Biometric values for the sampled tissues.
The symbiosis between the terms nature (plants, animals) and engineering has gained a large interest from the bioengineering research community (Bronzino, 2006). The concept is based on the idea that life has simple and effective rules to provide the highest efficiency with minimal requirements for energy resources and food supply. The result is a diversity of biomimetic systems, serving either biological replacements of tissue or organs (e.g. tissue engineering, artificial and bio-artificial organs), either purely technological process (e.g. swarm control, unmanned aerial vehicles, water and aerial vehicles, etc) (Cohen, 2006; Chirita, 2009).
The future of medicine is no longer ignorant to the adaptability of life forms to various environmental conditions and to various purposes, but it integrates these aspects as part of the intrinsic process of efficient evolution. Nowadays, biomaterials are becoming a
Recently, the term of
By copying ideas from nature and by implementing these simple yet effective procedures, the quality of a manifold of engineering processes can be increased significantly. However, the general problem of bioengineers remains the same: the manufacturing costs and healthcare risks. By definition, nature offers intrinsic solutions, produced by a natural chain of bio-chemical interactions. Hence, the regulation of all biological processes is more efficient in the nature than in an artificial framework. The biological feedback remain a key element in the maintenance of this intrinsic efficiency that nature performs on all living organisms. The intrinsic property of these natural materials with specific material properties and dynamic performance, is that of a highly-optimized, strictly defined structure and inter-relation of these structures to form living organisms.
Biopolymers are polymers produced by living organisms. Cellulose, starch, chitin, proteins, peptides, DNA and RNA are all examples of biopolymers, in which the monomeric units, respectively, are sugars, amino acids, and nucleotides. Chitin is a macromolecule found in the shells of crabs, lobsters, shrimps and insects. Chitin can be degraded by chitinase. Chitin fibers have been utilized for making artificial skin and absorbable sutures (Chirita, 2008). Chitin is insoluble in its native form but chitosan, the partly deacetylated form, is water soluble. The materials are biocompatible and have antimicrobial activities as well as the ability to absorb heavy metal ions. They also find applications in the cosmetic industry because of their water-retaining and moisturizing properties. Using chitin and chitosan as carriers, a water-soluble prodrug has been synthesized. Modified chitosans have been prepared with various chemical and biological properties (Chirita, 2001). Optical microscopy shows that those films that contain a lower amount of calcium and a higher content of silica are more uniform in appearance (Ionescu and Chirita, 2008). Collagen and elastin are extracellular matrix structural proteins that are important stress-bearing constituents of tissues. These fibers differ significantly in their mechanical properties, with collagen being three to four orders of magnitude stiffer than elastin. The advantages of using collagen products in medicine are its very low antigenicity, excellent histocompatibility, ease of association with other biologically active species such as glycose-aminoglycans, and its polyelectrolytic behavior. The reconstitution of collagen from solution into native fibers is also of interest because of its regenerative applications (Archer and Ralph, 2010; Hariton et al, 2007). For example, the fibroin produced by the silk worms (Bombix Mori), respectively the dragline produces by a kind of spider (Nephila Clavipes) are two examples of fibroid polymer which pose intrinsic resistance, elasticity and biocompatibility.
Another important aspect is that of structural optimization. Hierarchical structures are by definition a complex of micro- and macro-molecules, inter-woven by similar structures. This leads to the concept of multi-level hierarchies, which pose specific properties. In the case of wood cellulose, or cartilage collagen, the specific multi-level structure offers a manifold of applications (biomaterial properties). Within the process of natural growth, the biomaterial properties are of crucial importance, since they can lead to soft or hard tissue consistency. Nowadays, the progress in tissular replacement engineering has enabled the combination of biomaterials with regenerative characteristics, allowing the tissue to grow and interact with the natural tissue. Hitherto, the artificial materials (biomaterials) have not yet become as proficient as the natural materials, but efforts are being made in the field of vascular grafts (Chirita, 2009).
Many studies have been undertaken to develop acceptable small diameter vascular prostheses. Detailed knowledge of the mechanical properties of the arterial wall is crucial for understanding the changes which occur in the vascular system in case of arterioscleroses and aneurysm disease. The atherosclerosis is the essential characteristic of pathologies pressure causing diseases at the arterial level (e.g. plaque rupture, myocardial infarction, death ischemic. Hence, it is crucial to obtain constitutive equations that describe the mechanical properties of native tissues which can be used for diagnostic purposes (Mandru et al, 2009). The tissue growth, the blood clotting and the affecting blood elements are influenced by surface energy. Hence, the additional knowledge of the static contact angle, free surface energy, the interfacial tension and the critical superficial tension become essential for the purpose of medical replacements.
In this paper we present an overview of parametric models for the stress-strain relationship in artificial tissues for vascular replacements. Their values are compared to those of native tissues. The paper provides contributions in modeling aspects and in experimental analysis. The models and indexes presented in this chapter will help researchers gather insight into the required properties for restoration and hemo-compatibility of the native tissue and their relation to the desired properties in the synthetic tissues. As such, these properties are crucial in the improvement of natural inclusion, tissue compatibility and growth.
2. Materials and measurement protocol
The samples for native tissue assessment have been prevailed from three pigs, as presented in (Mandru et al, 2009). A biometric description of the sampled tissues is given in Table 1,
|Sample||Longitudinal length (mm)||Transversal length (mm)||Longitudinal width (mm)||Transversal width (mm)||Thickness (mm)|
The traction device depicted by figure 2 consists of a framework capable of bearing the major strengths, a fixed wooden plate, as well as a system able to apply the various testing force values.
The device is scheduled to pull the two extremes of the sample tested at a constant speed and to register continuous and simultaneous the strain of the sample. The system contains:
Figure 3 depicts the materials, cut in rectangular shapes with a custom-designed die of various sizes: 30 or 50 mm. The thicknesses of the tissue samples were determined in cross-sections by aid of optical microscopy. After the shape and dimension of the sample was determined, the sample was attached to the test-frame of the traction device, while fixed at its cephalic and caudal ends by using a custom-designed gripping device, specially developed to prevent slippage. The gripping device consisted of two opposing metal blocks fastened together to fix the inferior and superior ends. The measured stress-strain relationship are depicted in figure 4, for the longitudinal carotid artery, longitudinal and transversal thoracic aorta.
2. Parametric modelling
The parametric models presented in this chapter are based on power law modelling principles (Gao et al, 2007). These are compared to polynomial models, which are basic tools for data analysis (Ljung, 1999). For the first type of models, the corresponding energy feature was calculated using the Abaques® software platform. Since the modules of elasticity are not the most appropriate parameters to describe the arterial wall subjected to different deformation, the suggested models characterizing the features of energy seem to deliver more insight in the mechanical properties of the materials. Using the relation:
where denotes the stress (MPa), denotes the strain (%) and
The model parameters were estimated using a nonlinear least square optimization algorithm, making use of the MatLab® function LSQNONLIN. The optimization algorithm is a subspace trust region method and is based on the interior-reflective Newton method described in (Coleman and Li, 1996). The large-scale method for LSQNONLIN requires that the number of equations (i.e. the number of elements of cost function) must be at least as large as the number of variables. The large-scale method for lsqnonlin requires that the number of equations (
3. Results and discussion
The energy feature for carotid and thoracic artery using (1) was optimally captured by a 5th and a 6th order polynomial, respectively. The identified polynomial coefficients are given in Table 2, in which
For the power-law model coefficients, the values are given in Table 3. The corresponding modeling errors are given in Table 4. Although the polynomial representation offers minimal modeling errors, it has the dis-advantage of high number of parameters to be identified. On the other hand, at the expense of somewhat higher modeling errors, the power-law model from (2) has only three parameters to be identified. The identified model parameters are given in tables 3-4-5, along with the corresponding modelling errors, for the models (2), (3) and (4) respectively. For all models, the native data samples were
|longitudinal thoracic artery||0.029||0.070||0.011||-1.53||3.741||3.040||0,000|
From figures 5-7 one may conclude that all models capture reasonably well the experimental data. Notice that the identification was not subject to any physiological constraints, since no reference data was available apriori. The model from (2) was clearly outperformed by model (3), while model (4) could not reduce the modelling errors in a significant manner. The residual norm seemed to give most stable trend of error decrease as model complexity increases. All models seemed to best capture properties in the transversal thoracic aorta, perhaps due to a stronger nonlinear behavior. This suggests that non-constitutive models (i.e. lumped models) can prevalently describe native tissues with higher nonlinearity, without increasing significantly the numerical complexity of the model structure.
For all three sets of data, the two parts of the model from (4): and have different contribution related to two stress segments. In the first part, for
The variations in the magnitude of the model parameters can be related to variations in the data input (strain). A possible origin for the high variations in the first model parameter is that for lower strains, the power-law has smaller variations for higher values of parameters (saturation for strain variations with respect to variations in the model parameter). After a threshold value, the power law which takes into account both collagen and elastin distribution becomes less important with respect to the exponential term. It is difficult to compare our identified model parameters with data from literature, due to a lack of available information. To the authors knowledge, such lumped models do not exist in the literature on the respective native tissue.
In similar studies on dog arteries, deformations were computed using the dimensions of the unloaded free-floating vessel segment as a reference value (Dobrin, 1999). Blood vessels adapt morphologically and mechanically to increased wall stress. Some authors suggest that deformations should not be computed with respect to the retracted, unloaded state because the vessels never exist in vivo at these dimensions. Moreover, when fully unloaded, the vessels manifest evidence of residual stresses, ie, residual compression near the intima and residual tension near the outer margin of the media (Fung, 1990). As a result, when a ring of artery is transected, it springs open to assume a larger radius. All of these observations imply a highly integrated, interlocked anatomic system of elastin and vascular muscle where one element, elastin, cannot be extended without extending the other, i.e. the attached vascular muscle cells. Enzymatic degradation studies in vitro and physiological analysis in vivo suggest that the collagen fibers are loose, without substantially load-bearing at low and physiological pressures (Fung, 1990). These observations, coupled with observed uniformity of response of the elastic lamellae across the wall suggest that the artery wall behaves mechanically as though it were a homogeneous material, despite its marked histologic heterogeneity (Dobrin, 1999; Fung, 1990).
This chapter provides an overview of available tools and several parametric models to characterize the mechanical properties in both native and artificial tissues. A manifold of native tissue samples are analyzed and characterized. A novel concept has been presented for determining the mechanical properties of native and biomimetically formed arterial tissue using data from the energy function. The results have been found to be dependent on the surrounding environment, the existence of preconditioning, the static and dynamic experiments, e.g. the length of tissue specimen, the type of load, the loading speed, the sampled surface, the values and intervals of load variations, the residual strains, etc. The mechanical properties of the tissues may also depend on the status of the donor, as well as the conservation conditions of native tissues.
Furthermore, we presented alternative lumped models for stress-strain relationships in native tissues, capturing well the intrinsic properties.
This paper represent a part of un graduation work and is realized with the help of an Erasmus student mobility at the Higher Institute of Bio-Science, University Paris 12, France, based on a bilateral agreement with the Faculty of Medical Bio-Engineering, Iasi, Romania. The results presented in this paper are also realized in collaboration with the Research Institute „Petru Poni”, Departement of Polyadditon, Iasi, Romania. The authors acknowledge the technical support from the members of Surgical Center Henri Mondor, University Paris 12, France, and from the Research Institute „Petru Poni”, Departement of Polyadditon, Iasi, Romania.