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Velez A. et al. A study of the mechanical and electrical properties of the cortical bone based on age, biochemical factors and Nernst equation
A study of the mechanical and electrical properties of the
cortical bone based on age, biochemical factors and Nernst
equation
*Correspondence author: alvelez@pupr.edu
Received (11/09/2024), Accepted (13/12/2024)
Abstract. - - This study presents the development of a mathematical model to assess the performance of
oil strings during the drilling process of a reservoir, considering the dynamic conditions and operational
characteristics of the equipment during its functions, and taking into account the mechanical properties of
API K55 steel. The research resulted in a set of equations that model the behavior of stresses and
deformations experienced by the oil tools when transmitting torque, facilitating the opening of the
reservoir. A finite element analysis was conducted to evaluate the structural behavior of the strings and to
estimate the time required to reach permanent deformations, as well as the time before failure occurs.
Keywords: aging, calcium, PTH, pH, cortical bone, Young modulus, electrical conductivity, Nernst equation
and electro-stimulation.
Un estudio de propiedades mecánicas y eléctricas del hueso cortical a partir de la
edad, factores bioquímicos y la ecuación de Nernst
Resumen: Este artículo presenta una exploración en profundidad de la intrincada interacción entre las
propiedades mecánicas y eléctricas en sistemas biológicos, centrándose en las relaciones experimentales
entre el envejecimiento, la concentración de calcio, el pH y la PTH. La ecuación de Nernst es un principio
electroquímico fundamental, el cual se examinará por su relevancia en la comprensión de estos fenómenos
y su futura aplicación de electroestimulación para procesos de sanación del hueso cortical. El artículo
profundiza en el impacto del envejecimiento en el cuerpo humano, el papel del calcio y el pH en los
procesos fisiológicos, la importancia de la PTH y la aplicación de la ecuación de Nernst en sistemas
biológicos.
Palabras clave: envejecimiento, calcio, PTH, pH, hueso cortical, módulo de elasticidad, conductividad
eléctrica, ecuación de Nernst y electroestimulación.
Oscar Gilberto Dam
https://orcid.org/0000-0002-0594-6757
oscar.curmetals@gmail.com
Universidad Nacional Experimental Politecnica
“Antonio Jose de Sucre”
Vice-Rectorado Puerto Ordaz
Ciudad Guayana, Venezuela
Alex J.
Velez-Cruz
https://orcid.org/0000-0002-9289-5256
alvelez@pupr.edu
Polytechnic University of Puerto Rico
San Juan, PR-USA
https://doi.org/10.47460/athenea.v6i19.88
Tipo de artículo: de investigación científica
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Velez A. et al. A study of the mechanical and electrical properties of the cortical bone based on age, biochemical factors and Nernst equation
I. INTRODUCTION
Bioengineering is a multidisciplinary field that integrates biology, chemistry, physics, and engineering
principles to develop innovative solutions in healthcare and biomedical applications [1], [2]. Understanding
the mechanical and electrical properties of biological tissues, such as bone, is crucial for various
bioengineering applications, including the design of medical devices, drug delivery systems, and
assessments of bone health [3]. The Nernst equation, derived from electrochemistry, is a fundamental tool
that allows researchers to quantify the behavior of ions and electrical potential differences across biological
membranes [4]. In the field of bioengineering, especially in the characterization of cortical bone, the Nernst
equation is applied to determine the electrical properties of bone and the amount of electricity needed to
pass through bone membranes [5]. This article provides a comprehensive overview of the Nernst equation,
its theory, applications in bioengineering, and its specific relevance to cortical bone characterization. Bone
healing is a complex biological process influenced by various factors, including mechanical stress, growth
factors, cellular activities, and signaling pathways. However, electrical stimulation has been explored as a
potential modality to promote bone healing and suggests that specific electrical parameters can have a
positive impact on bone regeneration [6]. When electrical stimulation is used for bone healing, several
factors should be considered, including the type of electrical stimulation (e.g., direct current, pulsed
electromagnetic fields), the frequency, duration, and intensity of the stimulation, and how these parameters
affect cellular and tissue responses [7]. Vitamin D plays an indirect role in stimulating the mineralization of
the unmineralized bone matrix. After the absorption or skin production of vitamin D, the liver synthesizes
25-hydroxyvitamin D, and subsequently, the kidneys produce biologically active 1,25-dihydroxyvitamin D
[1,25-(OH)
2
D]. Serum 1,25-(OH)
2
D is responsible for maintaining serum calcium and phosphorus
concentrations adequate to allow passive mineralization of the unmineralized bone matrix. Serum 1,25-
(OH)
2
D primarily accomplishes this by stimulating the intestinal absorption of calcium and phosphorus.
Serum 1,25-(OH)
2
D also promotes the differentiation of osteoblasts and stimulates osteoblastic expression
[8]. Vitamin D, specifically vitamin D3
(cholecalciferol), plays a crucial role in various physiological processes
in the body, such as the regulation of calcium and phosphate metabolism. The primary active form of
vitamin D is calcitriol, which is formed in the skin from vitamin D3 (cholecalciferol) in the presence of
ultraviolet B radiation. Calcitriol acts in the intestines to increase the absorption of calcium and phosphate,
additionally, calcitriol promotes the reabsorption of calcium in the kidneys, thereby preventing its loss
through urine [9].
Calcium is an essential mineral that plays a vital role in many physiological processes, including muscle
contraction, nerve function, and blood clotting. Calcium is the most abundant divalent cation in the body,
representing about 2% of body weight, approximately 1,000 grams. It is distributed across various
compartments, with constant exchange flows subject to complex regulatory mechanisms. More than 98%
of the body's calcium is found in the bone compartment, of which approximately 1% is freely exchangeable
with extracellular fluid [10], [11]. Serum calcium exists in three (3) different forms: ionic or free form, which
accounts for approximately 50%; protein-bound, approximately 40%; and finally, about 10% forms
complexes with anions such as bicarbonate, citrate, phosphate, and lactate [12]. Ionic calcium and calcium
bound to anions constitute the ultra-filtrable fraction, with the ionic fraction being the only one with
biological activity and, therefore, subject to hormonal control. The circulating extracellular calcium pool
exists in three (3) different states, protein-bound, anion-bound, and free or ionized. Protein-bound, anion-
bound, and free or ionized calcium account for approximately 40-45 %, 5-10 %, and 45-50 % of the total
calcium in circulation respectively [13]. When calcium measurements are needed, there are two (2) options
to obtain the concentration, total calcium, and ionized calcium (iCa
2+
). The total calcium measurement is
the sum of the subfractions (protein-bound, anion-bound, and free or ionized). Total, calcium measurement
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Velez A. et al. A study of the mechanical and electrical properties of the cortical bone based on age, biochemical factors and Nernst equation
is widely used because it is an accurate representation of calcium homeostasis in most cases and can be
included as part of a routine blood collection. While total calcium measurement is valuable in many patients,
it can yield misleading results in situations where circulating protein concentrations are abnormal either by
excessive protein loss or impaired protein synthesis [14].
For these reasons, there exists a pressing clinical and analytical demand for the direct measurement of iCa
2+
.
The difficulty in measuring iCa
2+
arises primarily from the rigorous preanalytical conditions that must be
met. The equilibrium is influenced by pH levels, as the binding of calcium to proteins is notably sensitive to
changes in pH. Thus, pH change is inversely proportional to the concentration of iCa
2+
. Typically, changes
by 5 % for every 0.1-unit change in pH as hydrogen ions effectively compete with iCa
2+
for available negative
charges on proteins [15]. The application of pH-adjusted calcium was clinically useful, but a change in pH
that occurred after collection would affect the accuracy of the results by an error of 10% approximately [16].
Therefore, ion practice to correct the pH-adjusted free calcium measurements are recommended to multiply
the iCa2+ by 10 % approximately.
True Calcium =Reported Total Calcium+0.8 (4.0-Serum Albumin) (1)
where “True Calcium”; “Reported Total Calcium”; and “Serum Albumin” have units of mg/dL, m/dL, and g/dL
respectively. The concentration of calcium in the blood is tightly regulated by the PTH and other factors
[17]. Approximately, 90% of protein-bound calcium binds to albumin in a pH-dependent manner.
Alterations that decrease serum albumin values will decrease total serum calcium but will have a smaller
effect on ionized calcium concentration. In general, each g/dL of albumin binds approximately 0.2 mmol/L
(0.8 mg/dL) of calcium, so to correct hypoalbuminemia, it is necessary to add 0.2 mmol/L to the total calcium
concentration for every g/dL decrease in albumin concentration from the normal values of 4.0 g/dL [12],
[18]. The binding of calcium to albumin is also affected by the pH of the extracellular fluid. Acidemia will
decrease protein binding and increase ionized calcium. For every 0.1 decrease in ionized pH, calcium
increases approximately by 0.05 mmol/L. The exact regulation of serum calcium is controlled by calcium
itself through a calcium receptor and various hormones, the most important of which are PTH and 1,25-
dihydroxyvitamin D
3
(1,25(OH)
2
D
3
). Maintaining appropriate calcium equilibrium, and therefore serum
calcium levels, is a complex and dynamic process involving calcium absorption and excretion in the
intestines, filtration, and reabsorption in the kidneys, and its storage and mobilization in the skeleton.
Calcium homeostasis refers to the regulation of the calcium ions concentration in the extracellular fluid [19].
Normal serum calcium concentration varies between laboratories but is usually 8.5 to 10.5 mg/dL (2.1 to
2.6 mmol/L) and it represents the sum of the three circulating fractions mentioned above [20].
Table 1. Calcium intakes by life stage.
LSG
(Yr.)
AI
(mg)
EAR
(mg)
RDA
(mg)
TUIL
(mg)
MALES
19-30
—
800
1,000
2,500
31-50
—
800
1,000
2,500
51-70
—
800
1,000
2,000
> 70
—
1,000
1,200
2,000
FEMALES
19-30
—
800
1,000
2,500
31-50
—
800
1,000
2,500
51-70
—
1,000
1,200
2,000
> 70
—
1,000
1,200
2,000
LSG = Life Stage Group; AI = Adequate Intake; EAR = Estimated Average Requirement; RDA = Recommended Dietary
Allowance; TUIL = Tolerable Upper Intake Level, The LSG unit is years (Yr.). The symbol (>) means greater than [21].
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Velez A. et al. A study of the mechanical and electrical properties of the cortical bone based on age, biochemical factors and Nernst equation
On the other hand, the body's pH is regulated by various systems, including calcium regulation systems.
Acid-based balance is important for maintaining the normal functioning of enzymes and metabolic
processes. When blood calcium levels decrease, the release of PTH can be activated, which in turn can
influence acid-base balance. Acidosis, characterized by a lower-than-normal blood pH, can affect the
binding of calcium to proteins and, as a result, influence ionized calcium levels in the blood. This can have
an impact on hormonal response and calcium homeostasis. The PTH is secreted by the parathyroid glands
in response to low levels of calcium in the blood. PTH increases the reabsorption of calcium in the kidneys,
thereby releasing more calcium into the bloodstream. PTH stimulates the release of calcium and phosphate
from the bones, which raises the concentration of calcium in the blood. Additionally, PTH plays a crucial
role in regulating calcium levels in the body, with one of its primary targets being bone tissue. Below, it is
describing the mechanism of action of PTH in bone and its principal functions:
• Stimulation of Osteoclast Activity: PTH activates osteoclasts, which are cells that resorb bone.
• Inhibition of Osteoblast Activity: Although PTH primarily stimulates bone resorption, it can also
indirectly inhibit the activity of osteoblasts, reducing bone formation under certain conditions [23].
• Calcium Homeostasis: PTH plays a central role in maintaining serum calcium levels within a narrow
range. This calcium is then available for vital physiological functions such as muscle contraction and
nerve signaling.
• Response to Hypocalcemia: When blood calcium levels decrease, the secretion of PTH increases.
This hormone acts rapidly to mobilize calcium from bone tissue, ensuring that the body maintains
the necessary levels for normal physiological processes.
• Bone Remodeling: PTH is a key regulator of bone remodeling, which involves both bone resorption
and formation. By promoting bone resorption, PTH contributes to the removal of old or damaged
bone tissue and the release of stored calcium. This, in turn, allows for the deposition of new bone
matrix when conditions are appropriate.
In this study, the investigation was carried out to explore the relationship between calcium concentration,
age, PTH, and pH using an electrochemistry equation and experimental data from mechanical and electrical
properties of the cortical bone. We have explored the significance of the Nernst equation in elucidating ion
transport across biological membranes and its role in maintaining cellular electrical potentials, let's delve
into the complexities of determining the precise electrical requirements for bone healing.
II. FIELDS OF INTEREST TO THE SUBJECT
The Nernst equation describes the relationship between the concentration of ions and the electric potential
difference (voltage) across a membrane or at an electrode interface. This equation is crucial for
understanding ion transport phenomena across biological membranes, including cell membranes, and
provides insights into how cells maintain their electrical potential as well as the electrical potentials at a
cellular level. However, determining the exact amount of electricity needed for bone healing would require
a more comprehensive approach that considers all relevant biomechanical factors and mechanisms. For
that reason, experiments were conducted to determine the mechanical and electrical properties of the
cortical bone, emphasizing the experimental correlation between both properties through a statistical
analysis. Additionally, biochemical factors and components such as pH, PTH, and calcium concentration
were analyzed to understand their interaction and the biological response when electrical stimulation is
applied.
The Nernst equation is typically expressed as follows:
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Velez A. et al. A study of the mechanical and electrical properties of the cortical bone based on age, biochemical factors and Nernst equation
Where:
• E represents the electric potential difference (in volts) across a membrane or at an electrode.
• E
0
is the standard electrode potential, a reference value.
• R is the universal gas constant.
• T is the absolute temperature (in Kelvin).
• n is the number of electrons transferred in the reaction.
• F is the Faraday constant.
• [A
−
] y [A] are concentrations of the ion Ca
2+
on either side of the membrane or at the electrode
interface.
According to (2) above, the potential difference across a membrane is proportional to the concentration
gradient of the ions involved, where [Ca
2+
] in is the concentration of calcium ions inside the cell, and
[Ca
2+
]out is the concentration of calcium ions outside the cell and n is 2 due to the number of electrons
transferred from Ca
2+
. The Nernst equation illustrates how changes in ion concentrations can affect the
electric potential across a membrane. The electrical characterization of biological tissues is a great interest
in the bioengineering field, especially, obtaining electrical properties of biological tissues such as bone
structures. The most common electrical properties associated with bone studies include electrical
conductivity, permittivity, and impedance, which provide information about the composition, health, and
functionality of the tissue. The Nernst equation can be applied to assess the electrical behavior of biological
tissues and explore how different ions influence their electrical properties.
For example, the electrical conductivity of cortical bone depends on various factors, including ion
concentrations and the porosity of the bone matrix. Ions such as calcium (Ca²⁺) and phosphate (PO₄³⁻) play
a crucial role in bone tissue. The Nernst equation can be used to calculate the equilibrium potential for
these ions and understand how they influence the electrical conductivity of cortical bone. Studies have
shown that changes in bone health, such as osteoporosis or the presence of fractures, can alter the electrical
properties of cortical bone. By measuring the electrical conductivity of bone tissue, bioengineers can assess
bone quality and monitor bone health, providing valuable information for clinical diagnoses and treatment
planning. Electrostimulation has proven to be promising in promoting bone healing and regeneration.
Techniques such as Pulsed Electromagnetic Field Therapy (PEMF) involve the application of electric fields to
bone tissue to stimulate cellular responses that enhance bone growth. Bioengineers can utilize the Nernst
equation to calculate the electric potential required to influence specific ion concentrations within bone
tissue. This information helps optimize the design of electric stimulation devices for bone healing,
potentially speeding up the recovery process for individuals with bone fractures or orthopedic surgeries
[34].
III. METHODOLOGY
A. Methodology for literature review
The methodology described herein outlines a systematic and rigorous approach to the selection of research
papers in the fields of bioengineering and science. The process, consisting of thirteen distinct steps, is
designed to curate a collection of papers that meet stringent criteria for scientific excellence, relevance,
ethical standards, and potential impact on the advancement of knowledge within the realm of engineering
applications to biological systems. By employing a comprehensive and meticulous screening process, we
aim to ensure that only the most valuable and deserving research contributions are included in our final
selection. This methodology serves as a robust framework for the critical evaluation of scientific literature,
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Velez A. et al. A study of the mechanical and electrical properties of the cortical bone based on age, biochemical factors and Nernst equation
facilitating the identification of papers that make significant contributions to the fields of science and
bioengineering while upholding the highest standards of quality and ethics.
1. Initial Screening - Collecting a pool of research papers related to bioengineering and science topics.
2. Peer Review Evaluation - Exclude papers that have not undergone a thorough peer review process.
3. Relevance Assessment - Evaluate papers for their relevance to science and bioengineering fields.
Exclude papers that are not directly related to engineering applications to biological systems, or related
topics.
4. Scientific Rigor Evaluation - Assess the scientific rigor of the selected papers. Exclude papers that lack
well-designed experiments, appropriate statistical analysis, or robust methodology.
5. Clear Objectives and Hypotheses - Examine the papers for clear and well-stated objectives and
hypotheses. Exclude papers that do not effectively address these objectives.
6. Originality Check - Verify whether the research presents novel findings, methods, or applications that
contribute to the advancement of bioengineering knowledge. Exclude papers that do not meet this
criterion.
7. Significance Assessment - Determine whether the paper makes a substantial contribution to the
science and bioengineering fields. Exclude papers that do not tackle important problems, or advance
understanding in a meaningful way.
8. Clarity and Coherence Evaluation - Evaluate the organization and clarity of the papers. Exclude papers
poorly organized or with unclear writing that hinders effective communication of results, and
conclusions.
9. Ethical Review - Ensure that the research follows ethical standards, including the protection of human
and animal subjects and proper citation practices. Exclude papers that violate ethical guidelines.
10. Interdisciplinary Assessment - Consider whether the research demonstrates a strong interdisciplinary
approach, combining principles from engineering, biology, and other relevant sciences. Favor papers
that exhibit interdisciplinary characteristics.
11. Impact Factor Consideration - Consider the potential impact of research on healthcare, technology, or
engineering and science applications. Consider this as a positive factor when evaluating the papers.
12. Exclusion Criteria Application - Apply the exclusion criteria to the selected papers to exclude any that
meet any of the criteria mentioned in the exclusion list.
13. Final Selection - After applying all the criteria, select the papers that meet the inclusion criteria while
excluding those that meet any of the exclusion criteria. See Table 2 for Inclusion and Exclusion criteria.
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Table 2. Inclusion and exclusion criteria.
Criteria
Inclusion
Exclusion
Peer Review Journals: Papers should undergo a thorough peer
review process to assess their quality and validity.
Unsubstantiated Claims: Research with unsupported or
exaggerated claims should be rejected.
Relevance to Science and Bioengineering Fields: Relate to
applications of engineering principles to biological systems,
biomedical devices, or related topics.
Poor Methodology: Research with inadequate experimental
design, data collection, or statistical analysis may be rejected.
Scientific Rigor: Demonstrate a high level of scientific rigor,
including well-designed experiments, appropriate statistical
analysis, and robust methodology.
Plagiarism and Ethical Violations: Papers found to contain
plagiarism or ethical violations, such as fabrication or
falsification of data, should be rejected.
Clear Objectives: The objectives and hypotheses should be
clearly stated, and the paper should effectively address these
objectives.
Insufficient Originality: Papers that do not present significant
new contributions or merely replicate existing work may be
rejected.
Originality: The research should present novel findings,
methods, or applications that contribute to the advancement of
bioengineering knowledge.
Inadequate Presentation: Papers with poor organization,
unclear writing, or insufficient data presentation may be
rejected.
Significance: The paper should make a substantial contribution
to science and bioengineering fields, either by tackling
important problems, providing innovation, or advancing
understanding in a meaningful way.
Inadequate Ethical Considerations: Papers that do not adhere
to ethical standards regarding the use of human or animal
subjects or fail to disclose conflicts of interest may be
rejected.
Clarity and Coherence: The paper should be well-organized,
with clear writing to communicate results, discussion, and
conclusions effectively.
Lack of Relevance: Papers that are not related to science and
bioengineering or do not have a clear connection to the fields
should be rejected.
Ethical Practice: Research must follow ethical standards,
including human and animal subject protection, as well as
appropriate citation and avoidance of plagiarism.
Conflict of Interest: Papers with undisclosed conflicts of
interest that could bias the investigation, or its interpretation
should be rejected.
Interdisciplinary Nature: The research may be favored if it
demonstrates a strong interdisciplinary approach, combining
principles from engineering, biology, and other relevant
sciences or fields.
Poor Presentation: Papers with disorganized writing,
ineffective communication of results, unclear data
presentation, or inadequate explanations may be excluded.
Impact Factor: Consideration of the potential impact of research
on healthcare, technology, or any other applications within the
bioengineering and science fields.
Outdated or Irrelevant References: Papers that heavily rely on
outdated or irrelevant references may be rejected.
The keywords used to obtain the articles were as follows:
• “Calcium concentration” and “pH”
• “Calcium concentration” and “PTH”
• “Mechanical properties” and “Electrical properties”
• “Nernst equation” and “Electrochemical potentials”
• “aging” and “calcium”
• “Aging” and “Young modulus”
• “Vitamin D” and “Calcium absorption”
• “Calcium homeostasis” and “PTH mechanism”
• “Hormonal regulation” and “Bone health”
• “Bone healing” and “electrostimulation”
B. Methodology for experimental analysis
This methodology outlines the experimental procedures and analytical steps performed to correlate
mechanical and electrical properties of cortical bones obtained in the first phase of this investigation with
factors such as gender, age, calcium concentration, pH, and PTH levels, linking this data to the Nernst
equation for clinical application. The process consists of twelve distinct steps to perform the experimental
analysis of this research. The study aims to establish a relationship between these properties and use them
to predict the electric potential difference across cortical bone membranes for safe electrostimulation in
bone fracture healing.
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Velez A. et al. A study of the mechanical and electrical properties of the cortical bone based on age, biochemical factors and Nernst equation
1. Gather data related to demographic and biochemical factors such as gender, age, calcium
concentration, pH, and PTH levels. The data obtained shall not be more than 10 years back from
2023.
2. Prepare an organized table for the factors mentioned in Step 1 and provide it in the Results section.
3. Correlate demographic data with biochemical factors.
4. Correlate the mechanical and electrical properties with demographic data and biochemical factors
using statistical analysis.
5. Apply the Nernst equation to relate the electrical properties to ion concentration and membrane
potential.
6. Use the correlation obtained in Step 4 and the Nernst equation to predict the electric potential
difference (voltage) across cortical bone membranes.
7. Based on the predicted voltage, determine safe levels for electrostimulation in bone fracture
healing.
8. Provide clinical recommendations for electrostimulation therapy.
9. Provide recommendations for healthcare practitioners regarding the application of
electrostimulation for bone fracture patients, considering gender, age, calcium concentration, pH,
and PTH levels.
10. Summarize the findings regarding the correlation between mechanical and electrical properties of
cortical bones with biochemical factors.
11. Highlight the clinical implications and potential benefits of using the predicted voltage relationship
for electrostimulation applications in bone fracture healing.
12. Include all relevant references to prior studies, methodologies, and scientific literature related to
bone mechanics and fracture healing, bioimpedance, and electrostimulation.
IV. RESULTS
The basic analyzed data and corresponding results are described below.
A. Demographic and biochemical data
The gathered data used jointly with the mathematical model so developed is presented in Table 3 below.
Table 3. Demographic data based on biochemical factors.
AG = Age Group; CCB = Calcium Concentration in Blood; PTH-L = Parathyroid Hormone Levels; pH Sc. = Acidity/Alkalinity Scale.
AG unit is years (Yr.). The symbol (>) means greater than., CCB, PTH-L, andpH Sc. Values were obtained from [35], [36], [37].
The obtained results show that calcium concentration decreases with age due to changes in bone
metabolism and hormonal regulation. It was also found that PTH levels increase with age as a compensatory
mechanism to maintain calcium homeostasis. Furthermore, we observed that pH has a significant effect on
calcium concentration due to its impact on ionization states.
AG
(Yr.)
CCB
(mg/dL)
PTH-L
(pg/mL)
pH Sc.
(0-14)
MALES
19-30
8.6 - 10.0
10 - 55
7.35 - 7.45
31-50
8.6 - 10.2
10 - 50
7.35 - 7.45
51-70
8.6 - 10.4
10 - 55
7.35 - 7.45
> 70
8.6 - 10.5
10 - 65
7.35 - 7.45
FEMALES
19-30
8.6 - 10.0
10 - 50
7.35 - 7.45
31-50
8.6 - 10.2
10 - 50
7.35 - 7.45
51-70
8.6 - 10.4
10 - 55
7.35 - 7.45
> 70
8.6 - 10.5
10 - 65
7.35 - 7.45
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B. Mechanical and electrical properties correlation with demographic data, and biochemical factors
To correlate the obtained experimental data, conductivity and permittivity variables were plotted as show
in Fig. 1.
Fig. 1. Conductivity and Permittivity Relationship. Source: The authors.
For a better understanding of Fig. 1, it is assumed that the studied bone falls within either the
osteoporosis or normal condition, but as the osteoporosis bone can resist a tension stress of about 18.28
MPa, when compared this value with the obtained value of 28.6 MPa thus it is ‘possible to conclude as a
normal bone. Nevertheless, by using (3) and (4), it is also possible to get σ
Elec Max
y ε
a
values for the two
bones conditions respectively.
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Velez A. et al. A study of the mechanical and electrical properties of the cortical bone based on age, biochemical factors and Nernst equation
C. Mechanical and electric properties relationship
Fig. 2. (a) Left: Age effect on tensile stress; (b) Right: Young modulus (green male, blue women vs. age). Source: The
authors.
Fig. 3. Conductivity vs Young modulus, (a) left women, (b) right men. Source: The authors.
To investigate the relationships between mechanical and electrical properties, it was imperative to
determine the slope of the mechanical graphs for each of the samples, which signifies the modulus of
elasticity.
Fig. 4. Effect of pH in blood on the membrane’s electric potential. Source: The authors.
y = -2.4058x
2
+ 42.312x - 125.87
R² = 0.999
50
51
52
53
54
55
56
57
58
6,6 6,8 7 7,2 7,4 7,6 7,8
Membrane potential
(mV)
Blood pH
y = -0.0019x
2
+ 0.0524x + 43,663
R² = 0.9403
34
36
38
40
42
44
46
15 35 55 75
Tensile Strenght
(MPa)
Age (Years)
y = 0.1486x
2
- 10.32x + 405.34
R² = 0.9807
y = 0.452x
2
- 34.309x + 799.09
R² = 0.9794
0
200
400
600
800
1000
1200
20 40 60 80 100
Young Modulus (MPa)
Age (Years)
y = 1.3446e
0.0028x
R² = 0.9916
0
1
2
3
4
5
6
7
170 270 370 470 570
Conductivity (
μS/cm xE
-07)
Young Modulus (MPa)
y = 1.5859e
0.0019x
R² = 0.9757
0
2
4
6
8
10
12
150 650 1150
Conductivity (
μS/cm x E
-07)
Young Modulus (MPa)
30
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Velez A. et al. A study of the mechanical and electrical properties of the cortical bone based on age, biochemical factors and Nernst equation
CONCLUSIONS
In conclusion, the present research provides new insights into the complex relationship between calcium
concentration, age, PTH, and pH. The Nernst equation has been identified as a valuable application in the
field of bioengineering, particularly in the characterization of cortical bone. By understanding the electrical
properties of cortical bone and applying the Nernst equation, researchers can assess bone health, and
optimize electrical stimulation therapies for bone healing. This interdisciplinary approach demonstrates how
the principles of science and engineering can be harnessed to advance healthcare solutions and improve
the quality of life for individuals with bone-related conditions. The findings suggest that changes in these
factors can have significant implications for human health and disease. Further research is needed to fully
understand these relationships and develop effective interventions to prevent or treat related conditions by
means of define stimulation parameters through iterative experiments to achieve the desired biological
responses while minimizing potential side effects. Finally, further experimental tests will be useful to validate
the effectiveness of the designed electrical stimulation involving in vitro studies using samples of bone
tissue or in vivo studies with animal models.
ACKNOWLEDGMENT
I would like to express my sincere gratitude to UNEXPO, Puerto Ordaz, for their continuous support and
guidance throughout the process of this research, the preparation of this paper and transformative years.
Their insights and assistance have been instrumental in shaping the outcome of this work.
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AUTHORS
Alex J. Velez-Cruz, is an engineering doctoral student and mechanical engineer who was
born and race in Puerto Rico (PR). He is a faculty member of the BME Department at the
Polytechnic University of PR and is a young passionate researcher and an inventor that
works constantly in the product development area with the intent to serve and help people
in need.
Oscar Gilberto Dam, is a PhD in Engineering, specialized in metallurgical and industrial
applications. He is the Co-Founder of the Metallurgical and Materials Research Institute at
the UNEXPO. He is a well respectable and prestigious professor and metallurgical engineer
within the Latin American scientist community.
