Computationally modelling cell proliferation: A review.

Cell proliferation is vital for the development and homeostasis of the human body. For such to occur, cells go through the cell cycle during which they replicate their genetic material and ultimately complete cellular division, when one cell divides into two new cells with equal genetic material. However, if there are some errors or abnormalities during the cell cycle that disrupt the balance between cell death and proliferation, severe problems can occur, such as tumour development, which is currently one of the leading causes of death in the world. Nowadays, mathematical and computational models are used to understand and study several biological mechanisms and processes, namely cellular proliferation. Over the last forty-five years, several models have attempted to describe cell proliferation and its regulation. Due to the complexity of the process, numerous assumptions and simplifications have been considered. This work presents a review of some of these models, focusing mainly on mammalian or generic eukaryotic models. Previously published continuum, discrete and hybrid approaches are presented and compared, in order to understand and highlight the relevance and capabilities of these models, their shortcomings and future challenges.

Computational simulation of cellular proliferation using a meshless method.

BACKGROUND AND OBJECTIVE: During cell proliferation, cells grow and divide in order to obtain two new genetically identical cells. Understanding this process is crucial to comprehend other biological processes. Computational models and algorithms have emerged to study this process and several examples can be found in the literature. The objective of this work was to develop a new computational model capable of simulating cell proliferation. This model was developed using the Radial Point Interpolation Method, a meshless method that, to the knowledge of the authors, was never used to solve this type of problem. Since the efficiency of the model strongly depends on the efficiency of the meshless method itself, the optimal numbers of integration points per integration cell and of nodes for each influence-domain were investigated. Irregular nodal meshes were also used to study their influence on the algorithm. METHODS: For the first time, an iterative discrete model solved by the Radial Point Interpolation Method based on the Galerkin weak form was used to establish the system of equations from the reaction-diffusion integro-differential equations, following a new phenomenological law proposed by the authors that describes the growth of a cell over time while dependant on oxygen and glucose availability. The discretization flexibility of the meshless method allows to explicitly follow the geometric changes of the cell until the division phase. RESULTS: It was found that an integration scheme of 6 × 6 per integration cell and influence-domains with only seven nodes allows to predict the cellular growth and division with the best balance between the relative error and the computing cost. Also, it was observed that using irregular meshes do not influence the solution. CONCLUSIONS: Even in a preliminary phase, the obtained results are promising, indicating that the algorithm might be a potential tool to study cell proliferation since it can predict cellular growth and division. Moreover, the Radial Point Interpolation Method seems to be a suitable method to study this type of process, even when irregular meshes are used. However, to optimize the algorithm, the integration scheme and the number of nodes inside the influence-domains must be considered.

Finite element modelling of the surgical procedure for placement of a straight electrode array: Mechanical and clinical consequences.

A cochlear implant is an electronic device implanted into the cochlea to directly stimulate the auditory nerve. Such device is used in patients with severe-to-profound hearing loss. The cochlear implant surgery is safe, but involves some risks, such as infections, device malfunction or damage of the facial nerve and it can result on a poor hearing outcome, due to the destruction of any present residual hearing. Future improvements in cochlear implant surgery will necessarily involve the decrease of the intra-cochlear damage. Several implant related variables, such as materials, geometrical design, processor and surgical techniques can be optimized in order for the patients to partially recover their hearing capacities The straight electrode is a type of cochlear implant that many authors indicate as being the less traumatic. From the finite element analysis conducted in this work, the influence of the insertion speed, the friction coefficient between the cochlear wall and the electrode array, and several configurations of the cochlear implant tip were studied. The numerical simulations of the implantation showed the same pattern of the insertion force against insertion depth, thus indicating the different phases of the insertion. Results demonstrated that lower insertion speeds, friction coefficients and tip stiffness, led to a reduction on the contact pressures and insertion force. It is expected that these improved configurations will allow to preserve the residual hearing while reducing surgical complications.

Effect of mesh anchoring technique in uterine prolapse repair surgery: A finite element analysis.

The female pelvic cavity involves muscles, ligaments, endopelvic fasciae and multiple organs where different pathologies may occur, namely the pelvic organ prolapse (POP). The synthetic implants are used for the reconstructive surgery of POP, but severe complications associated with their use have been reported, mainly related to their mechanical properties (e.g., implant stiffness) and microstructure. In this study, we mimicked a transvaginal reconstructive surgery to repair the apical ligaments (uterosacral ligaments (USLs) and cardinal ligaments (CLs)), by modeling, their impairment (90% and 50%) and/or total rupture. The implants to reinforce/replace these ligaments were built based on literature specifications and their mechanical properties were obtained through uniaxial tensile tests. The main aim of this study was to simulate the effect of mesh anchoring technique (simple stich and continuous stitch), and compare the displacement magnitude of the pelvic tissues, during Valsalva maneuver. The absence/presence of the synthetic implant was simulated when total rupture of the CLs and USLs occurs, causing a variation of the vaginal displacement (9% for the CLs and 27% for the USLs). Additionally, the simulations showed that there was a variation of the supero-inferior displacement of the vaginal wall between different anchoring techniques (simple stich and continuous stitch) being approximately of 10% for the simulation USLs and CLs implant. The computational simulation was able to mimic the biomechanical behavior of the USLs and CLs, in response to different anchoring techniques, which can be help improving the outcomes of the prolapse surgery.

Mechanical Effects of a Maylard Scar During a Vaginal Birth After a Previous Caesarean.

Caesarean section is one of the most common surgeries worldwide, even though there is no evidence supporting maternal and perinatal long-term benefits. Furthermore, the mechanical behavior of a caesarean scar during a vaginal birth after caesarean (VBAC) is not well understood since there are several questions regarding the uterine wound healing process. The aim of this study is to investigate the biomechanical Maylard fiber reorientation and stiffness influence during a VBAC through computational methods. A biomechanical model comprising a fetus and a uterus was developed, and a chemical-mechanical constitutive model that triggers uterine contractions was used, where some of the parameters were adjusted to account for the matrix and fiber stiffness increase in the caesarean scar. Several mechanical simulations were performed to analyze different scar fibers arrangements, considering different values for the respective matrix and fibers stiffness. The results revealed that a random fiber arrangement in the Maylard scar has a much higher impact on its mechanical behavior during a VBAC than the common fibers arrangement present in the uninjured uterine tissue. An increase of the matrix scar stiffness exhibits a lower impact, while an increase of the fiber's stiffness has no significant influence.

Load adaptation through bone remodeling: a mechanobiological model coupled with the finite element method.

This work proposes a novel tissue-scale mechanobiological model of bone remodeling to study bone's adaptation to distinct loading conditions. The devised algorithm describes the mechanosensitivity of bone and its impact on bone cells' functioning through distinct signaling factors. In this study, remodeling is mechanically ruled by variations of the strain energy density (SED) of bone, which is determined by performing a linear elastostatic analysis combined with the finite element method. Depending on the SED levels and on a set of biological signaling factors ([Formula: see text] parameters), osteoclasts and osteoblasts can be mechanically triggered. To reproduce this phenomenon, this work proposes a new set of [Formula: see text] parameters. The combined response of osteoclasts and osteoblasts will then affect bone's apparent density, which is correlated with other mechanical properties of bone, through a phenomenological law. Thus, this novel model proposes a constant interplay between the mechanical and biological components of the process. The spatiotemporal simulation used to validate this new approach is a benchmark example composed by two distinct phases: (1) pre-orientation and (2) load adaptation. On both of them, bone is able to adapt its morphology according to the loading condition, achieving the required trabecular distribution to withstand the applied loads. Moreover, the equilibrium morphology reflects the orientation of the load. These preliminary results support the new approach proposed in this study.

A mathematical biomechanical model for bone remodeling integrated with a radial point interpolating meshless method.

Bone remodeling is a highly complex process, in which bone cells interact and regulate bone's apparent density as a response to several external and internal stimuli. In this work, this process is numerically described using a novel 2D biomechanical model. Some of the new features in this model are (i) the mathematical parameters used to determine bone's apparent density and cellular density; (ii) an automatic boundary recognition step to spatially control bone remodeling and (iii) an approach to mimic the mechanical transduction to osteoclasts and osteoblasts. Moreover, this model is combined with a meshless approach - the Radial Point Interpolation Method (RPIM). The use of RPIM is an asset for this application, especially in the construction of the boundary maps. This work studies bone's adaptation to a certain loading regime through bone resorption. The signaling pathways of bone cells are dependent on the level of strain energy density (SED) in bone. So, when SED changes, bone cells' functioning is affected, causing also changes on bone's apparent density. With this model, bone is able to achieve an equilibrium state, optimizing its structure to withstand the applied loads. Results suggest that this model has the potential to provide high quality solutions while being a simpler alternative to more complex bone remodeling models in the literature.

Investigating the birth-related caudal maternal pelvic floor muscle injury: The consequences of low cycle fatigue damage.

BACKGROUND: One of the major causes of pelvic organ prolapse is pelvic muscle injury sustained during a vaginal delivery. The most common site of this injury is where the pubovisceral muscle takes origin from the pubic bone. We hypothesized that it is possible for low-cycle material fatigue to occur at the origin of the pubovisceral muscle under the large repetitive loads associated with pushing during the second stage of a difficult labor. PURPOSE: The main goal was to test if the origin of the pubovisceral muscle accumulates material damage under sub-maximal cyclic tensile loading and identify any microscopic evidence of such damage. METHODS: Twenty origins of the ishiococcygeous muscle (homologous to the pubovisceral muscle in women) were dissected from female sheep pelvises. Four specimens were stretched to failure to characterize the failure properties of the specimens. Thirteen specimens were then subjected to relaxation and subsequent fatigue tests, while three specimens remained as untested controls. Histology was performed to check for microscopic damage accumulation. RESULTS: The fatigue stress-time curves showed continuous stress softening, a sign of material damage accumulation. Histology confirmed the presence of accumulated microdamage in the form of kinked muscle fibers and muscle fiber disruption in the areas with higher deformation, namely in the muscle near the musculotendinous junction. CONCLUSIONS: The origin of ovine ishiococcygeous muscle can accumulate damage under sub-maximal repetitive loading. The damage appears in the muscle near the musculotendinous junction and was sufficient to negatively affect the macroscopic mechanical properties of the specimens.

Application of an enhanced homogenization technique to the structural multiscale analysis of a femur bone.

Bone is a complex hierarchical material that can be characterized from the microscale to macroscale. This work demonstrates the application of an enhanced homogenization methodology to the multiscale structural analysis of a femoral bone. The use of this homogenization technique allows to remove subjectivity and reduce the computational cost associated with the iterative process of creating a heterogeneous mesh. Thus, it allows to create simpler homogenized meshes with its mechanical properties defined using information directly from the mesh source: the medical images. Therefore, this methodology is capable to accurately predict bone mechanical behavior in a fraction of the time required by classical approaches. The results show that using the homogenization technique, despite the differences between the used homogeneous and heterogeneous meshes, its mechanical behavior is similar. The proposed homogenization technique is useful for a multiscale modelling and it is computationally efficient.

Altered mechanics of vaginal smooth muscle cells due to the lysyl oxidase-like1 knockout.

The remodeling mechanisms that cause connective tissue of the vaginal wall, consisting mostly of smooth muscle, to weaken after vaginal delivery are not fully understood. Abnormal remodeling after delivery can contribute to development of pelvic organ prolapse and other pelvic floor disorders. The present study used vaginal smooth muscle cells (vSMCs) isolated from knockout mice lacking the expression of the lysyl oxidase-like1 (LOXL1) enzyme, a well-characterized animal model for pelvic organ prolapse. We tested if vaginal smooth muscle cells from LOXL1 knockout mice have altered mechanics including stiffness and surface adhesion. Using atomic force microscopy, we performed nanoindentations on both isolated and confluent cells to evaluate the effect of LOXL1 knockout on in vitro cultures of vSMCs cells from nulliparous mice. The results show that LOXL1 knockout vSMCs have increased stiffness in pre-confluent but decreased stiffness in confluent cultures (p* < 0.05) and significant decreased surface adhesion in pre-confluent cultures (p* < 0.05). This study provides evidence that the weakening of vaginal connective tissue in the absense of LOXL1 changes the mechanical properties of the vSMCs. STATEMENT OF SIGNIFICANCE: Pelvic organ prolapse is a common condition affecting millions of women worldwide, which significantly impacts their quality of life. Alterations in vaginal and pelvic floor mechanical properties can change their ability to support the pelvic organs. This study provides evidence of altered stiffness of vaginal smooth muscle cells from mice resembling pelvic organ prolapse. The results from this study set a foundation to develop pathophysiology-driven therapies focused on the interplay between smooth muscle mechanics and extracellular matrix remodeling.

Simulation of the uterine contractions and foetus expulsion using a chemo-mechanical constitutive model.

During vaginal delivery women sustain stretching of their pelvic floor, risking tissue injury and adverse outcomes. Since studies in pregnant women are limited with ethical constraints, computational models have become an interesting alternative to elucidate the pregnancy mechanisms. This research investigates the uterine contractions during foetus expulsion without an imposed trajectory. Such physical process is captured by means of a chemo-mechanical constitutive model, where the uterine contractions are triggered by chemical stimuli. The foetus descent, which includes both pushing and resting stages, has a descent rate within the physiological range. Moreover, the behaviour of the foetus and the uterus stretch agree well with clinical data presented in the literature. The follow-up of this study will be to obtain a complete childbirth simulation, considering also the pelvic floor muscles and its supporting structures. The simulation of a realistic rate of descent, including the pushing and resting stages, is of significant importance to study the pelvic floor muscles due to their viscoelastic nature.

A new numerical approach to mechanically analyse biological structures.

In this work, an advanced discretization meshless technique is used to study the structural response of a human brain due to an impact load. The 2D and 3D brain geometrical models, and surrounding structures, were obtained through the processing of medical images, allowing to achieve a realistic geometry for the virtual model and to define the distribution of the mechanical properties accordingly with the medical images colour scale. Additionally, a set of essential and natural boundary conditions were assumed in order to reproduce a sudden impact force applied to the cranium. Then, a structural numerical analysis was performed using the Natural Neighbour Radial Point Interpolation Method (NNRPIM). The obtained results were compared with the finite element method (FEM) and a solution available in the literature. This work shows that the NNRPIM is a robust and accurate numerical technique, capable to produce results very close to other numerical approaches. In addition, the variable fields obtained with the meshless method are much smoother than the FEM corresponding solution.

On the effect of labour durations using an anisotropic visco-hyperelastic-damage approach to simulate vaginal deliveries.

Injuries sustained by the pelvic floor muscles during childbirth are one of the major risk factors for the development of pelvic floor dysfunctions. The ability to predict the loss of the tissue integrity and the most affected regions prior to the childbirth would represent a compelling difference in choosing the appropriate management of labour. Previous biomechanical studies, using the finite element method, were able to simulate a vaginal delivery and analyse the mechanical effects on the pelvic floor muscles during the passage of the foetus. Complementing these studies, the aim of this work is to improve the characterization of the pelvic floor muscles, by using an anisotropic visco-hyperelastic constitutive model, including a continuum mechanics damage model. Viscoelasticity is a key feature to obtain more realistic results since biological tissues present relaxation effects that allow larger deformations without damage. This work analyses the reaction forces and the loss of tissue integrity sustained by the pelvic floor and evaluates the effects of different durations of labour. A delaying pushing technique of rest and descend is also studied in this work. The results obtained showed that the reaction forces vary with the duration of labour, with higher force levels associated with higher stretch rates. The pubovisceral muscle is the most affected of the levator ani, presenting an affected region of approximately 30%. The relaxation properties of the tissue contribute to diminish the damage levels, supporting the theory of delayed pushing applied in the second stage of labour.

Characterization of the passive and active material parameters of the pubovisceralis muscle using an inverse numerical method.

The mechanical characteristics of the female pelvic floor are relevant to understand pelvic floor dysfunctions (PFD), and how they are related with changes in their biomechanical behavior. Urinary incontinence (UI) and pelvic organ prolapse (POP) are the most common pathologies, which can be associated with changes in the mechanical properties of the supportive structures in the female pelvic cavity. PFD have been studied through different methods, from experimental tensile tests using tissues from fresh female cadavers or tissues collected at the time of a transvaginal hysterectomy procedure, or by applying imaging techniques. In this work, an inverse finite element analysis (FEA) was applied to understand the passive and active behavior of the pubovisceralis muscle (PVM) during Valsalva maneuver and muscle active contraction, respectively. Individual numerical models of women without pathology, with stress UI (SUI) and POP were built based on magnetic resonance images, including the PVM and surrounding structures. The passive and active material parameters obtained for a transversely isotropic hyperelastic constitutive model were estimated for the three groups. The values for the material constants were significantly higher for the women with POP when compared with the other two groups. The PVM of women with POP showed the highest stiffness. Additionally, the influence of these parameters was analyzed by evaluating their stress-strain, and force-displacements responses. The force produced by the PVM in women with POP was 47% and 82% higher when compared to women without pathology and with SUI, respectively. The inverse FEA allowed estimating the material parameters of the PVM using input information acquired non-invasively.

Viscous effects in pelvic floor muscles during childbirth: A numerical study.

During vaginal delivery, women sustain stretching of their pelvic floor, risking tissue injury and adverse outcomes. Realistic numerical simulations of childbirth can help in the understanding of the pelvic floor mechanics and on the prevention of related disorders. In previous studies, biomechanical finite element simulations of a vaginal delivery have been performed disregarding the viscous effects present on all biological soft tissues. The inclusion of the viscoelastic behaviour is fundamental, since it allows to investigate rate-dependent responses. The present work uses a viscohyperelastic constitutive model to evaluate how the childbirth duration affects the efforts sustained by the pelvic floor during delivery. It was concluded that viscoelasticity adds a stiffness component that leads to higher forces comparing with the elastic response. Viscous solutions are rate dependent, and precipitous labours could be associated to higher efforts, while lower reaction forces were denoted for normal and prolonged labours, respectively. The existence of resting stages during labour demonstrated the capability of the tissue to relax and recover some of the initial properties, which helped to lower the forces and stresses involved. The present work represents a step further in achieving a robust non-invasive procedure, allowing to estimate how obstetrical factors influence labour and its outcomes.

The human otitis media with effusion: a numerical-based study.

Otitis media is a group of inflammatory diseases of the middle ear. Acute otitis media and otitis media with effusion (OME) are its two main types of manifestation. Otitis media is common in children and can result in structural alterations in the middle ear which will lead to hearing losses. This work studies the effects of an OME on the sound transmission from the external auditory meatus to the inner ear. The finite element method was applied on the present biomechanical study. The numerical model used in this work was built based on the geometrical information obtained from The visible ear project. The present work explains the mechanisms by which the presence of fluid in the middle ear affects hearing by calculating the magnitude, phase and reduction of the normalized umbo velocity and also the magnitude and phase of the normalized stapes velocity. A sound pressure level of 90 dB SPL was applied at the tympanic membrane. The harmonic analysis was performed with the auditory frequency varying from 100 Hz to 10 kHz. A decrease in the response of the normalized umbo and stapes velocity as the tympanic cavity was filled with fluid was obtained. The decrease was more accentuated at the umbo.

Biomechanical properties of the pelvic floor muscles of continent and incontinent women using an inverse finite element analysis.

Pelvic disorders can be associated with changes in the biomechanical properties in the muscle, ligaments and/or connective tissue form fascia and ligaments. In this sense, the study of their mechanical behavior is important to understand the structure and function of these biological soft tissues. The aim of this study was to establish the biomechanical properties of the pelvic floor muscles of continent and incontinent women, using an inverse finite element analysis (FEA). The numerical models, including the pubovisceral muscle and pelvic bones were built from magnetic resonance (MR) images acquired at rest. The numerical simulation of Valsalva maneuver was based on the finite element method and the material constants were determined for different constitutive models (Neo-Hookean, Mooney-Rivlin and Yeoh) using an iterative process. The material constants (MPa) for Neo-Hookean (c1) were 0.039 ± 0.022 and 0.024 ± 0.004 for continent vs. incontinent women. For Mooney-Rivlin (c1) the values obtained were 0.026 ± 0.010 vs. 0.016 ± 0.003, and for Yeoh (c1) the values obtained were 0.031 ± 0.023 vs. 0.016 ± 0.002, (p < 0.05). Muscle displacements obtained in the numerical simulations of Valsalva maneuver were compared with the muscle displacements obtained through additional dynamic MRI. Incontinent women presented a higher antero-posterior displacement than the continent women. The results were also similar between MRI and numerical simulations (40.27% vs. 42.17% for Neo-Hookean, 39.87% for Mooney-Rivlin and 41.61% for Yeoh). Using an inverse FEA coupled with MR images allowed to obtain the in vivo biomechanical properties of the pelvic floor muscles, leading to a relationship between them for the continent and incontinent women in a non-invasive manner.

A general framework for the numerical implementation of anisotropic hyperelastic material models including non-local damage.

The highly nonlinear mechanical behaviour of soft tissues solicited within the physiological range usually involves degradation of the material properties. Mechanically, having these biostructures undergoing such stretch patterns may bring about pathological conditions related to the steady deterioration of both collagen fibres and material's ground substance. Tissue and subject variability observed in the phenomenological mechanical characterisation of soft tissues often hinder the choice of the computational constitutive model. Therefore, this contribution brings forth a detailed overview of the constitutive implementation in a computational framework of anisotropic hyperelastic materials with damage. Surmounting the challenge posed by the mesh dependency pathology requires the incorporation of an integral-type non-local averaging, which seeks to include the effects of the microstructure in order to limit the localisation phenomena of the damage variables. By adopting this approach, one can make use of multiple developed material models available in the literature, a combination of those, or even propose new models within the same numerical framework. The numerical examples of three-dimensional displacement and force-driven boundary value problems highlight the possibility of using multiple material models within the same numerical framework. Particularities concerning the considered material models and the damage effect implications to represent the Mullins effect, induced anisotropy, hysteresis, and mesh dependency are discussed.

Establishing the biomechanical properties of the pelvic soft tissues through an inverse finite element analysis using magnetic resonance imaging.

The mechanical characteristics of the female pelvic floor are relevant when explaining pelvic dysfunction. The decreased elasticity of the tissue often causes inability to maintain urethral position, also leading to vaginal and rectal descend when coughing or defecating as a response to an increase in the internal abdominal pressure. These conditions can be associated with changes in the mechanical properties of the supportive structures-namely, the pelvic floor muscles-including impairment. In this work, we used an inverse finite element analysis to calculate the material constants for the passive mechanical behavior of the pelvic floor muscles. The numerical model of the pelvic floor muscles and bones was built from magnetic resonance axial images acquired at rest. Muscle deformation, simulating the Valsalva maneuver with a pressure of 4 KPa, was compared with the muscle displacement obtained through additional dynamic magnetic resonance imaging. The difference in displacement was of 0.15 mm in the antero-posterior direction and 3.69 mm in the supero-inferior direction, equating to a percentage error of 7.0% and 16.9%, respectively. We obtained the shortest difference in the displacements using an iterative process that reached the material constants for the Mooney-Rivlin constitutive model (c10=11.8 KPa and c20=5.53 E-02 KPa). For each iteration, the orthogonal distance between each node from the group of nodes which defined the puborectal muscle in the numerical model versus dynamic magnetic resonance imaging was computed. With the methodology used in this work, it was possible to obtain in vivo biomechanical properties of the pelvic floor muscles for a specific subject using input information acquired non-invasively.

Finite element analysis of the transfer of sound in the myringosclerotic ear.

This work presents a biomechanical study of myringosclerosis (MS), an abnormal condition of the ear that produces calcification of the lamina propria of the eardrum. The study researched the transfer of sound to the stapes depending on the localization, dimension and calcification degree of the MS plaques. Results were obtained using a validated finite element model of the ear. The mechanical properties of the lamina propria were modified, in order to model MS plaques, using the rule of mixtures for particle composites considering that the plaques are made of hydroxyapatite particles in a matrix of connective tissue. Results show that the localization and dimension of the plaques are a factor of higher importance than calcification for loss of hearing through MS. The mobility of the stapes decreased with the presence of larger plaques and also when the tympanic annulus and the area of the handle of the malleus were involved.