed between age and rhh (rs = 0.12 [SFA], rs = 0.05 [pPA], rs = 0.03 [dPA]). Values of rhh were only 25–65% larger than values of rzz,

Fig. 4. Dependence of the longitudinal opening angle b on age for the SFA (A, red), pPA (B, blue) and dPA (C, green) segments of the femoropopliteal artery. Larger b indicates more flat axial strip.

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Fig. 5. Representative fits of the experimental data with constitutive model for proximal SFA of 16, 41 and 68 year old subjects. Each graph represents one biaxial loading protocol in the longitudinal and circumferential directions. Constitutive model parameters: 16 year old: c0 ¼ 18:30 kPa; c11 ¼ 9:81 kPa; c12 ¼ 0:31; c21 ¼ 2:53 kPa; c22 ¼ 2 3;4 3;4 3;4  1 1 2 2 6:88; c3;4 1 ¼ 2:14 kPa; c 2 ¼ 3:64; c ¼ 62:56 ðR ¼ 0:996Þ; 41 year old: c 0 ¼ 30:67 kPa; c 1 ¼ 13:82 kPa; c 2 ¼ 2:03; c 1 ¼ 9:36 kPa; c 2 ¼ 14:85; c 1 ¼ 1:43 kPa; c 2 ¼ 14:25; 2 3;4  c ¼ 53:29 ðR2 ¼ 0:994Þ; 68 year old: c0 ¼ 11:85 kPa; c11 ¼ 40:68 kPa; c12 ¼ 17:12; c21 ¼ 41:79 kPa; c22 ¼ 26:27; c3;4 ¼ 31:44 kPa; c ¼ 28:94; c ¼ 49:76 ðR ¼ 0:997Þ. 1 2

Fig. 6. Physiological and material characteristics of the superficial femoral artery (SFA), proximal popliteal artery (pPA) and distal popliteal artery (dPA) in subjects younger (blue, cyan) and older (red, magenta) than 45 years at diastole (blue, red) and systole (cyan, magenta): (A) physiological circumferential stretch; (B) in situ axial force (N); (C) anisotropy indexes A25 (blue, red) and A50 (cyan, magenta); and (D, E, F) physiological axial, circumferential and radial stresses in the SFA, pPA and dPA, respectively. Error bars represent standard error.

and in young subjects rhh was even smaller than rzz during diastole (P < 0.01) and just as high as rzz during systole (P = 0.10). Correlation of radial stress rrr with age was weak (rs = 0.36 [SFA], rs = 0.23 [pPA] and rs = 0.07 [dPA]), but nevertheless the increase in radial stress with age was statistically significant

(P < 0.01). Radial stress decreased with more distal arterial location (P = 0.03). Radial stress was > 5-fold smaller than circumferential stress rhh and did not change significantly from diastole to systole. Anisotropy decreased with age (rs = 0.44 [SFA], rs = 0.35 [pPA], rs = 0.29 [dPA]) and younger SFAs and dPAs were more

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anisotropic than older SFA and dPA (P = 0.03), but this was not statistically significant for the pPA (P = 0.20). Anisotropy increased with more distal arterial location (P < 0.01). 3.4. Histology The structure of the femoropopliteal artery wall exhibited a thickened external elastic lamina with elastin fibers oriented primarily in the longitudinal direction (Fig. 7). This longitudinal layer of elastin fibers appeared thicker, denser and less fragmented in younger arteries. A thickened external elastic lamina with longitudinally oriented fibers of elastin was present in all three segments of the artery, SFA, pPA and dPA, and was likely responsible for the curving of the axial strip intima outward during measurement of the longitudinal opening angle (Fig. 2, right panel). 4. Discussion PAD is strongly associated with aging and stiffening of the arteries [11,30–32]. Improved knowledge of the physiological and mechanical characteristics of human femoropopliteal arteries as they change with age is essential for better understanding of PAD pathophysiology and development of improved diagnostic and treatment modalities. Most existing studies of human femoropopliteal artery mechanical properties are limited to the proximal femoral artery [33] and utilize either duplex ultrasound (DUS) for nondestructive in vivo testing, or uniaxial tensile testing of excised cadaveric arteries [31,34–37]. However, in vivo DUS and uniaxial tensile experiments cannot sufficiently characterize the complex nonlinear, anisotropic properties of arterial tissue [14,17] and therefore cannot provide accurate information on physiological arterial wall characteristics. Biaxial testing is a more comprehensive experimental method for characterizing arterial tissue, and recently the biaxial properties of heavily diseased SFA and PA have been reported from patients requiring amputations for critical limb ischemia [11]. Because experimental evaluations of femoropopliteal artery mechanical properties are so scarce in the literature, our goal was to thoroughly study these properties in a large group

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of subjects and determine how the mechanical properties change with age. Our results demonstrate that most femoropopliteal arteries younger than 70 years of age are longitudinally pre-stretched in situ. The amount of pre-stretch decreases 0.088 per decade of life, and after 70 years the artery may continue to become longer and more tortuous. Axial pre-stretch has a fundamental role in arterial mechanics and is believed to help conserve energy so the artery does no axial work during the pulse cycle [38]. Axial prestretch in the femoropopliteal artery may also prevent buckling [11] as the artery deforms with limb flexion and extension during locomotion [9]. The microstructure of the femoropopliteal artery wall facilitates this behavior, exhibiting a thickened external elastic lamina with a distinct layer of longitudinally oriented elastin fibers—a structural organization different from larger elastic arteries, such as the aorta. Elastin is produced and organized primarily during the perinatal period [38] and since elastin matures early in life [39], elastic laminae stretch as vessels grow, resulting in considerable tension during maturity. Dobrin et al. [40] and Zeller and Skalak [41] reported that in healthy arteries nearly all axial pre-stretch is due to the presence of elastin. Collagen and smooth muscle, on the other hand, turnover continually, which result in collagen being under residual compression [41]. Along with other accompanying changes in cellular and extracellular matrix composition, the degradation and fragmentation of elastin due to aging, cyclic mechanical stress, proteolytic destruction and disease decreases axial pre-stretch and increases the longitudinal opening angle, exactly as observed in this study. It is important to distinguish between the in situ axial prestretch and the in vivo axial pre-stretch because they are not always equal [42]. The in vivo axial pre-stretch is the pre-stretch at which changes in the internal pressure do not affect the axial force, which allows the artery to function in the energy-efficient manner [11]. Although in situ and in vivo axial pre-stretches may be similar for young arteries [43,44], Schulze-Bauer et al. [42] and our recent work [11] have demonstrated that for senior arteries this may not be the case, and the in situ axial pre-stretch may be substantially smaller than the in vivo axial pre-stretch, suggesting that arteries loose energy-efficient function as they become

Fig. 7. Representative transverse (left) and longitudinal (right) arterial sections of a 29 and 67 year old SFA demonstrating thickened external elastic laminae and longitudinal elastin fibers (right panels). Note fragmentation and degradation of the elastin in the external elastic lamina and vascular smooth muscle changes in the media of the older subject. Verhoeff-Van Gieson stain: elastin is black, collagen is red and smooth muscle is brown.

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older and more diseased. Since in this paper we are not investigating the in vivo axial pre-stretch, we stress the importance of further studies to compare the in situ and the in vivo axial pre-stretch values [11]. In addition to pre-stretch, we calculated certain physiological characteristics of the femoropopliteal artery by utilizing biaxial testing and constitutive modeling. Our data demonstrate that physiological circumferential stretch, axial force and axial stress decreased with age by 55–75%, 0.4–0.8 N and 1.7- to 2.3-fold, respectively. Circumferential stress did not change and remained between 39 and 67 kPa, while radial stress increased 1.3- to 2-fold with age. This indicates that the arterial wall likely remodels with age by adapting to new environments and equilibrating to a homeostatic stress state [38,45] that attempts to maintain circumferential stress at a steady-state level. Arterial adaptation may be influenced by sustained alterations in flow or pressure, or by exposure to external mechanical influences, such as limb flexion. To maintain the multiaxial stress state towards homeostatic values [38], the artery may compensate for high stress in one direction by decreasing the stress (by virtue of decreasing strain) in another direction [46]. In particular, arteries may employ compensatory mechanisms to equilibrate the circumferential stress by controlling local axial force and reducing the stretch in the axial direction [38]. These mechanisms may involve tissue remodeling, including fragmentation or degradation of elastin, increased deposition of collagen, and proliferation or hypertrophy of smooth muscle [38], all leading to decreased compliance and increased arterial wall stiffness. The majority of femoropopliteal arteries were more compliant longitudinally than circumferentially under equibiaxial loading, which agrees with previous findings examining severely diseased femoropopliteal arteries from amputation specimens [11]. Both longitudinal and circumferential compliance decreased with age and vascular disease. Since collagen fibers and smooth muscle cells have a preferred circumferential orientation [47–49] and function to regulate the lumen diameter and protect the artery from overstretch, overproduction of collagen and altered smooth muscle tone likely stiffen the artery circumferentially. On the other hand, degradation and fragmentation of axial elastin loosens and stiffens the femoropopliteal artery longitudinally. A combination of both mechanisms would result in stiffening of the tissue in both directions. Our study demonstrates that the anisotropy of the femoropopliteal artery decreased with age, suggesting that longitudinal stiffening is more profound than circumferential stiffening. The ability of the femoropopliteal artery to accommodate axial deformation during locomotion is therefore likely affected to a greater extent than its ability to stretch circumferentially during blood pressure pulsation. This longitudinal stiffening could lead to more severe arterial deformations during limb movement. These deformations are concentrated in specific areas of the thigh and leg [9], predisposing to disease development and treatment complications, such as restenosis and stent fracture. This study provides experimental measurements of the passive mechanical properties of the femoropopliteal artery. In vivo, however, these arteries are subjected to humoral and neural factors that can dynamically influence mechanical properties of the artery wall. Arterial wall calcification is frequently encountered in older arteries and this may also significantly affect wall properties. Further studies investigating these issues along with the effects of other cardiovascular risk factors on artery structure and mechanical properties are planned.

5. Conclusions The current study comprehensively characterizes the microstructure, mechanical and physiological characteristics of human

femoropopliteal arteries in relation to age. We demonstrate that femoropopliteal arteries are pre-stretched in situ in young subjects, and that the thick, longitudinally oriented elastin layer likely promotes energy-efficient arterial function and prevents buckling during locomotion. Degradation and fragmentation of elastin, deposition of collagen, proliferation of smooth muscle cells, and other structural changes occurring with age and disease result in decreased axial pre-stretch, overall stiffening of the artery, loss of energy-efficient arterial function, and a predisposition to more severe kinking during limb flexion. Disclosures The authors have no competing interests to disclose. Acknowledgements The authors wish to acknowledge the Nebraska Organ Recovery System (Kyle Herber and Thomas Woodford) for their help in procuring arteries for this study and the Charles and Mary Heider Fund for Excellence in Vascular Surgery. Appendix A. Figures with essential colour discrimination Certain figures in this article, particularly Figures 1–7, are difficult to interpret in black and white. The full colour images can be found in the on-line version, at http://dx.doi.org/10.1016/ j.actbio.2014.09.050. References [1] Mahoney EM, Wang K, Keo HH, Duval S, Smolderen KG, Cohen DJ, et al. Vascular hospitalization rates and costs in patients with peripheral artery disease in the United States. Circ Cardiovasc Qual Outcomes 2010;3:642–51. [2] Watt J. Origin of femoro-popliteal occlusions. Br Med J 1965;2:1455–9. [3] Mahoney EM, Wang K, Cohen DJ, Hirsch AT, Alberts MJ, Eagle K, et al. One-year costs in patients with a history of or at risk for atherothrombosis in the United States. Circ Cardiovasc Qual Outcomes 2008;1:38–45. [4] Adam DJ, Beard JD, Cleveland T, Bell J, Bradbury AW, Forbes JF, et al. Bypass versus angioplasty in severe ischaemia of the leg (BASIL): multicentre, randomised controlled trial. Lancet 2005;366:1925–34. [5] Conte MS, Bandyk DF, Clowes AW, Moneta GL, Seely L, Lorenz TJ, et al. Results of PREVENT III: a multicenter, randomized trial of edifoligide for the prevention of vein graft failure in lower extremity bypass surgery. J Vasc Surg 2006;43:742–51. [6] Schillinger M, Sabeti S, Loewe C. Balloon angioplasty versus implantation of nitinol stents in the superficial femoral artery. N Engl J Med 2006;354:1879–88. [7] Schillinger M, Sabeti S, Dick P, Amighi J, Mlekusch W, Schlager O, et al. Sustained benefit at 2 years of primary femoropopliteal stenting compared with balloon angioplasty with optional stenting. Circulation 2007;115:2745–9. [8] Siracuse JJ, Giles KA, Pomposelli FB, Hamdan AD, Wyers MC, Chaikof EL, et al. Results for primary bypass versus primary angioplasty/stent for intermittent claudication due to superficial femoral artery occlusive disease. J Vasc Surg 2012;55:1001–7. [9] MacTaggart J, Phillips N, Lomneth C, Pipinos I, Bowen R, Baxter B, et al. Threedimensional bending, torsion and axial compression of the femoropopliteal artery during limb flexion. J Biomech 2014;47(10):2249–56. [10] Ansari F, Pack LK, Brooks SS, Morrison TM. Design considerations for studies of the biomechanical environment of the femoropopliteal arteries. J Vasc Surg 2013;58(3):804–13. [11] Kamenskiy AV, Pipinos II, Dzenis YA, Lomneth CS, Kazmi SAJ, Phillips NY, et al. Passive biaxial mechanical properties and in vivo axial pre-stretch of the diseased human femoropopliteal and tibial arteries. Acta Biomater 2014;10:1301–13. [12] Sommer G, Holzapfel GA. 3D constitutive modeling of the biaxial mechanical response of intact and layer-dissected human carotid arteries. J Mech Behav Biomed Mater 2012;5:116–28. [13] Chuong CJ, Fung YC. On residual stresses in arteries. J Biomech Eng 1986;108:189–92. [14] Humphrey JD. Cardiovascular solid mechanics: cells, tissues, and organs. Berlin: Springer Verlag; 2002. [15] Holzapfel GA, Ogden RW. Modelling the layer-specific three-dimensional residual stresses in arteries, with an application to the human aorta. J R Soc Interface 2010;7:787–99.

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