Incorporating Organ Motion into Radiation Dose Planning
Hypo-fractionated stereotactic body radiation therapy (H-SBRT)
enables delivery of high levels of radiation dose that precisely
conform to a physician defined tumor geometry. Such therapy is
advantageous because it increases the likelihood of tumor control
and healthy tissue sparing. However, dose accumulation for H-SBRT
is particularly susceptible to organ motion because of the delivery
precision and dose conformity of the technique. Moreover,
respiratory-induced motion in the abdomen results in significant
movement of lesion targets during the breathing cycle. Sensitivity
to patient breathing complicates H-SBRT treatment of abdominal
lesions and may account for the observed discrepancies between
predictive indicators and clinical patient outcome statistics.
Techniques intended to compensate for respiratory motion have been
investigated, but very few have yet reached clinical practice.
Patients may exhibit markedly different breathing patterns between
treatment fractions or even during treatment. The fundamentally
random nature of respiration can have significant effects on dose
deposition and, as a result, dose depositions can vary significantly
from treatment to treatment. Failure to appropriately accommodate
for patient-specific breathing stochasticity can result in
under-dosing of the target and deposition of dangerous dose levels
to surrounding healthy tissue. Thus, it is essential to incorporate
an accurate prediction of the effects of the random nature of the
respiratory process on H-SBRT dose deposition for improved treatment
planning and delivery of H-SBRT. To date, no computational tools
exist to accomplish this goal. We present a means of characterizing
the underlying day-to-day variability of patient breathing and
calculate the resulting stochasticity in dose accumulation.
The Effect of Heart Position on the ECG
The
electrocardiogram (ECG) is ubiquitously employed as a diagnostic and
monitoring tool for patients experiencing cardiac distress and/or
disease. Though steps are taken to obtain ECGs under controlled
conditions, the recordings are known to be sensitive to a number of
factors. These sensitivities can affect diagnostic conclusions and
impair the utility of the ECG in successful patient monitoring. It
is widely known that changes in heart position resulting from
postural changes of the patient (sitting, standing, lying)
significantly effect the body surface potentials. However, few
studies systematically quantify the effects of heart displacement on
the ECG.
To quantify the effects of positional changes of the heart on the
ECG, I developed a framework for computing means and standard
deviations in torso potentials resulting from stochastic
distributions of heart position. This information enables
identification of the types of positional changes capable of inducing
artificially elevated ST segments in the ECG, possibly resulting in
false diagnosis of cardiac distress.
The Effect of Organ Conductivity on the ECG
Because numerical
simulation parameters may significantly influence the accuracy of the
results, evaluating the sensitivity of simulation results to
variations in parameters is essential. Although the field of
sensitivity analysis is well developed, systematic application of
such methods to complex biological models is limited due to the
associated high computational costs and the substantial technical
challenges for implementation.
In the case of the forward problem in electrocardiography, the lack of
robust, feasible, and comprehensive sensitivity analysis has left many
aspects of the problem unresolved and subject to empirical and
intuitive evaluation rather than sound, quantitative investigation.
I developed a systematic, stochastic approach to the analysis of
sensitivity of the forward problem of electrocardiography to the
parameter of inhomogeneous tissue conductivity. I appled this
approach to a two-dimensional, inhomogeneous, geometric model of a
slice through the human thorax and applied stochastic finite elements
based on the generalized Polynomial Chaos-Stochastic Galerkin (gPC-SG)
method to obtain the standard deviation of the resulting stochastic
torso potentials and thus identify the organ conductivities with
greatest impact on the ECG.
The Effect of Kinetic Transition Rates on Ion Channel Current
Markovian models of ion channels have
proven useful in the reconstruction of experimental data and
prediction of cellular electrophysiology. To explore the impact of
uncertainties in kinetic transition rate coefficients on the
predictions of Markovian ion channel models, I applied the
generalized Polynomial Chaos-Stochastic Galerkin (gPC-SG) method as
an alternative to Monte Carlo to calculate statistics of ion channel
current resulting from stochastic distributions of rate coefficients.
I extended and studied two different ion channel models: a reduced
model with a single open and closed state and a detailed model of the
cardiac rapidly activating delayed rectifier potassium current. My
experiments illustrate the characteristic changes in distributions of
state transitions and electrical currents through ion channels due to
random rate coefficients. Furthermore, the studies indicate the
applicability of the stochastic Galerkin technique for uncertainty
and sensitivity analysis of bio-mathematical models.