Loss of anisotropic properties in abdominal aorta aneurysm obtained from the xenograft rat model

Abstract

BACKGROUND:

Cellular treatments using mesenchymal stem cells (MSCs) cultured in 3D conditions constitute a solution to the classical surgery in treating abdominal aortic aneurysm (AAA). The recurrent question is: how this type of biotherapy changes the mechanical behavior of artery?

METHODS:

Experiments measurements based on xenograft rat model showed that the proposed cellular treatment leads to a decreasing radius and length of the AAA during its growth. An inverse finite element method was used to investigate the mechanical hyperelastic behavior of the AAA in the untreated case compared to the treated one.

RESULTS:

Although AAA leads a loss anisotropy while the cellular treatment does not restore it, it was shown that the stiffness of the arterial wall was improved. The numerical analysis of the stress distributions permitted to localize the stress concentration through the arterial wall and the probable zone of the rupture of the aneurysm developed from the xenograft rat model.

CONCLUSIONS:

The treatment of AAA with MSCs cultured in a 3D conditions constitutes a new challenge. Based on xenograft rat model, this study shows the potential of this cellular treatment to reduce the variation of the growth, the stiffness and the stress distributions.

Keywords

Abdominal aortic aneurysm cellular therapy inverse finite element method loss of anisotropy

1. Introduction

Abdominal Aortic Aneurysm (AAA) is a local enlargement caused by a weakening aortic wall in the abdominal zone [1,2]. It is well-known that first risk factors that cause an AAA are aging, male gender, cigarette smoking and hypertension. Note that a rupture of AAA has a mortality rate around 90% and it is considered as the third most common reason of cardiovascular death in the world. Currently, when the risk of an abdominal aorta rupture is high, the treatment of AAA is usually a surgery or to place an endovascular stent. It must be emphasized that these treatments are not always satisfactory because a high mortality rate of 5 to 10%. In order, the exact causes of a rupture of AAA are not clearly established but the two speculated factors in determining the rupture of an aneurysm are the enlargement of the diameter and peak wall stress through the arterial wall [3]. Indeed, diameter is the most frequently used parameter in detecting a possible rupture. However, many investigations have shown that small AAA may break while the ones with large diameters may remain stable. It is noticed that studies based on a membrane theory concluded that the diameter of the AAA does not provide a direct interpretation to the risk of rupture [4]. Indeed, the wall curvatures of the AAA also had a very significant influence on the maximum stress of the wall [4,5]. On the other hand, from a mechanical models, a rupture of AAA happens when the intensity of stress exceeds the strength of the wall. This then plays a crucial role to investigate the mechanical behavior of AAA. On the other hand, to improve the treatment of AAA, researches focused on a development of another method to handle the AAA are being done. Thus, fundamental research on animal model was developed from a xenograft rat protocol to test cellular or genetic therapy [6,7]. Note that unlike the elastase rat model [8], the xenograft rat model has the major advantage to generate a thrombus as observed in the human disease. This is important because it has an high role in transmission of the intraluminal pressure through the arterial wall [9,10]. Consequently, based on xenograft rat model, recent researches showed that mesenchymal stem cells (MSCs) are the most promising biotherapy to stabilize AAA and to reduce the stress variations [11,12]. Thus, Zidi and Allaire [11] showed that MSCs cultured in 2D conditions has a promising result as the treatment to stabilize or even to prevent the development of AAAs. This result was obtained from observing less increase in radius and length of the AAA for treated rats compared to the untreated ones. Moreover, based on membrane mechanical theory, it was shown that stress distributions decreased when the therapy is performed [11]. However, it must be emphasized that this approach is limited because MSCs have in vivo 3D environment and it has been proved that it influences their viability [12]. Furthermore, another major limitation that has been pointed out regards the membrane mechanical model that does not allow studying the stress distributions through the wall of AAA [7]. In a previous study [11], authors did not investigate the anisotropy change, even though this was suggested by other studies [3,13].

The objective of the present study is to explore the effects of MSCs cultured in a hyaluronic acid-based (HA) hydrogel on AAA obtained from the xenograft rat model. For that, based on geometrical measurements, AAA was approximated by an ellipsoidal shape with a variable thick. An inverse finite element method was used to investigate the anisotropic properties change of AAA wall made of a transverse isotropy hyperelastic material. Furthermore, the numerical model permitted to localize and to evaluate the peak stresses through the arterial wall in both untreated and treated cases.

2. Materials and methods

2.1. Xenograft rat model

All experiments were approved by the local Ethical Committee for Animal Research and performed in accordance with the European guidelines for animal care (2010/63/UE). The experimental protocol of xenotransplantation [6,12] is described in Fig. 1. Briefly, the abdominal aorta of a male guinea pig is extracted and decelullarized with a detergent, which is then grafted orthotropically to a male Lewis rat. After 14 days (D14), the AAA is created and the xenograft is removed from the blood flow by clamps. To treat the rat, MSCs are extracted from the bone marrow of male Fisher 344 rats, cultured in a HA hydrogel [12,14] and injected and through the lumen of the AAA. The geometrical measurements as diameter, length and thickness of AAA were made after 7 days (D21) in both treated and untreated cases. Thus, 12 rats are studied, 6 for each case and the geometrical measurements were performed under a beating heart before the cellular treatment and at D14 and D21.

2.2. Mechanical behavior of arterial wall

To describe the mechanical behavior of the abdominal aorta wall, the arterial tissue was assumed to be hyperelastic, incompressible and transverse isotropic [15,16]. To minimize the number of material parameters, the transverse isotropy was described by a simple fiber reinforcement defined in the reference configuration by the circumferential direction T. For that, Weiss’s strain energy function was used and given as follows $\begin{eqnarray}\displaystyle \text{W}(\text{I}_{1},\text{I}_{4})=\frac{E}{4(1+{\nu})}[(\text{I}_{1}-3)+{\beta}(e^{(\text{I}_{4}-1)}-\text{I}_{4})], & & \displaystyle\end{eqnarray}$ (1) where E, 𝜈 and 𝛽 are the Young’s Modulus, the Poisson’s ratio and the fiber material parameter respectively. Here, I₁ = tr(C) = tr(B) and I₄ = TCT are the first and the fourth principal strain invariants where C = F F and B = F F are the right and the left Cauchy--Green deformation tensors respectively and F is the deformation gradient tensor with F its transpose.

Furthermore, the incompressible condition leads to take 𝜈 = 0.5. Using (1), the Cauchy stress tensor 𝝈 is then written as $\begin{eqnarray}\displaystyle \boldsymbol{\sigma}=-\text{p}\mathbf{1}+2\frac{\partial \text{W}}{\partial \text{I}_{1}}\mathbf{B}+2\text{I}_{4}\frac{\partial \text{W}}{\partial \text{I}_{4}}\mathbf{t}\otimes \mathbf{t}, & & \displaystyle\end{eqnarray}$ (2) where p is the Lagrange multiplier enforcing the incompressibility condition, 1 is the identity tensor and $\mathbf{t}=\mathbf{FT}/\sqrt{\mathrm{I}_{4}}$ is the fiber reinforcement direction in the current configuration.

Thus, there are only two material parameters to be optimized, those are E and 𝛽 which described the elastin matrix and the fibrous component stiffness contributions in the AAA wall.

On the other hand, to study the mechanical behaviour of AAA wall, uniaxial mechanical tension may be simulated in the fiber direction by using the optimized values of 𝜞 = [E, 𝛽]. As a result, when tension along axis 1 is considered, yields the analytical deformation and stress as follows $\begin{eqnarray}\displaystyle x_{1}={\lambda}a_{1},\quad x_{2}={\lambda}^{-\frac{1}{2}}a_{2},\quad x_{3}={\lambda}^{-\frac{1}{2}}a_{3}, & & \displaystyle\end{eqnarray}$ (3) $\begin{eqnarray}\displaystyle {\sigma}_{11}={\sigma},∼{\sigma}_{ij}=0\quad \text{for others components of Cauchy stress tensor }\boldsymbol{\sigma}, & & \displaystyle\end{eqnarray}$ (4) where a _i and x _i are the reference and the current Cartesian coordinates respectively and 𝜎 is the magnitude of the traction at stretch 𝜆.

Thus, from (1), (2) and (3), it is straightforward to calculate the mechanical response in tension as $\begin{eqnarray}\displaystyle {\sigma}=\frac{E}{2(1+{\nu})}\left({\lambda}^{2}-\frac{1}{{\lambda}}\right)+2{\beta}{\lambda}^{2}(e^{({\lambda}^{2}-1)}-1). & & \displaystyle\end{eqnarray}$ (5)

2.3. Inverse finite element model

To investigate the mechanical properties change of the arterial provoked by AAA, an inverse finite element method has been employed. The numerical model has been built upon the software Feap V8.4 [17] where AAA was considered as a thick symmetric ellipsoidal shape (Fig. 2). Note that this form represents only the AAA part without the healthy artery. It is also noticed that the thickness of AAA has been considered varying where the thickest part is located in the middle due to the presence of the thrombus. In the upper and lower part of the wall, the thickness is similar to a healthy wall. Thus, the geometry can be easily constructed by using a transformation from elliptic coordinates (q ₁, q ₂, q ₃) to the Cartesian coordinates (x ₁, x ₂, x ₃). The transformation is given by $\begin{eqnarray}\displaystyle \left\{\begin{array}{@{}l@{}}x_{1}=c\sqrt{q_{1}^{2}-1}\sqrt{1-q_{3}^{2}}\cos q_{2}\\ x_{2}=c\sqrt{q_{1}^{2}-1}\sqrt{1-q_{3}^{2}}\sin q_{2}\\ x_{3}=cq_{1}q_{3}\\ \end{array}\right., & & \displaystyle\end{eqnarray}$ (6) where c is the focal distance.

It must be emphasized that several geometrical ratios were fixed as deformed length/initial length, deformed maximum external radius/ initial maximum external radius and deformed minimum external radius/ initial minimum external radius. They are taken respectively to 1.4, 1.0 and 1.0 and based on experimental measurements [18,19]. In addition, a loading condition of an uniform intraluminal pressure is imposed and corresponds to the measured mean pressure during the cardiac cycle as 100 mmhg. Because of the symmetries of the problem, only one eighth of AAA was meshed with linear hexahedral elements. Furthermore, residual stresses is neglected for AAA obtained from xenograft rat model [19]. On the other hand, the inverse finite element procedure has permitted to calculate the optimum value of 𝜞 = [E, 𝛽] with the considered strain-energy function (1). For that, the objective function is given by $\begin{eqnarray}\displaystyle f=(r_{M_{n}}-r_{M_{e}})^{2}+({\sigma}_{\mathit{VM}_{n}}-{\sigma}_{\mathit{VM}_{a}})^{2} & & \displaystyle\end{eqnarray}$ (7) where r _{M
_n}, r _{M
_e}, 𝜎_{VM
_n}, 𝜎_{VM
_a} are the numerical radius, the experimental measured radius, the numerical Von-Mises stress and the analytical membrane Von-Mises stress [7] respectively. The optimization procedure used a nonlinear least-squares minimization in Matlab R2014b (Mathworks Inc., USA). It must be emphasized that optimal values of 𝜞 = [E, 𝛽] were perturbed by ±0.1% and parameter identifications were re-performed to ensure the stability of the solutions with resulting variations of parameters below 1%.

2.4. Statistics

All experimental data were obtained as mean ± standard error (SE). Statistical analysis was performed by one-way ANOVA followed by Mann-Whitney U test and p < 0.05 was considered statistically significant.

3. Results and discussions

The geometrical measurements during the growth of AAA obtained from the xenograft model are given in Table 1. These results correspond to the treatment of AAA by using MSCs cultured in 2D culture conditions or in a HA hydrogel [12]. Thus, the effects of cellular treatment on geometrical changes of AAAs were investigated between D14 and D21.

Clearly, in comparison with the results obtained by a 2D culture [11], treatment with MSCs cultured in the HA hydrogel decreases more significantly the growth of AAAs.

On the other hand, the results of the optimized values 𝜞 = [E, 𝛽] of Weiss strain-energy function were obtained by the inverse finite element method based upon (7). They are given in Table 2.

It was shown that the parameter E increases by a greater amount (an increase of 0.026 MPa), compared to the treated case which is 0.003 MPa. Thus, we observed that the rigidity of the untreated artery wall increases much more than the treated case. It also appears that the fiber reinforcement of two untreated and treated cases no longer plays the role on the mechanical behavior of arterial wall. Indeed, it is striking to notice that the parameter 𝛽 is very close to zero and it clearly appears that the AAA tends to be isotropic vascular tissue. Note that these results are similar to those obtained with elastase rat model [20]. Thus, it should be noted that the cellular treatment does not reestablish the anisotropy which initially exists in healthy artery [15,21]. It must be also emphasized that regarding the anisotropy in the human AAA case, previous studies conclude differently showing an increased anisotropy [22] whereas others suggest it can be considered as isotropic [23]. This isotropy obtained may be due to the reorganization of the microconstituents of the artery wall seen on histological sections [12].

Furthermore, by using (5) with material parameters values given in Table 2, the uniaxial stress response of AAA wall may be illustrated (Fig. 3). It is then confirmed that the stiffness of the AAA wall increases in the untreated case compared to the treated one.

On the other hand, it is well-known that AAA is a complex disease that can be deadly when a rupture happens. For that reason, the distribution of Von-Mises stress has been calculated and investigated for the proposed approach based on the xenograft rat model. It is seen that the maximum intensity of the stress can be found in the junction of AAA and healthy artery (Fig. 4). Hence, it can also be concluded that the most probable zone of the rupture is in this junction. Also, the maximum Von-Mises stress is given in Table 3. It is then shown that the maximum Von-Mises stress increases a lot by more than 80%, and it increases on the treated case by less than 10%. Thus, the proposed numerical model indicates that the cellular treatment prevents the increase of the maximum stress of the wall.

4. Limitations

The proposed numerical approach uses an ideal geometry of AAAs. Even if further study with a more realistic geometry might be conducted, the present work has permitted to investigate the growth of AAAs and their mechanical properties change in the xenograft rat model. Thus, based on an inverse finite element method, the results show a loss of anisotropy of AAA wall. Note that the strain-energy function is here limited to two global material parameters. Indeed, different previous studies [13,15] considered the artery wall composed of an isotropic matrix material with two or four families of fibers with complex orientations. Furthermore, although arteries display an viscoelastic behavior when aneurysm [24] or atherosclerosis [25] are present, the proposed study focused on an elastic analysis. Thus, a visco-hyperelastic behavior law could be used to better investigate arterial wall mechanics in pathological conditions. However, sur-parametrization appears and would require robust optimization procedures.

5. Conclusion

The proposed study investigates the mechanical properties change of the AAA wall obtained from the xenograft rat model when cellular therapy with MSCs was used. It is shown that MSCs cultivated in an HA-based hydrogel, which reproduces a realistic in vivo environment, are more performant to decrease the growth of AAAs. Furthermore, based an inverse finite element analysis, it is obtained a loss of anisotropy of arterial wall both in untreated and treated case. It is also concluded that the cellular treatment decreases the rigidity of the wall and the maximum stress which then decreases the risk of rupture as well. These results tend to show that the proposed cellular treatment is better than the previous therapy based on MSCs cultured in 2D conditions. Thus, this contribution may be a challenge of this fundamental research concerning to help the development of cellular therapies to treat AAA.

Footnotes

Acknowledgements

This work is supported by CNRS, University Paris-Est Créteil and the European Union Grant (FP7- Health-200647, Fighting Aneurysmal Diseases). The authors gratefully acknowledge Dr. Faiza Mohand-Kaci and Dr Louise Marais (University Paris-Est Créteil, France) for their help in the experimental protocols.

Conflict of interest

None to report.

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