Finite element analysis of bone remodelling with piezoelectric effects using an open-source framework

Bone tissue exhibits piezoelectric properties and thus is capable of transforming mechanical stress into electrical potential. Piezoelectricity has been shown to play a vital role in bone adaptation and remodelling processes. Therefore, to better understand the interplay between mechanical and electrical stimulation during these processes, strain-adaptive bone remodelling models without and with considering the piezoelectric effect were simulated using the Python-based open-source software framework. To discretise numerical attributes, the finite element method (FEM) was used for the spatial variables and an explicit Euler scheme for the temporal derivatives. The predicted bone apparent density distributions were qualitatively and quantitatively evaluated against the radiographic scan of a human proximal femur and the bone apparent density calculated using a bone mineral density (BMD) calibration phantom, respectively. Additionally, the effect of the initial bone density on the resulting predicted density distribution was investigated globally and locally. The simulation results showed that the electrically stimulated bone surface enhanced bone deposition and these are in good agreement with previous findings from the literature. Moreover, mechanical stimuli due to daily physical activities could be supported by therapeutic electrical stimulation to reduce bone loss in case of physical impairment or osteoporosis. The bone remodelling algorithm implemented using an open-source software framework facilitates easy accessibility and reproducibility of finite element analysis made.

     

Tetrapolar measurement of electrical conductivity and thickness of articular cartilage

A tetrapolar method to measure electrical conductivity of cartilage and bone, and to estimate the thickness of articular cartilage attached to bone, was developed. We determined the electrical conductivity of humeral head bovine articular cartilage and subchondral bone from a 1- to 2-year-old steer to be 1.14+/-0.11 S/m (mean+/-sd, n =11) and 0.306+/-0.034 S/m, (mean+/-sd, n =3), respectively. For a 4-year-old cow, articular cartilage and subchondral bone electrical conductivity were 0.88+/-0.08 S/m (mean+/-sd, n =9) and 0.179+/-0.046 S/m (mean+/-sd, n =3), respectively. Measurements on slices of cartilage taken from different distances from the articular surface of the steer did not reveal significant depth-dependence of electrical conductivity. We were able to estimate the thickness of articular cartilage with reasonable precision (<20% error) by injecting current from multiple electrode pairs with different inter-electrode distances. Requirements for the precision of this method to measure cartilage thickness include the presence of a distinct layer of calcified cartilage or bone with a much lower electrical conductivity than that of uncalcified articular cartilage, and the use of inter-electrode distances of the current injecting electrodes that are on the order of the cartilage thickness. These or similar methods present an attractive approach to the non-destructive determination of cartilage thickness, a parameter that is required in order to estimate functional properties of cartilage attached to bone, and evaluate the need for therapeutic interventions in arthritis.     

Electro-mechanical behavior of wet bone--Part I: Theory

The remodeling properties of bones due to various stimuli have been of substantial interest to the scientists. Examination of electro-mechanical properties of bone and their relation to remodeling and osteogenesis have been investigated mainly by experimental means. In this study, by using continuum physics, it is shown that the remodeling of bones can be formulated theoretically in terms of electrical and mechanical effects. The interactions among the constituents of bone (bone matrix, bone salts, electrolytes and hydrogen ions) and effects of various stimuli (mechanical, electrical and chemical) on the remodeling mechanism of bone tissue are interpreted with this model. Moreover, the stimulation of osteogenesis by electrical means is predicted.     

Greater osteoblast proliferation on anodized nanotubular titanium upon electrical stimulation

Currently used orthopedic implants composed of titanium have a limited functional lifetime of only 10–15 years. One of the reasons for this persistent problem is the poor prolonged ability of titanium to remain bonded to juxtaposed bone. It has been proposed to modify titanium through anodization to create a novel nanotubular topography in order to improve cytocompatibility properties necessary for the prolonged attachment of orthopedic implants to surrounding bone. Additionally, electrical stimulation has been used in orthopedics to heal bone non-unions and fractures in anatomically difficult to operate sites (such as the spine). In this study, these two approaches were combined as the efficacy of electrical stimulation to promote osteoblast (bone forming cell) density on anodized titanium was investigated. To do this, osteoblast proliferation experiments lasting up to 5 days were conducted as cells were stimulated with constant bipolar pulses at a frequency of 20 Hz and a pulse duration of 0.4 ms each day for 1 hour. The stimulation voltages were 1 V, 5 V, 10 V, and 15 V. Results showed for the first time that under electrical stimulation, osteoblast proliferation on anodized titanium was enhanced at lower voltages compared to what was observed on conventional (nonanodized) titanium. In addition, compared to nonstimulated conventional titanium, osteoblast proliferation was enhanced 72% after 5 days of culture on anodized nanotubular titanium at 15 V of electrical stimulation. Thus, results of this study suggest that coupling the positive influences of electrical stimulation and nanotubular features on anodized titanium may improve osteoblast responses necessary for enhanced orthopedic implant efficacy.     

Basic Electrical Properties of Living Unstressed Rabbit Tibia

The presence of steady resting electrical potentials on the surface of living bone allows it, and other living tissues, to be considered as an electrical generator with a Thevenin equivalent circuit. By loading the generator component of bone with externally-applied resistors, fundamental electrical characteristics such as resistance, current, maximum generated power and power dissipated can be determined. This method has been applied to rabbit tibia.     

Mechanical and electrical interactions in bone remodeling

The natural remodeling and adaptation of skeletal tissues in response to mechanical loading is a classic example of physical regulation in biology. It is largely because it involves forces that do not seem to fit into the familiar schemes of biochemical controls that bone adaptation mechanisms have intrigued us for at least a century. The effect of electromagnetic fields on organisms is another example of this, and the two have become linked in an attempt to explain bone remodeling (“Yasuda's hypothesis”). This paper re-examines the roles of endogenous and exogenous electromagnetic fields in the response of bone to mechanical forces. A series of experiments is reviewed in which mechanical and electrical stimuli were applied to implants in the medullary canal of rabbit long bones. The results suggest that endogenously generated electrical currents are not required to initiate mechanically stimulated bone formation, but that direct mechanical effects on bone cells is the more likely scenario. Based on this and other evidence from the literature, it is suggested that when exogenous electromagnetic stimuli are applied, bone cells respond by modulating the activity of more primary activators such as hormones, growth factors, cytokines, and mechanical forces. Bioelectromagnetics 18:193–202, 1997. © 1997 Wiley-Liss, Inc.     

Capacitative pulsed electric stimulation of bone cells. Induction of cyclic-AMP changes and DNA synthesis

Pulsed electric stimulation, coupled capacitively to bone cells isolated from rat embryo calvaria, caused changes in the intracellular level of cyclic AMP and enhanced DNA synthesis. The capacitive method of electrical stimulation was characterized in terms of displacement currents (0.7-4.0 A) and voltages (10-54 V/cm) prevailing in the stimulation chamber. Changes, both in cyclic AMP and in incorporation of [3H]thymidine into DNA, were correlated with the strength of the applied electric field. Unlike the mechanical stimulation of bone cells, the electrical stimulus was not mediated by de novo synthesis of prostaglandins. The findings suggest that cyclic-AMP changes, induced by the capacitive electrical stimulation of bone cells, trigger DNA synthesis.     

Analysis of Bone Remodeling Under Piezoelectricity Effects Using Boundary Elements

Piezoelectric materials exhibit a response to mechanical-electrical coupling,which represents an important contribution to the electrical-mechanical interaction in bone remodeling process.Therefore,the study of the piezoelectric effect on bone remodeling has high interest in applied biomechanics.The effects of mechano-regulation and electrical stimulation on bone healing are explained.The Boundary Element Method (BEM) is used to simulate piezoelectric effects on bones when sheafing forces are applied to collagen fibers to make them slip past each other.The piezoelectric fundamental solutions are obtained by using the Radon transform.The Dual Reciprocity Method (DRM) is used to simulate the particular solutions in time-dependent problems.BEM analysis showed the strong influence of electrical stimulation on bone remodeling.The examples discussed in this work showed that,as expected,the electrically loaded bone surfaces improved the bone deposition.BEM results confirmed previous findings obtained by using the Finite Element Method (FEM).This work opens very promising doors in biomechanics research,showing that mechanical loads can be replaced,in part,by electrical charges that stimulate strengthening bone density.The obtained results herein are in good agreement with those found in literature from experimental testing and/or other simulation approaches.     

Numerical test concerning bone mass apposition under electrical and mechanical stimulus

ABSTRACT: This article proposes a model of bone remodeling that encompasses mechanical and electrical stimuli. The remodeling formulation proposed by Weinans and collaborators was used as the basis of this research, with a literature review allowing a constitutive model evaluating the permittivity of bone tissue to be developed. This allowed the mass distribution that depends on mechanical and electrical stimuli to be obtained. The remaining constants were established through numerical experimentation. The results demonstrate that mass distribution is altered under electrical stimulation, generally resulting in a greater deposition of mass. In addition, the frequency of application of an electric field can affect the distribution of mass; at a lower frequency there is more mass in the domain. These numerical experiments open up discussion concerning the importance of the electric field in the remodeling process and propose the quantification of their effects.     

The effect of gamma-irradiation on the temperature dependence of D.C. electrical conductivity of dry bone.

The effect of gamma-irradiation with doses from 10 to 500 kGy on the electrical conductivity (g) of dry bone was studied. Temperature measurement of electrical conductivity were made from 393 to 533 K. The dependence obtained indicates the increase in g with temperature. An increase in irradiation dose resulted in a decreased g value for each dose up to temperature 462 K. Temperature 462 K was interpreted as the temperature of collagen melting point in dry bone. Above 462 K, g values were dose independent. A dose of 500 kGy shifted the melting point to lower temperature. In addition, the activation energy for the charge conduction process was calculated. Obtained values for electrical conductivity and activation energy were typical for dielectrics and indicated degradation of the organic component of bone.     

Evidence of Electrical Hysteresis in Bones

The aim of this paper is to investigate: (1) the electrical behavior of bone samples when low (<100 mV) stationary voltages are applied; (2) the reproducibility of successive high impedance (200 TΩ) voltage measurements; and (3) the existence of a spontaneous potential, suggested by previous work. We studied 16 cow bone samples, eight fresh and eight old. We applied analysis of variance to verify the constancy of the bone resistance and the behavior of the time constants. We found that: (1) the existence of a spontaneous potential, on the order of magnitude 10 m V, is confirmed; (2) one constant of time, out of two in a double exponential model, strongly depends on the current direction (p < 0.001); (3) the characteristic voltage-current curve shows a hysteresis loop, maximum amplitude 15% of the full current range; and (4) voltage measurements should be considered perturbative with respect to the electrical response of the samples.     

Prospects on clinical applications of electrical stimulation for nerve regeneration

Regenerative capability is limited in higher vertebrates but present in organ systems such as skin, liver, bone, and to some extent, the nervous system. Peripheral nerves in particular have a relatively high potential for regeneration following injury. However, delay in regrowth or growth, blockage, or misdirection at the injury site, and growth to inappropriate end organs may compromise successful regeneration, leading to poor clinical results. Recent studies indicate that low-intensity electrical stimulation is equivalent to various growth factors, offering avenues to improve these outcomes. We present a review of studies using electric and electromagnetic fields that provide evidence for the enhancement of regeneration following nerve injury. Electric and electromagnetic fields (EMFs) have been used to heal fracture non-unions. This technology emerged as a consequence of basic studies [Yasuda, 1953; Fukada and Yasuda, 1957] demonstrating the piezoelectric properties of (dry) bone. The principle for using electrical stimulation for bone healing originated from the work of Bassett and Becker [1962], who described asymmetric voltage waveforms from mechanically deformed live bone. These changes were presumed to occur in bone during normal physical activity as a result of mechanical forces, and it was postulated that these forces were linked to modifications in bone structure. Endogenous currents present in normal tissue and those that occur after injury were proposed to modify bone structure [Bassett, 1989]. These investigators proposed that tissue integrity and function could be restored by applying electrical and/or mechanical energy to the area of injury. They successfully applied electrical currents to nonhealing fractures (using surgically implanted electrodes or pulsed currents using surface electrodes) to aid endogenous currents in the healing process. A considerable technological improvement was made with the noninvasive application of EMFs [Bassett et al., 1974] to accelerate fracture repair. This newer technique allowed the treatment of hard tissues without the complications of invasive electrode insertion. In addition, soft tissue injuries were now accessible for treatment by electromagnetic fields. In this article, we will first define the basic problems encountered in nerve injury and regeneration, and then review both in vitro and in vivo studies on the use of electric and electromagnetic fields to stimulate the healing process.     

Interruption of Electrical Conductivity of Titanium Dental Implants Suggests a Path Towards Elimination Of Corrosion

Peri-implantitis is an inflammatory disease that results in the destruction of soft tissue and bone around the implant. Titanium implant corrosion has been attributed to the implant failure and cytotoxic effects to the alveolar bone. We have documented the extent of titanium release into surrounding plaque in patients with and without peri-implantitis. An in vitro model was designed to represent the actual environment of an implant in a patient’s mouth. The model uses actual oral microbiota from a volunteer, allows monitoring electrochemical processes generated by biofilms growing on implants and permits control of biocorrosion electrical current. As determined by next generation DNA sequencing, microbial compositions in experiments with the in vitro model were comparable with the compositions found in patients with implants. It was determined that the electrical conductivity of titanium implants was the key factor responsible for the biocorrosion process. The interruption of the biocorrosion current resulted in a 4–5 fold reduction of corrosion. We propose a new design of dental implant that combines titanium in zero oxidation state for osseointegration and strength, interlaid with a nonconductive ceramic. In addition, we propose electrotherapy for manipulation of microbial biofilms and to induce bone healing in peri-implantitis patients.     

Effect of electrical stimulation-induced muscle force and streptomycin treatment on muscle and trabecular bone mass in early-stage disuse musculoskeletal atrophy

Objectives:

The aim was to determine whether daily muscle electrical stimulation (ES) and streptomycin treatment would have positive or negative effects on trabecular bone mass in disuse rats.

Methods:

Seven-week-old male F344 rats were randomly divided into five groups of eight animals each: an age-matched control group (CON); a sciatic denervation group (DN); a DN + direct electrical stimulation group (DN+ES); a DN + streptomycin treatment group (DN+SM); and a DN+ES+SM group. The tibialis anterior (TA) muscles in all ES groups were stimulated with 16mA at 10Hz for 30 min/day, six days/week, for one week. Bone volume and structure were evaluated using micro-CT, and histological examinations of the tibiae were performed.

Results:

Direct ES significantly reduced the disuse-induced trabecular bone loss. Osteoid thickness were also significantly greater in the ES groups than in the DN group. Micro CT and histomorphological parameters were significantly lower in the DN+ES+SM group than in the DN+ES group, while there were no significant differences between the DN and DN+SM groups.

Conclusions:

These results suggest that ES-induced muscle force reduced trabecular bone loss, and streptomycin treatment did not induce bone loss, but attenuated the effects of ES-induced muscle force on reducing the loss of disused bone.     

The effect of surface electrical stimulation on hyolaryngeal movement in normal individuals at rest and during swallowing.

Surface electrical stimulation is currently used in therapy for swallowing problems, although little is known about its physiological effects on neck muscles or swallowing. Previously, when one surface electrode placement was used in dysphagic patients at rest, it lowered the hyolaryngeal complex. Here we examined the effects of nine other placements in normal volunteers to determine 1) whether movements induced by surface stimulation using other placements differ, and 2) whether lowering the hyolaryngeal complex by surface electrical stimulation interfered with swallowing in healthy adults. Ten bipolar surface electrode placements overlying the submental and laryngeal regions were tested. Maximum tolerated stimulation levels were applied at rest while participants held their mouths closed. Videofluoroscopic recordings were used to measure hyoid bone and subglottic air column (laryngeal) movements from resting position and while swallowing 5 ml of liquid barium, with and without stimulation. Videofluoroscopic recordings of swallows were rated blind to condition using the National Institutes of Health-Swallowing Safety Scale. Significant (P < 0.0001) laryngeal and hyoid descent occurred with stimulation at rest. During swallowing, significant (P 相似文献   

Electrical Stimulation with Pemfs of an Aneurysmal Bone Cyst of the Tibia Which Recurred Twice After Curettage and Cancellous Bone Grafting

An aneurysmal cyst of the proximal tibia recurred twice after a surgical procedure of curettage and cancellous bone graft. PEMF stimulation was used and after 4 months of electrical stimulation bone healing was obtained. No recurrence was observed in a 2-year follow-up.     

Comments on Modification of Heart Function with Low Intensity Electromagnetic Energy

Although apparently successful clinically, the mechanism(s) of electro-osteogenesis is still unknown. It is clear that the electromechanical effects in bone may be an important factor affecting bone remodeling processes. Identification of the mechanism for the electromechanical response may be helpful in the understanding of how electrical stimulation affects fracture healing. In this review, we attempt to summarize the published data on the electromechanical properties of bone.     

Physical characteristics of bone composite materials

To study the effects of varying mineral content and various trace elements in bone composities on its electrical behavior and possible use in design of transducers, various physical, dielectric, piezoelectric, and electromechanical parameters have been measured. For electrical characterization of various such composites in the high-frequency region (1–108 MHz), variation of impedance (Z), phase angle (tan ), and relative output voltage with frequency has been examined. Furtherfore, the Curie temperature has been determined and the temperature variation of capacitance and loss factor (tan ) studied (24–225°C). Two types of bone composites were prepared and studied. First, powdered collagen and apatite obtained from full bone were mixed intimately in various proportions by weight to prepare eleven bone compositions. Second, such bone materials were made to contain 5–10% various doping foreign additives (A1Br₃, Na₂CO₃, SrCO₃, LiCO₃, Sb₂O₃, ZnO, Nb₂O₅, piezoelectric ceramic (PZT), and Pb(NO₃)₂. It has been observed that a bone composition of 50% collagen + 50% apatite has possible piezoelectric application and other compositions [85% collagen + 15% apatite, 90% collagen + 10% ZnO, and 90% bone + 10% Ba(OH)₂] have a sharp rise in capacitance near the Curie temperature. The Curie temperature is generally shifted towards higher values by additives. It is expected that such results will be relevant in characterizing bone behavior.     

Photoconductivity in bone and tendon.

Ultraviolet light can be used to stimulate electrical current flow in bone and tendon. This stimulated photocurrent is directional. In tendon the photocurrent parallel to the fibrils is greater than the photocurrent perpendicular to the fibrils. In bone, the longitudinal photocurrent is less than the transverse photocurrent.