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Advanced Biomechanics of
Physical Activity (KIN 831)
Lecture 8
Biomechanical Models and Modeling*
* Some of the material included in this presentation is derived from:
Nigg, B. M. (1994). In B. M. Nigg & W. Herzog (Eds.), Biomechanics of the Musculo-Skeletal System (pp.365-379).
West Sussex, UK:John Wiley & Sons.
What is a model?
Definitions
• Model – an object, plan, or theory that represents
or imitates many of the features of something else
(“an attempt to represent reality”)
• Deduction – logical reasoning from a known to
the unknown, from the general to the specific
• Induction – logical reasoning from particular
facts or individual cases to a general conclusion
• Validation (of a model) – providing evidence that
a model is strong and powerful
Definitions (continued)
• Biomechanical model – a representation
(microscopic or macroscopic) of a biological
system
• Free body diagram – simplified drawing of a
mechanical system, isolated from its surroundings,
showing all force vectors and torques
• Generalizable – the ability to make broader
application of a process or results
1. Working in groups of two,
carefully develop a model
(drawing) of a inanimate (not a
biological structure) mechanical
structure which you can show to
the class and define its function.
[These models should be relatively simple mechanical
systems.]
Example:
2. Using the example provided,
what do you know about the
model? List several
assumptions that have been
made about the model and
indicate why these assumptions
may have been made.
Model
•
Known Facts
• Assumptions
KNOWN FACTS (?):
F1s1 = F2s2
or
F1 = F2(s2/s1)
s1 = ½(s2)
ASSUMPTIONS:
1.
2.
3.
3. Refine the model (drawing) in
order to remove some of the
assumptions about the model.
You will be asked to show your
revised model and its
assumptions.
4. Attempt to simplify the model
and redraw it. Be prepared to
show and explain your simplified
model to the class.
Hints:
- possibly representing parts of the structures as a point masses and/or lines
- possibly representing the parts of the structure by its behavior according
to the laws of physics
Why are biomechanical
models used?
Why are biomechanical models used?
1. to simplify the understanding of the structure
and function of a biological system
2. to simply the kinematics and/or kinetics
analysis of the biological system
3. to remove the biological system from exposure
to potential adverse effects by exposing a
representative model and observing its
behavior
Purposes of models and modeling
1. to increase knowledge and insight about reality
2. to estimate or predict variables of interest
[The fact that insight and knowledge are
prerequisites for the development of a
model, but are also the purpose of using a model,
seems contradictory.]
Information used to construct a model
1. Knowledge of the system being modeled
–
Using knowledge of the system being modeled, to
move from general principles to specifics, is a
deductive process.
2. Experimental data that constitute system inputs
and/or outputs
–
Using experimental data, in an attempt to arrive at a
general conclusion that explains the data, is an
inductive process.
Deduction versus Induction
Information used:
knowledge
experimental data
Method used:
deduction
induction
unique solution
no unique solution
Expected results:
Constructing a model – information, method, and results
1. Knowledge may be preliminary assumptions.
2. In deductive model there may be many assumptions.
3. In inductive model there may be many possible answers.
Simplification
1. In general, simple is better.
2. Simple may not agree with reality.
3. The key to a model (modeling) is to know
what to include and what to eliminate; there is
a science and art to creating a model.
Validation of a model
1. Validation of a model means that evidence is
provided that the model is strong and powerful
for the task for which it has been designed (i.e.,
provision of cases for which the results of the
model corresponds to reality).
2. Validation may lead to increased confidence in
a model, but it never confirms that the model
corresponds to reality.
Three ways to validate a model
1. direct measurement – comparison of estimated
results from a model with actually measured
results (e.g., predicting projectile distances of
javelin from information about angle of
projection, height of release, and velocity of
release and comparing it to actually measured
projectile distances)
Three ways to validate a model
(continued)
2. indirect measurements – measurements of
another variable may be made and compared
with the value predicted for this variable from
the model (e.g., use of IEMG of the hamstring
muscles compared with the model’s predicted
value of knee flexion force)
Three ways to validate a model
(continued)
3. trend measurements – the quality of a model
depends on how well the trends predicted agree
with the trends measured (e.g., if the model
predicted that measured girths of the forearm
were linearly related to grip strength,
validation would require several input
variables and subsequent out put values)
Types of models
1. Analytical - deductive
2. Semi-analytical – many assumptions are used
because there are more unknowns than
equations to solve for the unknowns
3. Black box – regression models; functions used
to determine relationships between input and
output
4. Conceptual – used in hypothesis testing
Cyclical interaction between facts and theory
in scientific activities
theories
deduction
induction
“Science must start
with facts and end with
facts, no matter what
theoretical structures it
builds in between.”
description
prediction
evaluation
observation
facts
facts
1. Start with observation to build upon what is
known.
2. Describe what is known
3. Use the known facts to come to general
conclusions; induction)
4. Develop and test the predictions of theories
(models); deduction
5.
6.
7.
8.
Compare results with actual facts
Evaluate the process
Seek additional facts
Refine theories (models) and possibly
repeat the process
Why are biomechanical models used?
1. to simplify the understanding of the structure
and function of a biological system
2. to simply the kinematics and/or kinetics
analysis of the biological system
3. to remove the biological system from exposure
to potential adverse effects by exposing a
representative model and observing its
behavior
Why are biomechanical models used?
(continued)
4. to obtain information on the structure and
function of the biological system
5. to simplify the presentation of a complex
biological system
General steps in developing a
biomechanical model
[Prior to developing a biomechanical model the scientist must:
a) have a thorough understanding of existing facts,
b) make observations of the phenomena to be studied, and
c) develop an understanding of the integration of facts and observation.]
1.
2.
3.
4.
Define question to be answered
Define the system of interest
Review existing knowledge (literature review)
Select procedure (model) to be applied to solve research
question; research methods
5. Make simplifications and assumptions; decide what to
include and what not to include based on defendable
reasons
General steps in developing a
biomechanical model
[Prior to developing a biomechanical model the scientist must:
a) have a thorough understanding of existing facts,
b) make observations of the phenomena to be studied, and
c) develop an understanding of the integration of facts and observation.]
6. Formulate mathematical approach (e.g., statistical
methods) to be applied to data
7. Develop mathematical solution (results)
8. Evaluate the model
9. Discuss, interpret, and apply the results
10. Draw conclusions
What are categories of
biomechanical models?
1. Static versus dynamic
a.
b.
static implies constant linear and/or angular velocity (linear
and/or angular acceleration = 0)
dynamic implies changing linear and/or angular velocity
(linear and/or angular acceleration  0)
2. Object Dimension
a.
b.
c.
d.
point-mass (0 dimension)
line (1 dimension)
plane (2 dimensions)
solid (3 dimensions)
3. Space Dimension
a.
b.
c.
uni-axial
bi-axial
tri-axial (three dimensional Cartesian coordinate system)
What are categories of biomechanical
models? (continued)
4. Kinematic versus kinetic
a.
b.
kinematic implies a description of position without regard for
forces and torques
kinetic implies the forces and torques that cause linear and/or
angular accelerations
5. Uni-segment versus multi-segment
a.
b.
uni-segment implies internal and external forces and torques
multi-segment implies reactive forces (joint reaction force)
and torques (mutual net muscle moments across joints)
between segments
Input parameters for biomechanical
models
1. Direct measurement – actual measurements of
parameters used in the model (e.g., height, weight)
2. Indirect measurement – measures predicted from other
sources of information (e.g., location of the center of
mass of a segment of the body, segments proportion of
total body height, estimate of density of a body segment
3. Inverse dynamics – the use of linear and angular
acceleration parameters and information about
segmental mass and moment of inertia to determine
forces and torques
a.
b.
mass X acceleration = force (equation of linear motion)
moment of inertia X angular acceleration = torque or moment
(equation of angular motion)
What is a free body diagram?
Free body diagram
[simplified drawing of a mechanical system, isolated from
itssurroundings, showing all forces vectors and torques]
1. Particle (or point-mass) free body diagram –assumed
that kinematics of object can be represented by its
center of mass and its linear movement (e.g., parabolic
path of the center of mass of a long jumper in flight)
[Note that there is no angular motion associated with a point
mass.]
fy
fr
fx
=
mg = wt.
Free body diagram (continued)
[simplified drawing of a mechanical system, isolated from its
surroundings, showing all forces vectors and torques]
2. Segmental - can represent the human body mechanically
as a linked system of rigid segments moving about an
axes of rotation through joints
fyp

p

fxp
ay
ar
ax
mg = wt.
fxd
fyd
d
Assumptions
1. Rules for making assumptions
a.
b.
c.
d.
assumptions should not adversely or substantially affect the
results of the model (e.g., knee joint is pinned)
assumptions should generally simplify the model (e.g.,
assumptions should be able to be justified (e.g., linear and
angular accelerations are small and therefore can be
neglected)
assumptions should usually be made for unknowns (e.g.,
knee joint is frictionless)
2. Reasons for making assumptions
a. remove complexity from model
b. simplify computation and/or understanding
c. lack of knowledge