% !TEX root = ./busty_transcription.tex
\section{Discussion and future work}

The study of gene expression is one of the dominant themes of modern biology,
made all the more urgent by the dizzying pace at which genomes are being
sequenced. But there is a troubling Achilles heel buried in all of that genomic
data, which is our inability to find and interpret regulatory sequence. In
many cases, this is not possible even qualitatively, let alone the possibility
of quantitative dissection of the regulatory parts of genomes in a predictive
fashion. Other recent work has tackled the challenge of finding and annotating
the regulatory part of genomes \cite{Belliveau2018, Ireland2020}. Once we have
determined the architecture of the regulatory part of the genome, we are then
faced with the next class of questions which are sharpened by formulating them
in mathematical terms, namely, what are the input-output properties of these
regulatory circuits and what knobs control them?

The present work has tackled that question in the context of the first
regulatory architecture hypothesized in the molecular biology era, namely, the
repressor-operator model of Jacob and Monod~\cite{Jacob1961}. Regulation in that
architecture is the result of a competition between a repressor which inhibits
transcription and RNAP polymerase which undertakes it. Through the labors of
generations of geneticists, molecular biologists and biochemists, an
overwhelming amount of information and insight has been garnered into this
simple regulatory motif, licensing it as what one might call the ``hydrogen
atom'' of regulatory biology. It is from that perspective that the present paper
explores the extent to which some of the different models that have been
articulated to describe that motif allow us to understand both the average level
of gene expression found in a population of cells, the intrinsic cell-to-cell
variability, and the full gene expression distribution found in such a population
as would be reported in a single molecule mRNA Fluorescence \textit{in situ}
Hybridization experiment, for example.
We do so by contrasting two theoretical frameworks to think about the problem.
On the one hand, thermodynamic models are convenient ways to describe the
problem of gene regulation because of the relatively small number of parameters
compared with kinetic models, and the agnostic nature with respect to the full
reaction topology that leads to a transcription event. In addition, either
implicitly or explicitly, many approaches to gene regulation focus strictly on
occupancy and ideas such as $K_d$s, and thus is of great interest to test these
models. This comes with the limitation that thermodynamic models are only able
to make statements about mean gene expression of a quasi-steady state process.
On the other hand, kinetic models break those limitations, being able to make
explicit predictions about higher moments of the gene expression distribution,
and the transient states towards steady state, at the cost of propagating the
number of parameters, and demanding the full set of reactions

Our key insights can be summarized as follows. First, as shown in
Figure~\ref{fig1:means_cartoons}, the mean expression in the simple repression
architecture is captured by a master curve in which the action of repressor and
the details of the RNAP interaction with the promoter appear separately and
additively in an effective free energy. Interestingly, as has been shown
elsewhere in the context of the Monod-Wyman-Changeux model, these kinds of
coarse-graining results are an exact mathematical result and do not constitute
hopeful approximations or biological naivete \cite{Razo-Mejia2018, Chure2019}.
The fact that thermodynamic and kinetic models for the simple repression motif
can not only be reconciled, but are indistinguishable from each other at the
level of mean mRNA count is a consequence of the possible transitions between
promoter microstates. The promoter microstates in all models shown in Figure~1
can explicitly be separated into two groups: 1) promoters with repressor bound,
and 2) all other promoters states. The single path between these two groups of
states guarantees detailed-balance between the groups. We can therefore separate
\textit{expression} related transitions, which by definition must be out of
equilibrium, with \textit{regulation} transitions that can in principle be in
equilibrium. This implies that the probability distribution of the promoter
microstates not involving the repressor take the same functional form, allowing
us to write the fold-change as an effective free energy involving a regulation
term, $\Delta F_R$, and a promoter details term, $\rho$. We offer this argument
as a conjecture, and we suspect that a careful argument using the
graph-theoretic framework based on the Matrix-Tree
Theorem~\cite{Gunawardena2012}, might furnish a ``proof'' not with some
challenges as this theoretical framework applies, at the present, to finite
graphs.

To further dissect the relative merits of the different models, we must appeal
to higher moments of the gene expression probability distribution. To that end,
our second set of insights focus on gene expression noise, where it is seen that
a treatment of the constitutive promoter already reveals that some models have
Fano factors (variance/mean) that are less than one, at odds with any and all
experimental data that we are aware of~\cite{So2011, Jones2014}. This
theoretical result allows us to directly discard a subset of the models (models
1-3 in Figure~\ref{fig2:constit_cartoons}(A)) since they cannot be reconciled
with experimental observations. The two remaining models (models 4 and 5 in
Figure~\ref{fig2:constit_cartoons}) appear to contain enough microscopic realism
to be able to reproduce the data. A previous exploration of model 4 demonstrated
the ``sloppy''~\cite{Transtrum2015} nature of the model in which data on
single-cell mRNA counts alone cannot constrain the value of all parameters
simultaneously \cite{Razo-Mejia2020}. Here we demonstrate that the proposed
one-state bursty promoter model (model 5 in
Figure~\ref{fig2:constit_cartoons}(A)) emerges as a limit of the commonly used
two-state promoter model \cite{Peccoud1995, Shahrezaei2008, So2011, Sanchez2013,
Jones2014}. We put the idea to the test that this level of coarse-graining is
rich enough to reproduce previous experimental observations. In particular we
perform Bayesian inference to determine the two parameters describing the full
steady-state mRNA distribution, finding that the model is able to provide a
quantitative description of a plethora of promoter sequences with different mean
levels of expression and noise.

With the results of the constitutive promoter in hand, we then fix the
parameters associated with this class of promoters and use them as input for
evaluating the noise in gene expression for the simple repression motif itself.
This allows us to provide a single overarching analysis of both the constitutive
and simple repression architectures using one simple model and corresponding set
of self-consistent parameters, demonstrating not only a predictive framework,
but also reconciling the thermodynamic and kinetic views of the same simple
repression constructs. More specifically, we obtained values for the
transcription factor association and dissociation rates by performing Bayesian
inference on the full mRNA distribution for data obtained from simple-repression
promoters with varying number of transcription factors per cell and affinity of
such transcription factors for the binding site. The free energy value obtained
from these kinetic rates --computed as the log ratio of the rates-- agrees with
previous inferences performed only from mean gene expression measurements, that
assumed a thermodynamic rather than a kinetic
framework~\cite{Garcia2011a,Razo-Mejia2018}. Interestingly, to constrain the
binding and unbinding rates inferred for Figure~\ref{fig4:repressed_post_full},
all of the rates need to be simultaneously fit. This is because a single
combination of operator (repressor binding site) and aTc concentration
(repressor copy number) cannot constraint both rates independently, but only
their ratio (See Appendix~\ref{sec:bayesian} for further details).

It is important to be clear on the nature of the assumptions  present in all
models, including model 5 from Figure~\ref{fig2:constit_cartoons}(A). First, as
with many of the models used routinely in the analysis of transcription, the
models considered here imagine the promoter as existing in a series of discrete
states. This assumption is clearly an oversimplification due to effects such as
DNA supercoiling~\cite{Chong2014,Sevier2016} or DNA
looping~\cite{Boedicker2013a} which are both parameterized by  continuous
variables describing DNA shape; although there are formal and very interesting
ways of integrating out such degrees of freedom. Another facet of the models
used here is that they can feature irreversible processes characterized by only
a single rate process with no corresponding return pathway at odds with
thermodynamics. Such models are mathematically convenient and serve only as an
approximation to the more realistic situation in which the forward rates are
much larger than the backward rates. One consequence is that the inferred rates
for the transcription burst rate and burst size  can only be thought of as
effective rate constants. Another idealization of the models considered here is
that when computing the fold-change in gene expression (Section 2) we assume
that the translation efficiency of an mRNA transcript is the same in cells with
and without regulation. There might be some known biological effects that could
limit the applicability of this assumption such as cooperation between the
transcription and translation machinery~\cite{Proshkin2010}, or coupling of mRNA
transcription and degradation~\cite{Chen2015} among other potential effects.
Another implicit assumption in all of the models discussed here is that the
effects due to changes in gene copy number during the cell cycle have no effects
on the expression profile. For moderate growth rates such as those used
in~\cite{Jones2014} from which we obtained the data, at all points during the
cell cycle there are at most two copies of the gene of interest. In a recent
publication, we explored the effects that this change in gene dosage can have in
gene expression, finding that the effects are much more drastic at the protein
level~\cite{Razo-Mejia2020}.

More specifically, for model 5 from Figure~\ref{fig2:constit_cartoons}(A), it is
interesting to speculate what microscopic details are being coarse-grained by
our burst rate and burst size in Figure~\ref{fig2:constit_cartoons}(A), model 5.
Chromosomal locus is one possible influence we have not addressed in this work,
as all the single-molecule mRNA data from~\cite{Jones2014} that we considered
was from a construct integrated at the \textit{galK} locus. The results
of~\cite{Chong2014} indicate that transcription-induced supercoiling contributes
substantially in driving transcriptional bursting, and furthermore, their
Figure~7 suggests that the parameters describing the rate, duration, and size of
bursts vary substantially for transcription from different genomic loci.
Although the authors of~\cite{Englaender2017} do not address noise, they note
enormous differences in mean expression levels when an identical construct is
integrated at different genomic loci. The authors of~\cite{Engl2020} attribute
noise and burstiness in their single-molecule mRNA data to the influence of
different sigma factors, which is a reasonable conclusion from their data. Could
the difference also be due to the different chromosomal locations of the two
operons? What features of different loci are and are not important? Could our
preferred coarse-grained model capture the variability across different loci? If
so, and we were to repeat the parameter inference as done in this work, is there
a simple theoretical model we could build to understand the resulting
parameters?

In summary, this work took up the challenge of exploring the extent to which a
single specific mechanistic model of the simple-repression regulatory
architecture suffices to explain the broad sweep of experimental data for this
system. Pioneering early experimental efforts from the M\"{u}ller-Hill lab
established the simple-repression motif as an arena for the quantitative
dissection of regulatory response in bacteria, with similar work emerging in
examples such as the \textit{ara} and \textit{gal} operons as
well~\cite{Dunn1984b, Oehler1990, Weickert1993, Oehler1994, Schleif2000,
Semsey2002, SwintKruse2009}. In light of a new generation of precision
measurements on these systems, the definition of what it means to understand
them can now be formulated as a rigorous quantitative question. In particular,
we believe understanding of the simple repression motif has advanced
sufficiently that the design of new versions of the architecture is now
possible, based upon predictions about how repressor copy number and DNA binding
site strength control expression. In our view, the next step in the progression
is to first perform similar rigorous analyses of the fundamental ``basis set''
of regulatory architectures. Natural follow-ups to this work are explorations of
motifs such as simple activation that is regulated by a single activator binding
site, and the repressor-activator architecture, mediated by the binding of both
a single activator and a single repressor, and beyond. With the individual
input-output functions in hand, similar quantitative dissections including the
rigorous analysis of their tuning parameters can be undertaken for the ``basis
set'' of full gene-regulatory networks such as switches, feed-forward
architectures and oscillators for example, building upon the recent impressive
efforts from systems biologists and synthetic biologists~\cite{Milo2002,
Alon2007}.


\subsection{Ranged}
\subsubsection{Bow-type}
\begin{longtable}{|C{2cm} L{2cm} L{2cm} L{8cm}|}
\hline
\large{\textbf{Name}} &
\large{\textbf{Cost}} &
\large{\textbf{Handedness}} &
\large{\textbf{Damage}}
\\ \hline
\WeaponRow{Shortbow}{60 m}{Two}{
Depends on the ammunition, $\frac{AmmoDamage}{10}*Strength$
}{Shortbows are simple bows usually made for practice, sportsmanship or hunting rather than serious military use. They have a short range, and don't offer any bonuses to the damage caused by the arrows used. While the caused damage depends on the specific type of arrow used, such bows typically fail at penetrating armour.}
\WeaponRow{Longbow}{120 m}{Two}{
Depends on the ammunition, $\frac{AmmoDamage*1.5}{10}*Strength$
}{Longbows are sturdier bows roughly the height of their users. Typically used as weapons of war, they require quite a bit of strength to use, and thus, longbowmen are usually trained from a rather young age. They are famous for their long range, and their extra strength gives them some armour-penetrating ability, especially when used with bodkin arrows.}
\WeaponRow{Recurve Bow}{160 m}{Two}{
Depends on the ammunition, $\frac{AmmoDamage*1.5}{10}*Strength$
}{Bows where the limbs curve away from the archer when unstrung, typically made from composites of multiple materials, these weapons store and deliver energy more effectively than regular bows, but also require more strength to use. They are effectively shorter bows, but with the effectiveness of a longbow - though, they are also costlier to manufacture.}
\end{longtable}
\subsubsection{Crossbow}
\begin{longtable}{|C{2cm} L{2cm} L{2cm} L{8cm}|}
\hline
\large{\textbf{Name}} &
\large{\textbf{Cost}} &
\large{\textbf{Handedness}} &
\large{\textbf{Damage}}
\\ \hline
\WeaponRow{Stirrup Crossbow}{100 m}{Two}{
Depends on the ammunition
}{The earliest type of crossbow, it has a draw weight low enough to allow crossbowmen to draw the string back with their bare hands, but this also limits the maximum amount of draw weight such a crossbow can have, which in turn puts a limit on the strength of such a crossbow. With mundane ammunition, such crossbows are typically too weak to penetrate plate armour, merely causing dents.}
\WeaponRow{Goatsfoot Crossbow}{150 m}{Two}{
Depends on the ammunition, $AmmoDamage*1.5$
}{A variation of the stirrup crossbow - when draw weight is increased to the point that a crossbowman cannot pull the string back by their bare hands, some utilities are needed to do the job. The first of such utilities was the goat's foot lever, which slightly reduces rate of fire, but greatly increases the maximum draw weight - therefore maximum firepower - a crossbow can potentially have.}
\WeaponRow{Windlass Crossbow}{200 m}{Two}{
Depends on the ammunition, $AmmoDamage*2$
}{A further evolution of the crossbow - at one point, not even the goat's foot could lever could pull back the strings of the increasingly heavier crossbows, requiring a new utility to do the job: the windlass. Greatly increasing draw weight - potential firepower - at the expense of rate of fire, the windlass crossbow is only slighter faster to reload than a muzzle-loaded firearm, but compensates by penetrating platemail.}
\WeaponRow{Repeating Crossbow}{150 m}{Two}{
Depends on the ammunition, $\frac{AmmoDamage}{4}$ per shot
}{Effectively pump-action repeating crossbow, the repeating crossbow has low firepower and short range, but compensates by having quite a high rate of fire, making it effective at crowd-control against larger number of unarmoured opponents.}
\WeaponRow{Hand Crossbow}{80 m}{One}{
Depends on the ammunition, $\frac{AmmoDamage}{3}$
}{A pistol-shaped handheld crossbow small enough to be held in a single hand, it has a low firepower, short range and a rate of fire comparable to that of a stirrup crossbow, but compensates by being a lightweight hanheld weapon that can be held in a single hand.}
\end{longtable}
\subsubsection{Other}
\begin{longtable}{|C{2cm} L{2cm} L{2cm} L{8cm}|}
\hline
\large{\textbf{Name}} &
\large{\textbf{Cost}} &
\large{\textbf{Handedness}} &
\large{\textbf{Damage}}
\\ \hline
\WeaponRow{Sling}{50 m}{One}{
Depends on the ammunition
}{Ancient weapons that are used to hurl projectiles at the enemy - thus causing crushing damage -, short-ranged and inaccurate, they pack quite a punch when they actually hit their intended target.}
\WeaponRow{Javelin}{80 m}{One}{
\textit{Piercing:} $\frac{2d8 \pm modifiers}{5}*Strength$\hfill \break
\textit{Crushing:} $\frac{1d4 \pm modifiers}{5}*Strength$
}{Shorter spears that are made for throwing. Not much else can be said about them.}
\WeaponRow{Blowgun}{50 m}{Two}{
Depends on the ammunition, $\frac{AmmoDamage}{10}*Strength$
}{Primitive weapons where the projectiles are expelled from a narrow tube via the user's exhalation. Typically used with poisonous darts.}
\WeaponRow{Hand Cannon}{300 m}{Two}{
Depends on the ammunition
}{Primitive firearms powered by either gunpowder or a magical substance that fufills a similar function, hand cannons have an abysmally low rate of fire and a pathetically short range - even shorter than that of a shortbow, comparable to the pathetic range of repeating crossbows and hand crossbows - but compensate for all of this by having a devastating amount of firepower, and by making a loud noise that strikes fear into the hearts of uninitiated. At the weapon's effective range, no known armour can offer meaningful resistance to the bullets this weapon fires. The intended target's only hope for salvation is the weapon's infamously comical inaccuracy.}
\end{longtable}


\chapter{Parameterization of Human Knee Joints}
\label{sec:KneeParams}

The proposed and prototyped knee joint requires a specific input of patient parameters to achieve its goal of matching a person's knee movement. Therefore, a system must be developed to non-invasively identify a relationship between the flexion of the patient's knee joint and the linear movement of the shank away from the knee's joint center. There have been several attempts to parameterize the human knee joint using many different methods, including \cite{3DKinKneeJointOldStabby}, \cite{MRIKneeShape_Unloaded}, \cite{MRIKneeShape_Loaded}, and \cite{ModelAnalysisDeepKneeFlexion}. All of these studies focus on the tibiofemoral relationship, i.e. the bone movement within the lower limbs. However, rehabilitation exoskeletons connect to the skin of its user. Other studies have identified a difference between identifying knee kinematics through skin markers and bone pins \cite{reinschmidt1997effect}, suggesting there is in fact a distinct difference between tibiofemoral movement and skin movement around the knee. Therefore, an imaging workflow and software processing program needs to be developed to be able to parameterize a patient's knee movement with consideration to skin movement.

To identify the knee relationship, an imaging workflow as well as an accompanying software analysis tool is proposed and tested with pilot data. This imaging method uses a motion capture system to identify movement of specific markers attached to a person's skin. This will all be processed using a custom software workflow consisting of both Vicon image processing and custom Python scripts that will extract the parameters from the data. To test this workflow, an experiment is proposed using medical MR imaging to identify the kinematics of the knee joint, compare the developed knee joint to a traditional pin joint, and determine the relationship between the knee joint kinematics and the skin movement surrounding the knee.

\section{Proposed Method of Imaging}
\label{sec:ImaginKneeProcedure}

\begin{figure}[ht!]
    \centering
    \includegraphics[width=0.65\textwidth]{Figures/Param/StudyPatientPositioning.jpg}
    \caption{Depicts the patient position during motion capture. The patient will then flex and extend their knee while keeping the heel on the table.}
    \label{fig:ParamPatientPosition}
\end{figure}

The proposed imaging workflow can be split up into two major parts: the imaging session and the software processing. For flexibility and speed, the usage of a motion capture system is proposed, which can develop accurately track the position of motion dots. In this study, the motion capture system used was a 10-camera Vicon Vantage 5 \footnote{See Vicon system here: \url{https://www.vicon.com/hardware/cameras/vantage/}}, but any motion capture system is usable given enough precision.

To measure the knee flexion, a patient is placed on their back, shown in \autoref{fig:ParamPatientPosition}.Motion capture dots are then placed on the patient using double-sided tape to track the positions where the exoskeleton will attach to the skin. Two additional points can be placed on the knee for extra feedback and the final joint position, but are not necessary for the software system. Then, the patient will flex and extend their knee joint while keeping the heel on the table to stabilize the knee and prevent shanking. The placement of the patient should allow for a technician to help the patient bend their knee if their condition does not allow them to do so themselves. Once the data is collected, it can be processed by the parameterization software system.

\section{Parameterization Software}
% TODO: Add software flowchart
The collected data first goes through a Vicon workflow for processing. This will properly format the data, create virtual joints, and determine joint centers. This is done using the built-in tools called SCoRE (Symmetrical Center of Rotation Estimation) and SARA (Symmetrical Axis of Rotation Analysis). Additionally, a built-in tool will determine the angle of the knee joint using the four dots on each section of the patient's leg. This Vicon specific workflow can be exported, shared, and reused for others who are using a similar system. The output of the workflow is a CSV file which can be parsed by a custom script.

To finish the parameterization of the knee, custom software was developed and written in Python. This software utilizes the AiM Vicon Python module \footnote{The AiM Vicon Python module is an open-source project found here: \url{https://github.com/WPI-AIM/AIM_Vicon}} which parses the CSV file from above. The joint angle, SARA, SCoRE, and marker positions are extracted from the data and placed in their specified datatypes. Since the AiM Vicon module did not have all the tools needed for this project, I developed and contributed to the Python module. Additional features added include SARA and SCoRE support, a new 3D visualizer, and stability improvements when importing different workflows.

\begin{figure}[ht!]
    \centering
    \includegraphics[width=\textwidth]{Figures/Param/3D_Marker_Animation.png}
    \caption{An example of a possible output from the Parameterization Software System shown in a visualizer}
    \label{fig:SoftwareSampleData}
\end{figure}

With the data parsed and imported, the final step is to calculate the final joint angles and determine the linear extension between the thigh and shank. The axis of rotation from SCoRE and all marker positions are projected onto a plane, which is calculated to be approximately the same as the plane of the manufactured joint. Then the final distance and angle are calculated by drawing two virtual lines as shown in \autoref{fig:SoftwareSampleData}: 1. from the projected primary thigh marker to the projected SCoRE location and 2. from the projected SCoRE location to the projected primary shank marker. The lengths of these lines then become the calculated linear extension and the angle between these two lines become the flexion. These two metrics are then combined into a dataset, and a best fit quartic curve is selected to become the patient's knee parameters.

\section{Testing with Pilot Data}
Due to time constraints, IRB (Internal Review Board) approval was not obtained to run a full study. However, some data was used to develop the software platform that will analyze the data. The graphs in \autoref{fig:Subj1KneeParams} and \autoref{fig:Subj2KneeParams} show the relationships between the knee joint flexion (angle of the knee) and the linear extension (distance of the shank to the joint center).

\begin{figure}[ht!]
    \centering
    \includegraphics[width=\textwidth]{Figures/Param/Subj1_KneeProfile.png}
    \caption{A visualization of the angular flexion and linear extension of the shank from the joint center of the first dataset with subject 1. Subject bent and extended their knee joint 4 times.}
    \label{fig:Subj1KneeParams}
\end{figure}

\begin{figure}[ht!]
    \centering
    \includegraphics[width=\textwidth]{Figures/Param/Subj2_KneeProfile.png}
    \caption{A visualization of the angular flexion and linear extension of the shank from the joint center of the second dataset with subject 2. Subject bent and extended their knee joint 3 times.}
    \label{fig:Subj2KneeParams}
\end{figure}

The data displayed in \autoref{fig:Subj1KneeParams} has a variation of up to \(7mm\) for any given angle. However, what is most interesting is the difference in the direction of the flexion. When the knee joint angle is increasing (knee is being bent), the markers are closer together, compared to when the knee joint is decreasing. In any given direction of movement, variation is less than \(2mm\), suggesting that this seemingly cyclical trajectory is not due to measurement variations or inaccuracies.

\autoref{fig:Subj2KneeParams}'s data is seemingly less dependent on the knee joint angular velocity direction. All data is within a \(3mm\) variation at any given angle. The notable exception is the \(7mm\) spike that can be seen at roughly \(25^\circ\) mark. This can likely be explained by either an accidental shift in the markers or a slight measurement error in the motion capture system. However, there is not sufficient data to make a conclusion as to the reasoning.

The data analyzed both show that the maximum variation in skin movement through the flexion of the knee never exceeded \(7mm\), even with the outlier event from \autoref{fig:Subj2KneeParams}. In comparison, studies presented in \autoref{sec:KneeModel} describe a tibio\-femoral relationship that varies over \(40mm\) throughout the joint flexion. While these two data points are not statistically significant enough to make a conclusion for all human knees, the preliminary pilot data suggests that the skin movement is different than the tibiofemoral movement. An in-depth study is needed to make a definitive conclusion.

\section{Study Outline}

As a part of this thesis, an study was designed to test the developed parameterization software as well as the knee joint's capability to be customized to a specific person. However, due to time constraints, IRB (Internal Review Board) approval to run the human study was not obtained, and therefore the study was not run. The study's methodology is outlined below, and the IRB proposal documents are attached in \autoref{apx:ParamStudyDocs}.

Up to 6 subjects are to be selected to partake in this study. Each subject should not have any prior severe knee injury, and should be cleared to be imaged with an MRI. The study will start with imaging the knee using the motion capture procedures outlined in \autoref{sec:ImaginKneeProcedure}, and parameters will be selected using the parameterization software developed. These parameters will be used to manufacture an MRI safe personalized knee joint. Additionally, a second non-personalized pin joint will be manufactured and used as a control.

The second stage of the study will compare the fit of the two joints. The subject will undergo MR scans at up to 3 different knee angles, first with no joint and then subsequently with each type of joint. The movement (if any) of the joint in reference to the subjects body will be measured. A successful experiment should demonstrate that the customized knee joint moves less than a non-customized pin joint. Additionally, the tibiofemoral movement can be compared to the measured parameters to determine how much the skin moves relative to the knee joint.