Lecture Bone Repair
April 1,2016
ECEN 5031/4031
Electric and Magnetic Stimulation of
Bone and Tissues
• 1 Both electric and magnetic fields can
modulate growth processes.
• 2. The healing of bones that would not regrow
is the most widely used application in this
area.
• 3. Wound healing and soft tissue growth are
coming along more slowly.
•
Background
• 1. 5,000,000 bone fractures a year in US and
5% delayed or nonunion.
• 2. Multiple Approaches to applying Electric
Fields.
– A. Pulsed
– B. RF Carrier
– C. Sine waves
– D. Direct E fields or induced E fields with
𝜕𝐵
𝜕𝑡
Background
• 1. Acceleration of bone growth up 150% in
rats
• 2. Inhibit loss of bone in weightless
environment
• 3. One study showed best result with a sine
wave at 15Hz and 10µV/cm peak E field
• 4. Another study showed best results for
spinal fusion 10µA/cm2
Background
• Get bone regrowth with currents in the range of
–
i = 5 to 100µA
• Voltages of V= 1 to 100mV/cm at the repair site
and frequencies in range of 20 to 200kHz
• The electric field result in the stimulation of 28%
in cell proliferation, a 5 fold increase in growth
factor IGFII release ,and increases in osteoblast
receptors expression. Also modulation of Ca
Calmodulin binding and other changes in the
chemistry.
Background
• 1. 15 out of 20 randomized studies showed
effectiveness of EMF stimulation of bone
repair. 5 did not. Most of these studies used
PEMF
• 2. One study of surgical treatment of 569
ununited tibial bone fractures effective 82%
and of 1718 with PEMF 81%
• 3. Ultrasound also seems to work.
Some Clinical Studies on Soft Tissue.
• 1. Double blind treatment of pressure ulcers
84% closure with PRF vs 40% with no
treatment. Another study 60% closure vs 0
with no treatment.
• 2. Also studies showing reduction in edma by
seven fold on ankle sprains and pain decrease
by 50%.
• 3. Lots of others but also cases of no effects.
Lecture 26 April 4, 2016
• Models for Bone Repair.
• Background stress 0.1 to 2mV/cm under load.
• Less than 1mV/cm to maintain normal state.
• 60Hz at 9.6µV/cm inhibits osteoclast cell growth
• Rubin et.al.1996 Journal of Bone and Joint
Surgery.
Website for review on effects of EMF on plants
• http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4
769733/
Schematic for Coil and Probe
PMF Induced Electric Fields
• For an air core R, L circuit the current is given by
• The wave form for the induced voltage is given by
When the time constant τc=(R/L) is small you get constant
voltage for a linear increase in current.
Make L small so the driving voltage is < 25V
Induced Electric Field
The Induced E Fields
• 1.
• 2. At RF we get large
• 3. For non uniform fields we need
Electrochemical Information Transfer
Model
• 1. Art’s hypothesis is that the E field must be
large enough to effect ion binding and transport.
• 2. The signal must be on the same order as those
required to trigger a nerve pulse or a few
millivolts across the membrane.
• 3. The membrane is the site of the interaction
and involves Ca binding as the first step in a
cascade of events.
• 4. It involves voltage dependent binding of ions
or ligands and the displacement of water.
Equivalent Circuit for Membrane
Plus Chemical Ion Binding
Adds in Effects of Chemical Binding to
the Relaxation Time
• 1. The chemical processes take time. The
chemical flow the follows leads to a current
2. Additionally a coupling coefficient is needed
from the change in surface charge to a change in
the chemical reaction rates.
The Overall Results
• 1. The effective impedance is
• 2. The overall result is that you need to take into
account the chemical binding time constants and the
resulting chemical reaction times to calculate what sort
of signals and time constants you need for you
electrical or magnetic stimulations of the biological
processes.
• 3. So you have 2 time constants to worry about. τ1= 110µs, τ2= 20-200µs for fibroblasts and osteoblasts.
Results Show Bone Growth
• 1. Was directly related to the induced E field.
• 2. This was checked out in a ring dish.
• 3. Other data shows effects of weak magnetic
fields including DC or steady state.
• 4. Our new data by Julian shows an increase in
hyperpolarization by reducing the
magnetic field to < 1µT
ICR and Larmor Precession Model
• 1. We have talked about the Ion Cyclotron
Resonances and the problems with the theory.
• 2. Lorentz- Langevin Equation for a bound ion.
• 3. The solution is
Larmor Model
• For Static magnetic field of 50µT
•
fL= 18Hz for Ca++
Need small damping to the narrow line widths.
Leads to changes Ca –CaM binding.
I have a hard time with this theory for multiple
reasons.
Scanning of DC Magnetic Ca-CaM
Binding.
Pulsed RF and Static B=2 G on
Phosphorylation
Effects of Magnetic Field on Ca-CaM
Binding
Weak Electric Fields and S/N
• 1. There is a need to consider the fact that
cells can be longer than 10µm. Nerve cells can
be centimeters long.
• 2. Gap junctions can have low resistance and
this resistance can be modulated by repetitive
electrical pulses.
• 3. This can lead to concentration of the
electric fields at the end membrane.
Linear Model for Cells Connected by
Gap Junctions.
Impedance Values
• 1. The voltages at any point along the transmission line are
given by
• Where
Ion Binding Admittance
Trans-membrane Voltage as Function
of Frequency and Length
Transmission Line Characteristics.
• 1. Note the voltage decreases with increasing
frequency
• 2. It increases with length at low frequencies.
• 3. Increasing the gap resistance reduces the
ending membrane voltage.
• 4. This can give tissues different characteristics
than cells in culture.
• 5. The effects can be different at different
times in the cell cycle.
Effects of varying Gap Junction Resistance
Resonances
• 1. If we take into account the time delays
associated with the transport of the ions we
can get the equivalent of an inductor.
• 2. For voltage controlled K+ channels with
•
and
• the time constant is given by
• And the admittance is given by
An Equivlent Circuit for the K+
Channels
• 1
Resonate Frequency for E(ω)=10mV f=16Hz and
PEMF=40mV
• 1. Note these parameters work for an array of
cells and are variable.
Signal to Noise Requirements.
• 1. Need a good signal to noise ratio and a large
enough voltage to effect the binding energy.
• 2. The binding time constant is related to the
binding energy and the noise which is in the
range of 1 to 5ms for Ca-CaM. Need to translate
this into an equivlent circuit.
• 3.Need pulse signals components in the
frequency range 102 to 104 Hz
• 4. Pulse length, repetition rate, length of
exposures all make a difference.
Estimated Signal to Noise for Two Wave Forms
PRF at 27MHz E=10mV/cm and PEMF E=1mV/cm
• 1
PRF Modulation Ca-CaM with Burst Width
• 1
Lecture 27 April 6,2016
• Final paper due April 22, 2016
• Final Exam May 2,2016 from 1:30 to 4PM
Ultra Sound Stimulation
• 1. Ultra sound at less than 100mw/cm2 can
stimulate bone growth.
• 2. Commonly use signals 500µs bursts of
1.5MHz sine waves repeating at 200Hz at
30 to 50mW/cm2
• 3. The vibrations move the charge layers to
generate 1 to 10mV in the fluids.
Estimated Signal to Noise for Ca-CaM
Effects of the Initial State to EMF
• 1. Normal bone and tissue do not respond to
the same extant as the injured tissue and
bone.
• 2. Blood flow increase near injury and not
much in normal tissue.
• 3.
• 4.
US vs PMF for Bone Repair on
Chondrocytes in Culture
Membrane Admittance from the HH
Equations
• 1 Depends on the applied E as well.
Summary
• 1. Electric Field Effects on Bone Growth and
Mechanical Vibrations are Coupled.
• 2. The processes are time, amplitude, and
frequency dependent.
• 3. There are multiple processes happening in
parallel .
• 4. These fields work.
Coils for Bone Stimulation
44
Bone
45