A theoretical model for fibroblast-controlled growth of saccular cerebral aneurysms

A new theoretical model for the growth of saccular cerebral aneurysms is proposed by extending the recent constitutive framework of Kroon and Holzapfel [2007a. A model for saccular cerebral aneurysm growth by collagen fibre remodelling. J. Theor. Biol. 247, 775-787]. The continuous turnover of collagen is taken to be the driving mechanism in aneurysmal growth. The collagen production rate depends on the magnitude of the cyclic deformation of fibroblasts, caused by the pulsating blood pressure during the cardiac cycle. The volume density of fibroblasts in the aneurysmal tissue is taken to be constant throughout the growth process. The growth model is assessed by considering the inflation of an axisymmetric membranous piece of aneurysmal tissue, with material characteristics representative of a cerebral aneurysm. The diastolic and systolic states of the aneurysm are computed, together with its load-free state. It turns out that the value of collagen pre-stretch, that determines growth speed and stability of the aneurysm, is of pivotal importance. The model is able to predict aneurysms with typical berry-like shapes observed clinically, and the predicted wall stresses correlate well with the experimentally obtained ultimate stresses of this type of tissue. The model predicts that aneurysms should fail when reaching a size of about 1.2-3.6 mm, which is smaller than what has been clinically observed. With some refinements, the model may, however, be used to predict future growth of diagnosed aneurysms.     

A computational model for collagen fibre remodelling in the arterial wall

As the interaction between tissue adaptation and the mechanical condition within tissues is complex, mathematical models are desired to study this interrelation. In this study, a mathematical model is presented to investigate the interplay between collagen architecture and mechanical loading conditions in the arterial wall. It is assumed that the collagen fibres align along preferred directions, situated in between the principal stretch directions. The predicted fibre directions represent symmetrically arranged helices and agree qualitatively with morphometric data from literature. At the luminal side of the arterial wall, the fibres are oriented more circumferentially than at the outer side. The discrete transition of the fibre orientation at the media-adventitia interface can be explained by accounting for the different reference configurations of both layers. The predicted pressure-radius relations resemble experimentally measured sigma-shaped curves. As there is a strong coupling between the collagen architecture and the mechanical loading condition within the tissue, we expect that the presented model for collagen remodelling is useful to gain further insight into the processes involved in vascular adaptation, such as growth and smooth muscle tone adaptation.     

A disorder of collagen biosynthesis in patients with cerebral artery aneurysm

12 patients with subarachnoid hemorraghe due to rupture of a cerebral aneurysm were examined clinically for symptoms and signs of a connective tissue disorder and biochemically for details of the biosynthesis of collagen. No uniform clinical pattern of any connective tissue disorder was seen in these patients, although selected signs were observed. Skin fibroblast cultures were then established. The rate of procollagen production in two cell lines was reduced by 40% and 50%, respectively, and the intracellular accumulation of hydroxyl[¹⁴C]proline (as a percentage of total hydroxy[¹⁴C]proline) was increased by 70% in each relative to eight control cell lines. No difference was found in the degree of intracellular degradation of procollagen. After pulse-labelling, however, the radioactive procollagen was secreted into the medium in 1 h in the control cells, but required at least 3 h in the two aneursym patient cell lines. The results, thus, suggest that delayed secretion of procollagen rather than increased intracellular degradation led to the reduction in the rate of procollagen synthesis in these two fibroblast lines from patients with cerebral artery aneurysm.     

A generalized packing model for type I collagen

Only tail tendon (TT) collagen has a sharp X-ray diffraction pattern, so that packing models for the equatorial arrangement of molecules in collagen fibrils have been developed primarily for TT collagen. A more general structure is developed applicable to all type I collagen tissues. Comparison of water content-equatorial diffraction spacing plots of several collagens shows all have essentially the same dry state diffraction spacing but differ as water content increases. TT collagen has the least spacing and the sharpest pattern. The interplanar spacing of the Hulmes-Miller quasi-hexagonal model for TT collagen was used to calculate the intermolecular spacing, which matched the observed diffraction spacing for bone matrix collagen. It is inferred that wet bone matrix collagen packs in a rectangular pattern because of the interaction between the many intermolecular crosslinks and the water absorbed on the collagen molecules. This argument also indicates that TT collagen packs into a quasi-hexagonal scheme because there are fewer intermolecular crosslinks than in bone matrix collagen.     

A nonlinear dynamical mechanism for bruit generation by an intracranial saccular aneurysm

 Intracranial saccular aneurysms have been clinically observed to emit a transient sound, a bruit, on each heartbeat. The mechanism causing the bruits has been a matter of contention. A qualitative analysis of the nonlinear dynamical properties of the Shah-Humphrey model for periodic pressure forcing of a thin-necked saccular aneurysm, using the Fung nonlinear constitutive model for the aneurysm material, shows that a small blood pressure jump on each beat, whether the pressure is weakly aperiodic or periodic, induces transients in the radial deformation response of the aneurysmal wall on each heartbeat. These transient vibrations, which have a component with frequency near the natural frequency of the system but are not resonant phenomena and which decay rapidly to a limit cycle during each distinct forcing pressure cycle, can generate the bruits. Received: 21 November 2000 / Revised version: 9 August 2001 / Published online: 23 August 2002 Mathematics Subject Classification (2000): 92B99, 70K40, 70K05 Key words or phrases: Intracranial saccular aneurysm – Bruit – Spectrum – Nonlinear dynamics – Transients – Vortex shedding – Fung model     

A fibre reorientation model for orthotropic multiplicative growth

The main goal of this contribution consists in the development of a remodelling framework for orthotropic continua whereby the underlying symmetry group is incorporated via two fibre families. Special emphasis is placed on the modelling of biological tissues at finite deformations. Besides the incorporation of a referential mass source, anisotropic growth is addressed by means of a multiplicative decomposition of the overall deformation gradient into an elastic and a growth distortion. Projected quantities of a configurational growth stress tensor are advocated as driving forces for time-dependent saturation–type evolution of the principal values of the growth distortion. Moreover, the reorientation of both fibre families, which directly affects the strain energy as well as the growth distortion itself, is guided by analyzing critical energy points. In particular, a time-dependent formulation is developed which aligns the fibre directions according to the principal stretch directions. Finally, the proposed framework is embedded into a finite element context so that representative numerical examples, examining growth and resorption in volume and density together with fibre reorientation, close this study.     

Inverse method of stress analysis for cerebral aneurysms

We present a method for predicting the wall stress in a class of cerebral aneurysms. The method hinges on an inverse formulation of the elastostatic equilibrium problem; it takes as the input a deformed configuration and the corresponding pressure, and predicts the wall stress in the given deformed state. For a membrane structure, the inverse formulation possesses a remarkable feature, that is, it can practically determine the wall tension without accurate knowledge of the wall elastic properties. In this paper, we present a finite element formulation for the inverse membrane problem and perform material sensitivity studies on idealized lesions and an image-based cerebral aneurysm model.     

A bone remodelling model coupling microdamage growth and repair by 3D BMU-activity

Bone as most of living tissues is able, during its entire lifetime, to adapt its internal microstructure and subsequently its associated mechanical properties to its specific mechanical and physiological environment in a process commonly known as bone remodelling. Bone is therefore continuously renewed and microdamage, accumulated by fatigue or creep, is removed minimizing the risk of fracture. Nevertheless, bone is not always able to repair itself completely. Actually, if bone repairing function is slower than microdamage accumulation, a type of bone fracture, usually known as stress fracture, can finally evolve. In this paper, we propose a bone remodelling continuous model able to simulate microdamage growth and repair in a coupled way and able therefore to predict the occurrence of stress fractures. The biological bone remodelling process is modelled in terms of equations that describe the activity of basic multicellular units. The predicted results show a good correspondence with experimental and clinical data. For example, in disuse, bone porosity increases until an equilibrium situation is achieved. In overloading, bone porosity decreases unless the damage rate is so high that causes resorption or stress fracture.Research partially supported by Diputación General de Aragón project P–008/2001) and National Network IM3 (Molecular and Multimodal Medical Imaging, Spanish Ministry of Health, Associated Partner, 300++, 2003-2005)     

Observing growth steps of collagen self-assembly by time-lapse high-resolution atomic force microscopy

Insights into molecular mechanisms of collagen assembly are important for understanding countless biological processes and at the same time a prerequisite for many biotechnological and medical applications. In this work, the self-assembly of collagen type I molecules into fibrils could be directly observed using time-lapse atomic force microscopy (AFM). The smallest isolated fibrillar structures initiating fibril growth showed a thickness of approximately 1.5 nm corresponding to that of a single collagen molecule. Fibrils assembled in vitro established an axial D-periodicity of approximately 67 nm such as typically observed for in vivo assembled collagen fibrils from tendon. At given collagen concentrations of the buffer solution the fibrils showed constant lateral and longitudinal growth rates. Single fibrils continuously grew and fused with each other until the supporting surface was completely covered by a nanoscopically well-defined collagen matrix. Their thickness of approximately 3 nm suggests that the fibrils were build from laterally assembled collagen microfibrils. Laterally the fibrils grew in steps of approximately 4 nm, indicating microfibril formation and incorporation. Thus, we suggest collagen fibrils assembling in a two-step process. In a first step, collagen molecules assemble with each other. In the second step, these molecules then rearrange into microfibrils which form the building blocks of collagen fibrils. High-resolution AFM topographs revealed substructural details of the D-band architecture of the fibrils forming the collagen matrix. These substructures correlated well with those revealed from positively stained collagen fibers imaged by transmission electron microscopy.     

A mathematical model for the growth of the abdominal aortic aneurysm

We present the first mathematical model to account for the evolution of the abdominal aortic aneurysm. The artery is modelled as a two-layered, cylindrical membrane using nonlinear elasticity and a physiologically realistic constitutive model. It is subject to a constant systolic pressure and a physiological axial prestretch. The development of the aneurysm is assumed to be a consequence of the remodelling of its material constituents. Microstructural recruitment and fibre density variables for the collagen are introduced into the strain energy density functions. This enables the remodelling of collagen to be addressed as the aneurysm enlarges. An axisymmetric aneurysm, with axisymmetric degradation of elastin and linear differential equations for the remodelling of the fibre variables, is simulated numerically. Using physiologically determined parameters to model the abdominal aorta and realistic remodelling rates for its constituents, the predicted dilations of the aneurysm are consistent with those observed in vivo. An asymmetric aneurysm with spinal contact is also modelled, and the stress distributions are consistent with previous studies.     

A role for glycosaminoglycans in the development of collagen fibrils

Extensive data on the glycosaminoglycan (GAG) composition and the collagen fibril diameter distribution have been collected for a diverse range of connective tissues. It is shown that tissues with the smallest diameter collagen fibrils (mass-average diameter less than 60 nm) have high concentrations of hyaluronic acid and that tissues with the largest diameter collagen fibrils (mass-average diameter approximately 200 nm) have high concentrations of dermatan sulphate. It is suggested that the lateral growth of fibrils beyond a diameter of about 60 nm is inhibited by the presence of an excess of hyaluronic acid but that this inhibitory effect may be removed by an increasing concentration of chondroitin sulphate and/or dermatan sulphate. It is also postulated that high concentrations of chondroitin sulphate will inhibit fibril growth beyond a mass-average diameter of approximately 150 nm. Such an inhibition may in turn be removed by an increasing concentration of dermatan sulphate such that it becomes the dominant GAG present in the tissue.     

Radio aneurysm coils for noninvasive detection of cerebral embolization failures: a preliminary study

The rupture of a cerebral aneurysm is the most common cause of subarachnoid hemorrhage. Endovascular embolization of the aneurysms by implantation of Guglielmi detachable coils (GDC) has become a major treatment approach in the prevention of a rupture. Implantation of the coils induces formation of tissues over the coils, embolizing the aneurysm. However, blood entry into the coiled aneurysm often occurs due to failures in the embolization process. Current diagnostic methods used for aneurysms, such as X-ray angiography and computer tomography, are ineffective for continuous monitoring of the disease and require extremely expensive equipment. Here we present a novel technique for wireless monitoring of cerebral aneurysms using implanted embolization coils as radiofrequency resonant sensors that detect the blood entry. The experiments show that commonly used embolization coils could be utilized as electrical inductors or antennas. As the blood flows into a coil-implanted aneurysm, parasitic capacitance of the coil is modified because of the difference in permittivity between the blood and the tissues grown around the coil, resulting in a change in the coil's resonant frequency. The resonances of platinum GDC-like coils embedded in aneurysm models are detected to show average responses of 224–819 MHz/ml to saline injected into the models. This preliminary demonstration indicates a new possibility in the use of implanted GDC as a wireless sensor for embolization failures, the first step toward realizing long-term, noninvasive, and cost-effective remote monitoring of cerebral aneurysms treated with coil embolization.     

Novel chitosan/collagen scaffold containing transforming growth factor-beta1 DNA for periodontal tissue engineering

The current rapid progression in tissue engineering and local gene delivery system has enhanced our applications to periodontal tissue engineering. In this study, porous chitosan/collagen scaffolds were prepared through a freeze-drying process, and loaded with plasmid and adenoviral vector encoding human transforming growth factor-beta1 (TGF-beta1). These scaffolds were evaluated in vitro by analysis of microscopic structure, porosity, and cytocompatibility. Human periodontal ligament cells (HPLCs) were seeded in this scaffold, and gene transfection could be traced by green fluorescent protein (GFP). The expression of type I and type III collagen was detected with RT-PCR, and then these scaffolds were implanted subcutaneously into athymic mice. Results indicated that the pore diameter of the gene-combined scaffolds was lower than that of pure chitosan/collagen scaffold. The scaffold containing Ad-TGF-beta1 exhibited the highest proliferation rate, and the expression of type I and type III collagen up-regulated in Ad-TGF-beta1 scaffold. After implanted in vivo, EGFP-transfected HPLCs not only proliferated but also recruited surrounding tissue to grow in the scaffold. This study demonstrated the potential of chitosan/collagen scaffold combined Ad-TGF-beta1 as a good substrate candidate in periodontal tissue engineering.     

A therapeutic approach for diabetic wound healing using biotinylated GHK incorporated collagen matrices

Chronically elevated blood glucose levels result in reduced leukocyte function and cell malnutrition, which contribute to a high rate of wound infection and associated healing problems in diabetic patients. In the present study, the role of biotinylated GHK peptide (BioGHK) incorporated collagen biomaterial was tested for wound healing in diabetic rats. The rate of wound contraction and the levels of collagen, uronic acid, protein and DNA in the granulation tissue were determined. Further, the concentration of nitric oxide and other skin antioxidants was also monitored during the study. In diabetic rats treated with BioGHK incorporated collagen (Peptide Incorporated Collagen--PIC), the healing process was hastened with an increased rate of wound contraction. Glutathione (GSH) and ascorbic acid levels in the skin of streptozotocin-induced diabetic rats were higher in the PIC group as compared to control (Untreated) and collagen (Collagen Film--CF) treated groups. Superoxide dismutase (SOD) and catalase (CAT) activity was altered in all the groups. In vitro fibroblast cell culture studies suggest that PIC promotes fibroblast growth. Histological evaluation by haematoxylin-eosin and Masson's trichrome method revealed epithelialization, increased synthesis of collagen and activation of fibroblasts and mast cells in the PIC group. This study provides a rationale for the topical application of BioGHK incorporated collagen as a feasible and productive approach to support diabetic wound healing.     

Enhanced global mathematical model for studying cerebral venous blood flow

Here we extend the global, closed-loop, mathematical model for the cardiovascular system in Müller and Toro (2014) to account for fundamental mechanisms affecting cerebral venous haemodynamics: the interaction between intracranial pressure and cerebral vasculature and the Starling-resistor like behaviour of intracranial veins. Computational results are compared with flow measurements obtained from Magnetic Resonance Imaging (MRI), showing overall satisfactory agreement. The role played by each model component in shaping cerebral venous flow waveforms is investigated. Our results are discussed in light of current physiological concepts and model-driven considerations, indicating that the Starling-resistor like behaviour of intracranial veins at the point where they join dural sinuses is the leading mechanism. Moreover, we present preliminary results on the impact of neck vein strictures on cerebral venous hemodynamics. These results show that such anomalies cause a pressure increment in intracranial cerebral veins, even if the shielding effect of the Starling-resistor like behaviour of cerebral veins is taken into account.     

A structural constitutive model for the human lens capsule

Published data on the mechanical performance of the human lens capsule when tested under uniaxial and biaxial conditions are reviewed. It is concluded that two simple phenomenological constitutive models (namely a linear elastic model and a Fung-type hyperelastic model) are unable to provide satisfactory representations of the mechanical behaviour of the capsule for both of these loading conditions. The possibility of resolving these difficulties using a structural constitutive model for the capsule, of a form that is inspired by the network of collagen IV filaments that exist within the lens capsule, is explored. The model is implemented within a rectangular periodic cell. Prescribed stretches are imposed on the periodic cell and the network is allowed to deform in a non-affine manner. The performance of the constitutive model correlates well with previously published test data. One possible application of the model is in the development of a multi-scale analysis of the mechanics of the human lens capsule.