Lasers in Surgery and Medicine 39:731–746 (2007)
Heat Shock Protein Expression and Injury Optimization
for Laser Therapy Design
Marissa Nichole Rylander, PhD,1* Yusheng Feng, PhD,2 Jon Bass, PhD,3 and Kenneth R. Diller, PhD4
1
Department of Mechanical Engineering and School of Biomedical Engineering and Sciences, Virginia Tech
Corporate Research Center Building XV MC 0493, 1880 Pratt Drive, Blacksburg, Virginia 24061
2
Department of Mechanical Engineering, The University of Texas at San Antonio, One UTSA Circle,
San Antonio, Texas 78249-0670
3
Institute for Computational Engineering and Sciences, The University of Texas at Austin,
1 University Station Stop C0200, Austin, Texas 78712
4
Biomedical Engineering Department, The University of Texas at Austin, 1 University Station C0800,
Austin, Texas 78712-0238
Background and Objectives: Hyperthermia can induce
heat shock protein (HSP) expression in tumor regions
where non-lethal temperature elevation occurs, enhancing
cell viability and resistance to chemotherapy and radiation treatments typically employed in conjunction with
thermal therapy. However, HSP expression control has
not been incorporated into current thermal therapy
design. Treatment planning models based on achieving
the desired post-therapy HSP expression and injury
distribution in the tumor and healthy surrounding tissue
can enable design of more effective thermal therapies that
maximize tumor destruction and minimize healthy tissue
injury.
Study Design/Materials and Methods: An optimization
algorithm for prostate cancer laser therapy design was
integrated into a previously developed treatment planning model, permitting prediction and optimization of the
spatial and temporal temperature, HSP expression, and
injury distributions in the prostate. This optimization
method is based on dosimetry guidelines developed from
measured HSP expression kinetics and injury data for
normal and cancerous prostate cells and tumors exposed to
hyperthermia
Results: The optimization model determines laser parameters (wavelength, power, pulse duration, fiber position,
and number of fibers) necessary to satisfy prescribed HSP
expression and injury distributions in tumor and healthy
tissue. Optimization based on achieving desired injury and
HSP expression distributions within the tumor and normal
tissue permits more effective tumor destruction and diminished injury to healthy tissue compared to temperature
driven optimization strategies.
Conclusions: Utilization of the treatment planning
optimization model can permit more effective tumor
destruction by mitigating tumor recurrence and resistance
to chemotherapy and radiation arising from HSP expression and insufficient injury. Lasers Surg. Med. 39:731–
746, 2007. ß 2007 Wiley-Liss, Inc.
ß 2007 Wiley-Liss, Inc.
Key words: hyperthermia; heat shock proteins; thermal
injury; prostate cancer; treatment planning model; laser
therapy
INTRODUCTION
The effectiveness of hyperthermic therapies, such as
thermal ablation (i.e., high temperature T > 558C based
tissue coagulative treatments), local hyperthermia (low
temperature 42–448C), or hyperthermia sensitization
as an adjuvant to radiotherapy, chemotherapy, brachytherapy, and thermally mediated drug or gene deliveries,
can be compromised due to heat shock proteins (HSP)
induction in regions of the tumor where non-lethal
temperature elevation occurs [1–3]. Molecular chaperons
such as HSP assist in refolding and repair of denatured
proteins and aid in synthesis of new proteins in response
to injury in both normal and cancerous cells [4–6]. Applied
thermal stress can induce the offsetting effects of
over-expressed HSP and hyperthermia-mediated cell
necrosis. Although HSP perform critical functions in the
normal cell, upregulation of HSP in tumor cells following
thermal stress can lead to poor treatment outcomes by
enhancing tumor cell viability and imparting cellular
resistance to chemotherapy and radiation treatments
which are generally employed in conjunction with hyperthermia [1–3]. HSP have been implicated in many roles of
therapeutic resistance including multi-drug resistance [7],
regulation of apoptosis [8], and modulation of p53 functions
Contract grant sponsor: Abell-Hanger Foundation; Contract
grant sponsor: National Science Foundation Award; Contract
grant numbers: CTS-0332052, CNS-0540033.
*Correspondence to: Marissa Nichole Rylander, PhD, Department of Mechanical Engineering and School of Biomedical
Engineering and Sciences, Virginia Polytechnic and State University, Corporate Research Center Building XV MC 0493, 1880
Pratt Drive, Blacksburg, VA 24061. E-mail: [email protected]
Accepted 18 August 2007
Published online in Wiley InterScience
(www.interscience.wiley.com).
DOI 10.1002/lsm.20546
732
RYLANDER ET AL.
[9] for a broad range of neoplastic tissues due to upregulated expression in cancer cells and through induction by
thermal stress. Therefore, developing treatment planning
models coupled with optimization models for thermal
therapy design are crucial for producing the desired posttherapy HSP expression and tissue injury to permit
maximum tumor destruction and preservation of healthy
surrounding tissue.
Numerous studies have discussed treatment planning
models designed to predict the tissue response to laser
irradiation [10–19]. However, we developed the first
treatment planning model to permit prediction of HSP
expression in addition to the temperature and injury
fraction (defined in Eq. 13) associated with laser heating
of the prostate [20,21]. This model was based on measured
thermally induced HSP expression and injury fraction in
prostate cells and tumors [22,23].
In order to permit both prediction of the tissue response
and optimization of the therapy design prior to laser
therapy, we developed an optimization model which is
integrated into our existing treatment planning predictive
model. Optimization models employ objective functions
which are derived from stipulated criteria and involve the
quantity of interest being optimized. Objective functions
serve to define how accurately an outcome complies with
the set of prescribed criteria. Computational strategies
for optimization of hyperthermia therapy design have
previously focused on defining objective functions based
on criteria for controlling only temperature in the tumor
and healthy surrounding tissue [24,25]. The chosen
temperature criteria were based on inducing sufficient
tumor destruction and minimizing healthy tissue injury.
The preferred criteria for optimization have consisted of
achieving a post-therapy outcome of T 438C in the tumor
and T < 428C in the healthy tissue region. Specially
designed objective functions have also been created to
avoid ‘hot spots’ in the healthy tissue while minimizing ‘cold
spots’ in the tumor [24,25]. Although progress has been
made in the development of these optimization methods,
induction of HSP expression has not been previously
considered in hyperthermia optimization. The threshold
for inducing both thermal injury and HSP expression is
T ¼ 438C. The presence of thermally induced denatured
proteins associated with hyperthermia stimulates HSP
expression elevation. Therefore, if temperatures exceed
this threshold during therapy, but the heating duration
employed is insufficient to fully coagulate proteins in any
portion of the tumor, the treatment may be compromised
due to increased HSP expression.
An optimization strategy with more stringent criteria is
presented in this study motivated by producing the desired
HSP expression and injury responses in the tumor and
healthy surrounding tissue. This optimization method is
based on dosimetry guidelines developed from measured
HSP kinetics and cell injury data for normal and cancerous
prostate cells and tumors exposed to hyperthermia [22,23].
The treatment planning optimization model permits
determination of the optimal laser parameters (laser
wavelength, power, pulse duration, optical fiber position,
and number of fibers) necessary to satisfy a prescribed posttherapy HSP expression and injury fraction distribution in
the tumor and healthy tissue to achieve maximum tumor
destruction and preservation of healthy tissue. In this
article, the optimization process is driven through
the minimization of objective functions based on desired
HSP expression and injury fraction. The optimization
strategy is also compared to the conventional method of
temperature-based laser protocol determination.
The optimization computational model was utilized in
the design of laser irradiation of prostate tumors. Since
prostate cancer is the second leading cause of cancer related
deaths in the United States, designing effective therapies is
of the utmost importance [26]. HSP27 and HSP70 (number
denotes molecular weight in kilodaltons) have been linked
to poor prognosis in prostate cancer [27], inhibition of
apoptosis [2], and resistance to chemotherapy and radiation following thermal stress [28–30].
The optimization strategy presented in this article
focuses on achieving maximum prostate tumor destruction
and minimizing injury to healthy surrounding tissue
by manipulating the distribution of HSP27 and HSP70
expression and injury fraction in the tumor and normal
prostate tissue through specification of optimal laser
parameters.
LASER THERAPY DESIGN METHODOLOGY
Computational Model
Before the tissue response to thermal therapy can be
optimized, a computational framework must be developed
to predict the temperature history, injury fraction, and
HSP27 and HSP70 expression associated with a hyperthermia protocol. In previous work, we created a finite
element computational treatment planning model for
predicting these quantities following laser therapy
[20,21]. The models for predicting HSP27 and HSP70
expression and injury fraction were based on measured
HSP expression and injury data in prostate cells and
tissues [22,23]. The optimization algorithm discussed in
this article was integrated into the treatment planning
model to permit not only prediction, but optimization of
laser therapy design. In the following sections, the treatment planning model will be discussed briefly to elucidate
the methods for calculating the temperature history, injury
fraction, and HSP27 and HSP70 expression which are
necessary for the optimization process.
Model discretization and simulation. A threedimensional finite element model consisting of a prostate
with an interior tumor was generated using Hypermesh1 (see
Fig. 1), a commercial pre- and post-processing design tool. The
computational model including a three-dimensional, linear,
hexahedral mesh, boundary conditions, and material properties were subsequently exported from Hypermesh using a
neutral file format compatible with the ProPHLEX1 developer’s environment. ProPHLEX is a robust hp-adaptive finite
element solver environment for modeling systems of linear
1
Hypermesh and ProPHLEX are registered software tools from Altair
Engineering, Troy, Michigan.
HSP EXPRESSION AND INJURY OPTIMIZATION
Fig. 1. Meshed Geometry representing the prostate (shown in
blue) with an interior tumor (shown in red).
and non-linear partial differential equations. These systems
can include scalar and/or vector equations and can also be
steady-state or transient. ProPHLEX provides a customizable
interface for specifying the governing transport equations
and boundary conditions, optimization of the finite element
mesh for a given target solution tolerance, visualization of the
temperature, injury fraction, and HSP27 and HSP70 expression profiles throughout the tissue, and optimization features
to facilitate identification of target irradiation parameter
values.
The ProPHLEX package has several advantages that
make it an excellent choice for modeling the Penne’s bioheat equation which is of particular interest in this work.
ProPHLEX contains a versatile, robust, adaptive finite
element kernel for dynamic mesh optimization whereby
elements are locally refined (subdivided) or locally enriched
(increased polynomial order) at virtually any instant in the
solution process. This important feature enables accurate
representation of irregular geometry, such as tumors or
other biological objects. ProPHLEX also contains an error
estimation module that provides quantitative information
about the quality of the numerical solution permitting high
fidelity numerical solutions to be obtained with a prescribed
error tolerance. Finally, the ProPHLEX developer’s environment includes an integrated post-processing module for
displaying numerical results for primitive solution quantities and for studying user defined quantities of interest.
Benchmarking and verification of the Pennes’ bio-heat
model and solutions obtained using ProPHLEX were
performed in a multi-stage process wherein several
intermediate solvers were built on the ProPHLEX kernel.
These solvers include: a linear steady-state heat conduction
solver, a non-linear steady-state heat conduction solver, a
transient linear heat conduction solver, and finally a fully
nonlinear unsteady bio-heat transfer solver. The accuracy
otumor
733
of the Pennes’ bioheat transfer model and ProPHLEX
software for predicting the temperature, HSP27, and
HSP70 expression was verified by comparing computational solutions with Magnetic Resonance Thermometry
measured temperature and HSP expression data measured
with immmunostaining and confocal microscopy.
Numerical methods. The numerical methods of choice
in the simulations involved utilization of h–p adaptive finite
element methods in the spatial dimension and fully implicit,
theta family, finite difference methods in the temporal
dimension. The h–p adaptive feature refers to the ability to
adaptively refine the mesh by subdividing element size
(decreasing h) or increasing the polynomial order (enlarging
p). This permits exponential convergence by optimizing both
mesh size and the polynomial order of the elements such that
the numerical error is reduced to a specified precision.
In the following sections the methodology employed in
the treatment planning model for determining the
temperature, injury fraction, and HSP27 and HSP70
expression will be discussed. Understanding of the predictive model components is essential prior to explanation
of the optimization implementation strategy.
Temperature prediction. The temperature distribution in the prostate tumor and surrounding healthy tissue
was determined using the Pennes’ bio-heat equation
[31,32], defined in Eq. (1), which includes the thermal
effects of local blood perfusion and a term for light energy
absorption due to the laser source:
ct rt
@T
¼ rðkðTÞ rTÞ ob ðTÞcb ðT Ta Þ þ Qðx; y; zÞ ð1Þ
@t
where ct, rt, Ta, and cb are the specific heat and density of
the tissue, arterial blood temperature, and specific heat of
the blood, respectively. The Pennes’ equation is based
on the hypothesis that the influence of blood perfusion on
the temperature distribution within the tissue can be
represented as volumetrically distributed heat sinks or
sources. Previous research has demonstrated that the
temperature prediction provided by the Pennes’ equation
corresponds closely with measured temperature with
Magnetic Resonance Thermometry (MRTI) during laser
irradiation of prostate tumors [20]. The precision of the
fit between the MRTI measured and model predicted
temperature was determined by the correlation coefficient
of 0.987 (value of 1 denotes a perfect fit).
The temperature-dependent thermal conductivity of the
tissue and blood perfusion are denoted by k and ob,
respectively. The nonlinear temperature dependence of
thermal conductivity and perfusion were incorporated
into the model to give a more precise measure of the
temperature distribution. The mathematical formulation
employed for the nonlinear effects of the temperaturedependent blood perfusion in the tumor is shown in the
following equation [24].
8
< 0:833
¼ 0:833 ðT 37:0Þ4:8 =5:438 103 ;
:
0:416
9
T < 37:0
=
37:0 T 42:0
ðkg=s=m3 Þ
;
T > 42:0
ð2Þ
734
RYLANDER ET AL.
Although the temperature dependence of thermal conductivity for tissue has not been fully characterized, the
thermally variant properties of water are well known in
the range of 20–1008C. Since the tissue thermal conductivity is highly dependent on the water content, the
temperature-dependent thermal conductivity for prostate
tissue can be determined by Eq. (3) where z is a dimensionless correction factor and wc is the water content of prostate
tissue, 0.511 [10].
kðTÞ ¼ 4:19ð0:133 þ 1:36 zwc Þ 101
ðW=mKÞ
ð3Þ
where z¼1þ1.78103(T208C).
The rate of laser energy absorbed per unit volume within
the tissue is given by
Qðx; y; zÞ ¼ ma Fðx; y; zÞ
m
X
i¼1
fi ¼
m
X
i¼1
3Pi mtr
expðmeff jjr ri jjÞ
4pjjr ri jj
ð5Þ
where i (W/m2) is the fluence associated with each laser
probe, Pi (W) is the power associated with each laser
probe, r is the position vector from the origin (center of
sphere), ri (i ¼ 1. . .m) is the position vector of each laser
probe (where m is the number of laser probes), and kk
denotes the Euclidean norm. The transport attenuation
and effective irradiation coefficients represented as mtr
(m1) and meff (m1), respectively, are determined by Eqs.
(6) and (7). The scattering coefficient and anisotropy factor
are denoted as ms (m1) and g, respectively [10,12,33]. In
Eq (5), we assume that the distances between each laser
applicator are greater than the maximum diameter of the
influence region of heat applied by each applicator so that
utilizing Eq (5) is valid.
mtr ¼ ðma þ ms ð1 gÞÞ
meff ¼ ð3ma mtr Þ
1=2
Parameter
Symbol
Value
l
ma
ms
g
rt
rb
ct
cb
Ta
810 nm
4.6 m1
1,474.4 m1
0.9
1,045 kg/m3
1,058 kg/m3
3,639 J/kgK
3,840 J/kgK
310 K
Diode laser wavelength
Absorption coefficient of canine prostate
Scattering coefficient of canine prostate
Anisotropy factor of canine prostate
Density of prostate tissue
Density of blood
Specific heat of prostate tissue
Specific heat of blood
Arterial blood temperature
ð4Þ
where ma (m1) and F (W/m2) are the irradiation absorption
coefficient and fluence, respectively [33]. An optical fiber
with a spherical scattering applicator is employed for
irradiation resulting in a homogenously distributed radiation pattern in the tissue. Diffusion theory provides an
accurate approximation to the radiative transport equation
in this application since the wavelength employed for
irradiation is in the infrared region of the spectrum
where the scattering coefficient of tissue is much larger
than the absorption coefficient. Since intra-tumoral heating
is simulated in all cases assuming a spherical tumor
geometry, the diffusion approximation yields the following
expression for the fluence (F) distribution:
F¼
TABLE 1. Optical and Thermal Properties Employed
in the Model [12,34]
of choice can be easily implemented. We assume that
the volume consisting of the prostate with interior tumor
is surrounded by interstitial fluid such that at the
prostate tumor surface there will be heat exchange due to
convection with this surrounding fluid (assumed to have
the properties of water). As a result, a convective boundary
condition was imposed on all external surfaces of the
prostate with interior tumor depicted in Figure 1 except for
the interface between the healthy tissue and tumor.
Therefore, the following boundary condition was imposed
on the surface P which consists of all boundary surfaces
non-contiguous with the tumor according to:
k
2Tðx; y; z; tÞ
¼ hðTs T1 Þ GP
2n
where k is the tissue thermal conductivity (defined in
Eq. 3), rT/rn is the normal derivative of the temperature
on the boundary, and Ti is the initial tissue temperature
defined as 378C. The expressions employed for calculating the average Nusselt number (NuDav), assuming the
prostate and tumor can be approximated as a cylinder
and the convection coefficient needed for quiescent water
surrounding tissue surfaces with convective boundaries,
are shown in Eqs. (9–11):
(
)2
1=6
0:387 RaD
NuDav ¼ 0:60 þ
ð9Þ
½1 þ ð0:59= PrÞ9=16 8=27
where Pr is the Prandtl number and RaD is the Rayleigh
number as defined below:
ð6Þ
RaD ¼
ð7Þ
The optical parameters ma, ms, and g employed in
determining the fluence were measured for canine prostate
at a wavelength of 810 nm. Optical and thermal property
values for prostate and blood are summarized in Table 1
[12,34]. Parameter values employed in the simulation are
summarized in Table 1.
Depending on the method of heating (intra-tumoral or
external heating) and heating source, boundary conditions
ð8Þ
gbðTs T1 ÞD3
a
ð10Þ
where g is the local acceleration due to gravity (m/
second2), b is the volumetric thermal expansion coefficient
coefficient (1/K) evaluated at the mean value of the
surface and water temperatures, is the kinematic
viscosity (m2/second), and a is thermal diffusivity (m2/
second). The values for Ts and T1 were stipulated as 310
and 295 K, respectively. The parameters Pr, , and a were
evaluated for water at 295 K with values of 0.849,
1.55105 m2/second, and 2.18105 m2/second, respec-
HSP EXPRESSION AND INJURY OPTIMIZATION
tively [35]. The convection coefficient for quiescent water
surrounding the tumor is determined by Eq. (11):
h¼
NuDav k
D
ð11Þ
where k is the thermal conductivity of the tissue and D is
the diameter of the tumor. The radius of the simulated
tumor was 6 mm since typical PC3 tumors grown on
mice attain a maximum spherical volume of 1 cm3 prior to
exhibiting necrotic cores.
Injury fraction prediction. The injury predictive
model was developed based on measured cell viability
profiles using propidium iodide staining measured with a
flow cytometer in normal prostate (RWPE-1) and prostate
cancer (PC3) cells following water bath heating for thermal
stimulation temperatures of 44–608C [22]. H&E staining
was also performed on laser irradiated prostate tumors to
gain a better understanding of the correlation between
temperature and tissue injury in vivo [23]. Tissue injury
associated with the thermal therapy can accurately be
predicted according to the Arrhenius injury model [36]:
OðtÞ ¼ A
Zt
eðEa =<TðtÞÞ dt
ð12Þ
0
where O is defined as the injury index, A (1/s) is a scaling
factor, Ea (Jmol1) is the injury process activation energy,
(Jmol1 K1) is the universal gas constant, and T(K) is
the instantaneous absolute temperature of the cells
during stress, which is a function of time, t(s). Previously
measured prostate cancer and normal prostate cell
viability and prostate tumor injury data following hyperthermia enabled determination of the constitutive parameter values A and Ea [22,23].
The injury index, O, will rise indefinitely with increasing
temperature and extended heating durations with complete cell injury represented by infinity. In order to more
meaningfully represent the injury, another parameter was
employed for determining injury in the finite element
simulations. The tissue injury was represented by the
injury fraction, FD in all simulations and is given by:
FD ¼ 1 expO
ð13Þ
Native tissue is represented by FD ¼ 0 (O ¼ 0) and tissue
with complete cell death is denoted as FD ¼ 1 (when ! 1)
[10].
HSP 27 and HSP70 prediction. The predictive model
for HSP27 and HSP70 expression was also based on
measured HSP expression kinetics data for cancerous
(PC3) and normal (RWPE-1) prostate cells using Western
blotting techniques [22]. In order to account for differential
HSP expression between in vitro and in vivo systems, the
HSP expression predictive model was further refined by
characterizing the HSP27 and HSP70 distribution through
immunostaining and confocal microscopy in laser irradiated prostate tumors [23]. At present, the HSP induction
pathway is not fully characterized and is hypothesized
to involve numerous biochemical mediators. We propose a
735
model that describes HSP expression as a function of
temperature and heating duration which is adequately
supported by our previously measured experimental data
[20,21]. Based on the experimental data, HSP27 and
HSP70 expression induced by a transient temperature
field can be characterized by the following equation [20,21]:
@Hðt; TÞ
¼ f ðt; TÞ Hðt; TÞ
@t
ð14Þ
where f(t,T) corresponds to the rate of HSP induction due
to a thermal stimulus and H(t,T) is the concentration
of HSP. We select f ðt; TÞ ¼ ða b1 tg1 Þ which captures
the characteristics of measured thermally-induced HSP
expression. Based on experimental observations, the
asymptotic behavior of this model is embodied in
lim Hðt; TÞ ¼ 0 for extensive heating durations due to
t!1
extreme injury and protein denaturation. We further
assume that H(t,T) is a function with a continuous first
derivative. As a result, the HSP expression concentration
can be represented by:
Hðt; TÞ ¼ Aeðatbt
g
Þ
ð15Þ
where a, b, and g are parameters which are independent
of time, but are dependent on temperature, with g > 1 and
A is a temperature dependent constant. Since the basal
value of H(t,T) ¼ 1 at t ¼ 0 due to normalization, A ¼ 1 for
the measured data set. All HSP expression parameters
were then determined by the least square approach.
Unique HSP expression parameters were determined for
HSP27 and HSP70 for both PC3 and RWPE-1 cells and
prostate tumors [22,23]. The HSP expression model was
integrated into the treatment planning model to enable
prediction and optimization of the thermally induced HSP
response.
The accuracy of the model prediction of HSP expression
was verified in previous work by comparing the model
predicted HSP27 and HSP70 expression with measured
expression data from immunofluorescence and confocal
microscopy analysis following irradiation of PC3 tumors
in vivo [23]. The correlation coefficient between measured
and model predicted HSP27 and HSP70 are both 0.99,
verifying the accuracy of the model for HSP expression
prediction.
Development of Optimization Criteria
Measured HSP kinetics and injury data for PC3 and
RWPE-1 cells and prostate tumors enabled the correlation
between HSP expression and injury to be determined due to
a thermal stimulus [22,23]. An optimal thermal therapy for
cancer treatment is defined by complete eradication of the
tumor without thermal injury to the normal surrounding
tissue. Since the solution to Eq. (1) cannot be discontinuous,
the best possible therapy is to completely eradicate all
cancerous cells while keeping the normal cell injury at
a minimum. Tumor destruction is paramount in the
design of the thermal therapy and can only be achieved by
eliminating HSP expression and achieving an injury
threshold throughout the tumor region (described by
736
RYLANDER ET AL.
Criterion 1 below). HSP expression elevation within
the tumor will increase the risk of tumor recurrence
and resistance to subsequent chemotherapy and radiation, compromising the success of the entire therapy.
Injury minimization coupled with HSP expression induction in the healthy tissue is an important therapy design
criteria, but a secondary priority (described by Criterion
2 below). Induction of HSP expression in the healthy
tissue will mitigate tissue injury associated with repeated
thermal therapies or adjuvant treatments, thereby permitting improved patient recovery of tissue function. In order
to achieve the optimal therapy, criteria prescribing
the desired HSP expression and injury fraction in both
the tumor and healthy tissue were developed to drive the
optimization process:
Criterion 1: In the tumor region, cancerous cell destruction requires maximum levels of injury exposure such that
FD dT where dT is a prescribed injury fraction value; and
HSP27 and HSP70 expression must be diminished below its
basal level of expression such that HSP27;70 sT where sT
represents a minimum specified HSP expression value.
Criterion 2: In the surrounding healthy tissue, normal
cells must receive minimal thermal injury such that
FD dH where dH is the prescribed injury fraction value;
and elevated HSP27 and HSP70 expression must be
induced such that HSP27;70 > sH where sH represents a
specified HSP expression value.
The values for the stipulated injury fraction (dT and dH)
and HSP expression (sT and sH) will depend on the therapy
paradigm and tissue type due to differing injury sensitivity
and HSP expression characteristics. Specific numerical
values were implemented to illustrate the optimization
process, but alternative criterion sets may also be applied
depending on the application and desired outcome. Figure 2
illustrates the desired therapy outcome for injury fraction
and HSP27,70 expression (HSP27 and 70 expression) we
stipulated for both the tumor and healthy prostate tissue
based on our measured cellular and tissue injury and HSP
expression data [22,23]. The computational domain G
employed for specifying these constraints is also depicted
in which G ¼ GT [ GH is the region occupied by the tumor,
GT, and the healthy tissue region, GH. Based on the
measured and normalized HSP expression kinetics data,
the basal level of both HSP27 and HSP70 expression was
valued at one. As a result, we chose the target tumor HSP
expression value, sT, within GT to be below 1.0 mg/ml to
eliminate tumor protection. Significant HSP expression
induction capable of providing protection was observed for
HSP27 expression values ranging from 2 to 10.0 mg/ml and
HSP70 expression values ranging from 2 to 3.5 mg/ml. As a
result, we specified our target HSP27 and HSP70 expression induction values, sH, in GH to be greater than 2.0 mg/
ml. A single HSP expression parameter was chosen to
represent both HSP27 and HSP70 in the tumor and healthy
tissue (sT and sH) since we desire elimination of both HSP
in the tumor and elevation of both HSP in healthy tissue for
comparable parameter values. Separate values can also
be stipulated when necessary for molecules that have
different expression characteristics. Complete tumor
destruction is the main priority so success was defined by
reaching an injury fraction value, dT, of 1.0 within GT. In
order to minimize healthy tissue injury, we stipulated an
injury fraction, dH, less than 0.1 within GH.
It is difficult to achieve both criteria simultaneously.
Priority must be given to the most important therapy
design criterion. Weighting schemes will be discussed in
the following section to permit priority to be stipulated
within the objective function driving the optimization.
Since eradicating the tumor is the highest priority,
satisfying Criterion 1 is given the highest preference.
Objective Function Development
Injury fraction (FD)-based objective function. In
this section, optimization methods based upon the desired
injury fraction, HSP expression, and the conventional
temperature threshold method will be explored separately
to illustrate the impact of optimizing each quantity on
therapy outcome. However, a single objective function
comprising injury fraction, HSP expression, and temperature could also be employed to simultaneously optimize all
quantities.
First, objective functions based on both injury fraction
and HSP expression were derived from the criteria
mentioned above. The objective function for injury fraction,
driven optimization is shown in the equation below:
Z
JFD ¼ c
ðFDT ðx; y; z; tp Þ dT Þ2 dV
þ
Z
GT
ð16Þ
ðFDH ðx; y; z; tp Þ dH Þ2 dV
GH
Fig. 2. Desired outcome and geometric domain G ¼ GT [ GH
for optimal laser therapy design.
where JFD represents the injury fraction objective function, c represents a weight employed for attributing
priority to controlling injury in the tumor, FDT (x,y,z,sp)
and FDH (x,y,z,sp) represent the model-predicted injury
fractions for tumor and healthy tissue, respectively, due to
the selected source parameters, and sp represents the
pulse duration employed for irradiation. We want to
heavily penalize the tumor injury fraction term if it does
not satisfy the prescribed value in order to achieve
complete tumor destruction. As a result, we can define
HSP EXPRESSION AND INJURY OPTIMIZATION
the weighting term, c, by selecting a value based on how
extensively we want to penalize this term if the prescribed
damage fraction in the tumor is not satisfied. Higher
values of c translate into more conservative therapies
where tumor destruction is maximized at the expense of
normal tissue injury. The weighting terms were chosen
similarly for the HSP expression and temperature objective functions discussed subsequently since we want to
penalize noncompliance of all these quantities within the
tumor when specified criteria are not satisfied. All c values
were selected to be 100. In order to satisfy the criteria for
the desired damage fraction, we chose dT ¼ 1.0 for complete
destruction in the tumor and dH ¼ 0.1 for minimal damage
in the healthy tissue.
HSP expression-based objective function. The
objective function formulated for HSP27 and HSP70
expression based optimization is shown in the equation
below:
Z
2
JHSP27;70 ¼ c
ðHSPT27;70 ðx; y; z; tp Þ sT Þ dV
þ
Z
GT
2
ð17Þ
ðHSPH
27;70 ðx; y; z; tp Þ sH Þ dV
GH
where JHSP27;70 represents the HSP27 and HSP70 expression objective function, c represents a weight employed for
attributing priority to controlling HSP expression in the
tumor, HSPT27;70 (x,y,z,sp) and HSPH
27;70 (x,y,z,sp) represent
the model-predicted HSP27 and HSP70 for tumor and
healthy tissue respectively associated with selected
source parameters, and sp represents the pulse duration
employed for irradiation. We chose sT ¼ 0.1 for elimination
of HSP27 and HSP70 expression in the tumor and sH ¼ 2.0
for significant HSP27 and HSP70 expression in the
healthy tissue. The same objective function was chosen
to represent both HSP27 and 70 expression since we desire
elimination of both HSP in the tumor and elevation of both
HSP in healthy tissue with nearly identical parameter
values.
Temperature-based objective function. The criteria of T 438C in the tumor and T < 428C in the healthy
tissue region has been applied as optimization criteria in
previous studies [24,25]. The objective function is defined
according to the following equation:
Z
JTemp ¼ c
ðTT ðx; y; z; tp Þ bT Þ2 dV
þ
Z
GT
ð18Þ
ðTH ðx; y; z; tp Þ bH Þ2 dV
GH
where JTemp represents the temperature objective function, c represents a weight employed for attributing
priority to incurring significant temperature elevation in
the tumor, TT and TH represent the model predicted
temperatures due to the selected laser parameters for the
tumor and tissue respectively, bT and bH represent the
desired temperature values in the tumor and healthy
737
tissue respectively, and sp represents the pulse duration
employed for irradiation. Determination of the values of bT
and bH are described below.
Traditional therapy design methods stipulate maintaining the tumor temperature at 438C for 30 minutes. Due to
the extensive heating duration, this therapy may not be
clinically relevant. In order to simulate a more realistic
laser therapy within the time constraints of a clinical
setting, an equivalent thermal dose in minutes at 438C (t43)
was determined for use in the temperature driven optimization according to the following equation:
ðt43 ÞN ¼
N
X
Rð43
CTi Þ
Dt;
i¼1
¼
0:25;
Ti < 43 C
0:50;
Ti 43 C
with R
ð19Þ
where Dt is the time between measurements (1 s), Ti is the
temperature in degrees Celsius for the ith measurement,
and R is a constant empirically derived from hyperthermia
experiments in living tissue [37]. Our previously measured
thermally induced HSP expression kinetics and injury
cellular data were based on heating at temperatures of
44–608C for 1–30 minutes. Since the optimization results
for damage fraction, HSP expression, and temperature are
to be directly compared, we selected a heating protocol
within the experimental range for developing the temperature objective function. The Ti value was chosen as 488C,
which yielded an equivalent thermal dose of 1 min. This
heating protocol fits nicely within our measured data set.
As a result, the value of bT was chosen to be 488C and the
pulse duration employed in the simulation was 1 minute.
Damage fraction minimization in the healthy tissue
was also a therapy design priority so the value of bH was
specified as 378C.
Optimization Method
Optimization strategies. The goal of the optimization
strategy is to determine a set of laser parameters such
that the objective function driving the optimization
is minimized. Let X represent the parameter set, X ¼ (Pi,
li, xi, yi, zi) for i ¼ 1,. . .L where Pi is the laser power
positioned at (xi,yi,zi), li is the laser wavelength, and L is the
number of laser sources employed for irradiation. The three
optimization strategies employed can be formally posed as
follows:
(1) Injury fraction-based optimization problem:
Find X such that JF D ¼ min JFD ðXÞ
(2) HSP27,70 expression-based optimization problem:
Find X such that JHSP
¼ min JHSP27;70 ðXÞ
27;70
(3) Temperature-based optimization problem:
¼ min JTemp ðXÞ
Find X such that JTemp
A single objective function was chosen initially to drive
each optimization process. In order to achieve successful
738
RYLANDER ET AL.
optimization, the difference between the predicted and
desired values within each objective function must
be minimized. For instance, when employing the damage
fraction-based optimization, laser parameters were determined such that the difference between the FDT (x,y,x,t) and
FDH (x,y,z,t) predicted by the chosen laser parameters and
the specified damage fraction (dT and dH) determined
from the criteria are minimized. All three optimization
problems are designed such that Pi, li, xi, yi, zi can be
optimized independently or simultaneously over the preset
parameter space. Identical computational methods for
determination of temperature, damage fraction, and HSP
expression associated with laser heating were employed.
The optimization algorithm subsequently discussed was
integrated into the treatment planning predictive model to
enable specification of optimal laser parameters.
Steepest descent method. The optimization algorithm utilized was based on the steepest descent method
which computes the local minima for the desired objective
functions [38]. The general premise of the steepest descent
method is that the gradient at any point, rJi , points in the
direction in which Ji is increasing most rapidly. It follows
that rJi points in the direction in which Ji is decreasing
most rapidly, called the direction of steepest descent. As a
result, minimization is along the steepest direction, rJi .
In combination with line search methods, the steepest
descent method was shown to be very effective in
determining the parameter set that minimizes the objective
function specified. The optimization process outlined
below in Figure 3 describes the major steps comprising
the steepest descent method applied to determination of
optimal laser parameters for therapy design for a single
source although the code is capable of optimizing multiple
sources.
RESULTS
Typical Laser Therapy Outcomes
A three dimensional volume consisting of a prostate
with an interior tumor was employed for all simulations. In
order to better visualize the temperature, injury fraction,
and HSP27 and HSP70 expression distributions, all
results were shown from the top view. The coarsely meshed
region represents the normal tissue and the interior finely
meshed region denotes the tumor. Two laser sources
positioned intra-tumorally were employed for irradiation
in all simulations to permit adequate treatment of the
tumor region. The wavelength and pulse duration utilized
were 810 nm and 1 minute, respectively.
Before discussing therapy outcome results achieved
through optimization, we will illustrate two possible treatment outcome extremes that can transpire without implementation of optimization methods in design of laser therapy.
The inefficiency of these therapies will demonstrate the need
for the optimization and provide a reference for comparison
with the optimized therapy outcomes. The first therapy
outcome simulated involves laser sources specified as P1 ¼
0.5 W positioned at (x1,y1,z1) ¼ (5.0,1.6,0.1) mm and P2 ¼
0.15 W positioned at (x2,y2,z2) ¼ (3.6,1.3,0.1) mm. The simu-
lation results for this therapy design are shown in Figure 4.
This therapy outcome represents a possible treatment
extreme where insufficient temperature elevation, minimal
incurred injury, and elevated HSP27,70 expression levels
occurred throughout the tumor. This therapy will not
completely eradicate the tumor leading to a high likelihood
of tumor survival and recurrence. This therapy fails to
achieve the most important therapy design Criterion 1 for
tumor destruction. The only acceptable quality of this therapy
is that the healthy surrounding tissue did not incur any
injury.
The other common treatment outcome extreme can be
illustrated by the following simulation involving laser
sources specified as P1 ¼ 1.6 W positioned at (x1,y1,z1) ¼
(5.0,1.6,0.1) mm and P2 ¼ 1.1 W positioned at (x2,y2,z2) ¼
(3.6,1.3,0.1) mm as shown in Figure 5. This therapy
effectively caused significant temperature elevation within
the tumor and satisfied the first design criteria of complete
tumor destruction by effectively eliminating HSP27,70
expression and achieving the desired FDT in the entire
tumor region. Due to complete tumor destruction, this
therapy may be characterized as an acceptable treatment.
However, the extensive temperature elevation, injury, and
lack of HSP27,70 expression in the healthy tissue bordering
the tumor will ultimately lead to dramatic tissue injury and
loss of function. This therapy is deemed sub-optimal since it
does not also satisfy our second criteria by minimizing
healthy tissue injury by inducing HSP expression. Both
unacceptable treatment outcomes most likely arose from
non-optimal design of the laser therapy which may be due
to employing incorrect laser protocol parameters including
improper power levels, insufficient heating duration, or
inappropriate number and placement of probes. Implementing an optimization strategy is vital to achieving both
tumor destruction and minimal healthy tissue injury.
HSP Expression-Based Optimization
Laser power and position for both laser sources were
considered in the optimization strategies while the wavelength and pulse duration were held constant at 810 nm
and 1 minute respectively. The z-coordinate for position
was chosen to be 0.1 mm, which was in the middle of the
tissue and tumor.
In order to verify whether the laser parameter specified
by the optimization algorithm yielded optimal results, the
post-therapy distributions of injury fraction and HSP
expression were evaluated to verify that they satisfied the
previously defined criteria. Numerical simulations confirmed by experimental observation demonstrated that dH
and dT chosen to be 0.4 and 0.6 were adequate criteria for
denaturation of HSP and complete cell death in the tumor
and minimal injury and elevated HSP expression in the
healthy tissue.
The HSP27,70 based optimization algorithm was
employed to achieve a more optimal post-therapy outcome
as shown in Figure 6. An initial guess of P1 ¼ 1.0 W
positioned at (x1,y1,z1) ¼ (5.0,1.6,0.1) mm and P2 ¼ 0.5 W at
(x2,y2,z2) ¼ (3.6,1.3,0.1) mm was stipulated. The specified
optimal parameters from the treatment planning optimiza-
HSP EXPRESSION AND INJURY OPTIMIZATION
739
Fig. 3. Steepest Descent algorithm employed in determination of optimal laser source
parameters.
tion model for this therapy were P1 ¼ 1.29 W positioned at
(x1,y1,z1) ¼ (5.2,1.8,0.1) mm and P2 ¼ 0.7 W located
at (x2,y2,z2) ¼ (3.8,1.5,0.1) mm. This therapy satisfied
Criterion 1 by effectively eliminating HSP27,70 expression
below the prescribed level of 1 and maximizing injury in the
tumor to the threshold value of 0.6. This therapy also
accomplished Criterion 2 by inducing elevated HSP27,70
expression and minimal injury in the healthy tissue
740
RYLANDER ET AL.
Fig. 4. Treatment outcome extreme for therapy without optimization for P1 ¼ 0.5 W and
P2 ¼ 0.15 W depicting (a) temperature, (b) injury fraction, (c) HSP27, and (d) HSP70
distribution following therapy.
bordering the tumor according to the specified criteria. This
laser therapy effectively eradicates the tumor while
enhancing recovery of injured healthy tissue along the
tumor border. This protocol is an excellent therapy design
option achieved by utilization of the treatment planning
optimization model in the laser therapy design.
Injury Fraction-Based Optimization
The FD objective function was also employed for laser
therapy design with an initial guess of P1 ¼ 1.0 W
positioned at (x1,y1,z1) ¼ (5.0,1.6,0.1) mm and P2 ¼ 0.5 W
located at (x2,y2,z2) ¼ (3.6,1.3,0.1) which is identical to the
input guesses employed in the HSP27,70 driven optimization. The optimized parameter set is specified as P1 ¼ 1.09
W positioned at (x1,y1,z1) ¼ (5.10,1.7,0.1) mm and P2 ¼ 0.59
W positioned at (x2,y2,z2) ¼ (3.7,1.40,0.1) mm. Although the
parameters specified by the HSP27,70 based optimization
were P1 ¼ 1.29 and P2 ¼ 0.70, the therapy outcome results
were both satisfactory by achieving the stipulated HSP
expression and injury fraction distributions in both the
tumor and healthy tissue, thereby satisfying both criteria
as shown in Figure 7. The HSP27,70 based optimization
clearly optimized the HSP expression distribution more
effectively by decreasing the HSP70 concentration more
significantly throughout the entire tumor although the
HSP27 expression was nearly identical. The HSP27,70
driven optimization also elevated the maximum tumor
temperature by an additional 48C as compared to the FD
driven optimization.
Temperature-Based Optimization
In order to compare the effectiveness of the temperature
optimization strategy with the FD and HSP27,70 expression
based optimization, the temperature objective function was
employed in the optimization algorithm. Input guesses
identical to those employed for the optimal FD and HSP
expression based optimization, P1 ¼ 1.0 W positioned at
(x1,y1,z1) ¼ (5.0,1.6,0.1) mm and P2 ¼ 0.5 W at (x2,y2,z2) ¼
(3.6,1.3,0.1) mm were utilized in the temperature
based optimization. The parameter set specified following
optimization were P1 ¼ 0.54 W positioned at (x1,y1,z1) ¼
(5.04,1.64,0.1) mm and P2 ¼ 0.34 W located at (x2,y2,z2) ¼
(3.64,1.34,0.1) mm. Figure 8 illustrates the therapy
outcome for the temperature based optimization strategy
HSP EXPRESSION AND INJURY OPTIMIZATION
741
Fig. 5. Treatment outcome extreme for therapy without optimization for P1 ¼ 1.6 W and
P2 ¼ 1.1 W depicting (a) temperature, (b) injury fraction, (c) HSP27, and (d) HSP70
distribution following therapy.
which yields an extremely suboptimal therapy. The
optimization algorithm effectively achieves the targeted
tumor temperature of 488C (321 K) and causes minimal
temperature elevation in the healthy tissue. However,
insufficient injury is incurred and significant levels of
HSP27,70 are induced in the tumor region which will
undoubtedly result in enhanced tumor viability and resistance to subsequent therapies. By enforcing the stricter FD
and HSP27,70 driven optimization strategy, more effective
laser therapies can be designed which enable complete
tumor destruction and diminished probability of tumor
recurrence through HSP27,70 expression control.
Table 2 compares various computational qualities for the
FD, HSP27,70, and temperature based optimization strategies as simulated in Figures 4–8. These quantities consist
of the objective function associated with the optimized
therapy, number of convergence steps to obtaining the
optimized solution, and CPU time required to achieve
convergence and minimization of the objective function.
The objective function minimum, convergence steps, and
CPU time are similar for all cases. Even though the
temperature driven optimization yields a suboptimal
therapy design, it still possesses a similar objective optimum
value because it adequately satisfies the temperature
criteria employed in developing the objective function.
DISCUSSION
An optimization treatment planning model was designed
that specifies the most appropriate laser parameters to
permit complete tumor destruction by maximizing injury
and eliminating HSP expression in the tumor. The model
also permits preservation of the healthy surrounding tissue
by minimizing the tissue injury and enhancing recovery by
induction of HSP expression. This is the first optimization
model based on tissue injury and HSP expression control.
Previous studies have based their optimization strategy on
achieving T 438C in the tumor region and T < 428C in the
healthy tissue [20,21]. Extended heating durations of
30 minutes are required to induce sufficient thermal injury
for these therapies. In order to design therapies that
do not exceed the time constraints of a clinical setting,
an equivalent thermal dose at T ¼ 438C for 30 min was
742
RYLANDER ET AL.
Fig. 6. Therapy outcome based on HSP expression-based optimization for an initial guess
of P1 ¼ 1.0 W and P2 ¼ 0.5 W depicting (a) temperature, (b) injury fraction, (c) HSP27, and
(d) HSP70 distribution following therapy.
determined. The equivalent thermal dose of 488C for 1 min
enabled comparison with the HSP and injury fraction based
optimization. The computational results demonstrated the
inadequacy of the temperature-based method in designing
laser therapies. The temperature-based optimization
yielded an insufficient amount of thermal injury and high
levels of HSP expression in the tumor. Without imposing
more stringent constraints and objective functions based on
desired thermal injury fraction and HSP expression, the
lack of thermal injury and elevated HSP expression in the
tumor is certain to result in tumor recurrence and
resistance to subsequent chemotherapy and radiation
treatments.
Criteria based on the desired injury fraction and HSP
expression in the tumor and healthy tissue were employed
to design objective functions for optimizing these quantities. The criteria for development of the objective functions
and their minimization were based on measured thermally
induced HSP27 and HSP70 expression kinetics and injury
in prostate cancer and normal cells and tissues [22,23]. The
injury predictive model was based on measured cell
viability profiles using propidium iodide staining measured
with a flow cytometer in normal prostate (RWPE-1) and
prostate cancer (PC3) cells following water bath heating for
thermal stimulation temperatures of 44–608C [22]. The
HSP expression predictive model was based on measured
thermally induced HSP27 and HSP70 expression kinetics
data using Western blotting techniques following water
bath heating of RWPE-1 and PC3 cells [22]. In order to
account for differential HSP expression between the
in vitro and in vivo systems, the HSP expression predictive
model was further refined by characterizing the HSP27 and
HSP70 distribution through immunostaining and confocal
microscopy in laser irradiated prostate tumors [23]. H&E
staining was also performed on the irradiated prostate
tumors to gain a better understanding of the correlation
between temperature and tissue injury associated with
laser heating [23]. A lower thermal threshold was observed
for destruction of PC3 tumors in vivo compared to their
in vitro counterparts under similar conditions due to the
presence of the vascular network in vivo as observed by
other researchers [39,40]. The HSP expression and injury
HSP EXPRESSION AND INJURY OPTIMIZATION
743
Fig. 7. Therapy outcome based on injury fraction-based optimization for an initial guess
of P1 ¼ 1.0 W and P2 ¼ 0.5 W depicting (a) temperature, (b) injury fraction, (c) HSP27, and
(d) HSP70 distribution following therapy.
models based on cellular data were valid for the prostate
tumors, but new HSP expression and injury parameters
were required to accurately represent the in vivo HSP
expression and injury responses [20–23]. Implementation
of both HSP expression and injury fraction objective
functions based on cellular and tissue data in the
optimization process permitted successful selection of truly
optimal therapies with maximum injury and elimination of
HSP expression in the tumor and minimum injury and HSP
expression elevation in the healthy tissue.
The Pennes’ bioheat equation was employed for prediction of the temperature distribution in laser irradiated
prostate tissue. This equation assumes that the blood
perfusion effect is homogeneous and isotropic and that the
thermal equilibration occurs in the microcirculatory capillary bed. In considering perfusion as a non-directional
term, the directional convective mechanism is neglected
[31]. Continuum models for bio-heat transfer such as those
developed by Wulff [41] and Klinger [42] have addressed
the isotropic issue of the Pennes’ perfusion term, but do
not address the site of heat exchange. Chen-Holmes have
formulated the most fully developed continuum model
taking into account the significance of vessel thermal
equilibration length and accounting for predominant heat
transfer occurring in the arterioles and venules [43].
Although these continuum models have attempted to more
accurately model the perfusion term, they have had limited
use due to the complexity of their implementation,
difficulty of evaluating the perfusion term, and the inability
to address closely spaced countercurrent artery-vein pairs.
Another limitation of the Pennes’ model is that it does
not account for specific vasculature architecture such as
countercurrent arteries and veins and the location of
these structures within the tissue. Weinbaum-Jiji-Lemons
developed a vasculature based model to better account for
countercurrent vessels not previously addressed in the
before mentioned models [44–46]. The limitations of this
model are again the difficulty of implementation and that
the vein and artery diameters are required to be identical.
Further studies by Wissler [47] have pointed out the
unlikelihood of a single model applying to all the vascular
structures within the tissue. Charney’s work has discussed
744
RYLANDER ET AL.
Fig. 8. Therapy outcome based on temperature-based optimization for an initial guess
of P1 ¼ 0.5 Wand P2 ¼ 0.3 W depicting (a) temperature, (b) injury fraction, (c) HSP27, and
(d) HSP70 distribution following therapy.
the use of hybrid model in which both the Weinbaum-Jiji
and Pennes’ model have been employed to model the
peripheral and deep muscle tissue respectively [48]. Despite
the limitations of the Pennes’ model, it has been widely used
and found to be valid for many situations. Previous research
has demonstrated that the temperature prediction provided
by the Penne’s equation corresponds closely with measured
data using Magnetic Resonance Thermometry during laser
irradiation of prostate tumors [20,21].
The steepest descent method for optimization was
capable of determining effective laser parameters based
on specified objective functions developed from strict
criteria related to the desired tissue response. Alternate
optimization strategies such as Newton’s or quasiNewton’s method could deliver a better convergence rate,
however, its utilization will provide minimal improvement
due to the existing efficiency of the adaptive finite element
algorithm which reaches convergence within very few steps
and requires minimal CPU time. Although the proposed
optimization algorithm is a local optimization scheme,
clinically relevant optimal parameter sets can be determined within a prescribed practical range.
Incorporating appropriate thermal and optical properties for the tissue of interest for the temperatures and
TABLE 2. Comparison of Computational Characteristics for the Three
Optimization Strategies
Metric for optimization
Injury fraction
HSP expression
Temperature
J (optimum)
Convergence steps
CPU time (seconds)
0.0075
0.0056
0.0097
18
25
20
71
94
78
HSP EXPRESSION AND INJURY OPTIMIZATION
wavelengths considered is critical to achieving accurate
prediction and optimization of the tissue response to laser
therapy. The availability of measured thermal properties
for the desired temperature range and optical properties
for target wavelengths for normal and cancerous prostate tissue is limited. Optical properties for native canine
prostate were specified for normal human prostate tissue at
a wavelength of 810 nm. To diminish error associated with
input parameters, optical and thermal measurements
must be performed for the wavelength and temperatures
studied. Currently, the model does not incorporate the
dynamic optical properties associated with denaturation
of proteins during the laser heating process, which may
lead to alterations in tissue absorption and scattering
properties. However, the model does include the nonlinear
temperature dependence of perfusion and thermal conductivity, which was found to decrease the predicted
temperature by 5%.
CONCLUSION
An optimization algorithm for thermal therapy design was
integrated into a predictive treatment planning model
for prostate cancer laser therapy. The optimization model
possesses the unique capability of specifying the most
appropriate laser parameters based on desired HSP expression and injury fraction in both the tumor and healthy tissue.
The criteria and objective functions for optimization were
based on measured thermally-induced HSP expression
kinetics and injury in normal and cancerous prostate cells
and prostate tumors. Utilization of this optimization model
will enable a physician to evaluate treatment alternatives to
better design a patient-specific therapy to achieve maximum
destruction of the tumor and injury minimization of healthy
tissue by controlling HSP expression and injury.
ACKNOWLEDGMENTS
This research was funded by the Abell-Hanger Foundation, the National Science Foundation Award Numbers
CTS-0332052 and CNS-0540033, and the Robert and Prudie
Leibrock Professorship in Engineering at the University of
Texas at Austin.
REFERENCES
1. Madersabacher S, Grobl M, Kramer G, Dirnhofer S,
Steiner G, Marberger M. Regulation of heat shock protein
27 expression of prostatic cells in response to heat treatment.
Prostate 1998;37:174–181.
2. Gibbons NB, Watson RWG, Coffey R, Brady HP, Fritzpatrick
JM. Heat shock proteins inhibit induction of prostate cancer
cell apoptosis. Prostate 2000;45:58–65.
3. Roigas J, Wallen ES, Loening SA, Moseley PL. Effects of
combined treatment of chemotherapeutics and hyperthermia
on survival and the regulation of heat shock proteins in
Dunning R3327 prostate carcinoma cells. Prostate 1998;34:
195–202.
4. Kiang JG, Tsokos GC. Heat shock protein 70 kDa: Molecular
biology, biochemistry, and physiology. Pharmacol Ther
1998;80: 183–201.
5. Martin J, Horwich A, Hartl FU. Prevention of protein
denaturation under heat stress by the chaperonin hsp60.
Science 1992;258:995–998.
745
6. Weich H, Buchner J, Zimmermann R, Jakob U. HSP90
chaperones protein folding in vitro. Nature 1992;358:169–
170.
7. Ciocca DR, Clark GM, Tandon AK, Fuqua SAN, Welch WJ,
McGuire WL. Heat shock protein hsp70 in patients with
auxiliary lymph node-negative breast cancer: Prognostic
implications. J Natl Cancer Inst 1993;85:570–574.
8. Tomei LD, Cope FO. Apoptosis: The molecular basis of cell
death. , Spring Harbor, NY: Cold Spring Harbor Laboratory
Press; 1991. pp 1–30.
9. Levine AJ, Momand J, Finlay CA. The p53 tumor suppressor
gene. Nature 1991;351:453–456.
10. Zhu D, Luo Q, Zhu G, Liu W. Kinetic thermal response and
injury in laser coagulation of tissue. Lasers Surg Med 2002;
31:313–321.
11. Kim B, Jacques SL, Rastegar S, Thomsen S, Motamedi M.
Nonlinear finite-element analysis of the role of dynamic
changes in blood perfusion and optical properties in laser
coagulation of tissue. IEEE J Select Top Quantum Electron
1996;2:922–933.
12. Anvari B, Rastegar S, Motamedi M. Modeling of intraluminal
heating of biological tissue: Implications for treatment of
benign prostatic hyperplasia. IEEE Trans Biomed Eng 1994;
41:854–864.
13. Mohammed Y, Verhey J. A finite element method model to
simulate laser interstitial thermo therapy in anatomical
inhomogeneous regions. BioMed Eng OnLine 2005;4:1–16.
14. Roggan A, Mesecke-von Rheinbaben I, Knappa V, Vogl T,
Mack MG, Gerner C, Albrecht D, Muller G. Applicator
development and irradiation planning in laser-irradiated
thermotherapy (LITT). Biomed Tech 1997;42:332–333.
15. Schwarzmaier HJ, Yaroslavsky IV, Yaroslavsky AN, Fiedler
V, Ulrich F, Kahn T. Treatment planning for MRI-guided
laser-induced interstitial thermotherapy of brain tumors—
The role of blood perfusion. J Magn Reson Imaging 1998;8:
121–127.
16. Sturesson C, Andersson-Engels S. A mathematical model for
predicting the temperature distribution in laser-induced
hyperthermia: Experimental evaluation and applications.
Phys Med Biol 1995;40:2037–2052.
17. Prapavat V, Roggan A, Walter J, Beuthan J, Klingbeil U,
Muller G. In vitro studies and computer simulations to assess
the use of a diode laser (850 nm) for laser-induced thermotherapy (LITT). Lasers Surg Med 1996;18:22–33.
18. Beacco CM, Mordon SR, Brunetaud JM. Development and
experimental in vivo validation of mathematical modeling of
laser coagulation. Lasers Surg Med 1994;14:362–373.
19. Olsrud J, Wirestam R, Peterson B, Tranberg K. Simplified
treatment planning for interstitial laser thermotherapy by
disregarding light transport: A numerical study. Lasers Surg
Med 1999;25:304–314.
20. Rylander MN, Feng Y, Zhang J, Bass J, Stafford RJ, Hazle
J, Diller KR. Optimizing heat shock protein expression
induced by prostate cancer laser therapy through predictive
computational models. J Biomed Optics 2006;11:04111131–
04 11131–16.
21. Rylander MN, Feng Y, Bass J, Diller KR. Thermally induced
injury and heat shock protein expression in cells and tissues.
Ann N Y Acad Sci 2005;1066:222–242.
22. Rylander MN, Feng Y, Diller KR, Aggarwal S. Thermally
induced HSP27, 60,and 70 expression kinetics and cell
viability in normal and cancerous prostate cells. In review.
23. Rylander MN, Stafford RJ, Eliott A, Shetty A, Hazle J, Diller
KR. Characterization of HSP27 and 70 expression in laser
irradiated prostate tumors with nanoshell inclusion. In
preparation.
24. Lang J, Erdman B, Seebass M. Impact of nonlinear heat
transfer on temperature control in regional hyperthermia.
IEEE Trans Biomed Eng 1999;46:1129–1138.
25. Erdman B, Lang J, Seebass M. Optimization of temperature
distributions for regional hyperthermia based on a nonlinear
heat transfer model. Ann N Y Acad Sci 1998;858:36–46.
26. Gittes RF. Carcinoma of the prostate. N Engl J Med 1991;324:
236–245.
27. Cornford PA, Dodson AR, Parsons KF, Desmond AD,
Woolfenden A, Fordham M, Neoptolemos JP, Ke Y, Foster
746
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
RYLANDER ET AL.
CS. Heat Shock Protein expression independently predicts
clinical outcome in prostate cancer. Cancer Res 2000;60:
7099–7105.
Oesterreich S, Weng CN, Qiu M, Hilsenbeck SG, Fuqua SAW.
The small heat shock protein hsp27 is correlated with growth
and drug resistance in human breast cancer cell lines. Cancer
Res 1993;53:4442–4448.
Richards EH, Hickey E, Weber L, Masters JR. Effects of overexpression of the small heat shock protein HSP27 on the heat
and drug sensitivities of human testis tumor cells. Cancer
Res 1996;56:2446–2451.
Barnes JA, Dix DJ, Collins BW, Luft C, Allen JW. Expression
of inducible Hsp70 enhances the proliferation of MCF-7
breast cancer cells and protects against the cytotoxic effects of
hyperthermia. Cell Stress Chaperones 2001;6:316–325.
Pennes HH. Analysis of tissue and arterial blood temperatures in the resting forearm. J Appl Physiol 1948;1:93–122.
Wissler EH. Pennes paper revisited. J Appl Physiol 1998;85:
35–41.
Star W. Diffusion theory of light transport. In: Welch AJ,
Gemert M, editors. Optical-thermal response of laser-irradiated tissue. New York: Plenum Press; 1995. pp 166–169.
Diller KR, Valvano JW, Pearce JA. Bioheat Transfer. In:
Kreith F, editor. CRC Handbook of thermal engineering.
Boca Raton: CRC Press; 2000. pp 4114–4187.
Incropera F, DeWitt D. Fundamentals of heat and mass
transfer. New York: John Wiley and Sons; 1996. pp 482–505.
Henriques FC. Studies of thermal injury V, The predictability
and the significance of thermally induced rate processes
leading to irreversible epidermal injury. Arch Pathol 1947;43:
489–502.
Hirsch LR, Stafford RJ, Bankson JA. Nanoshell-mediated
near-infrared thermal therapy of tumors under Magnetic
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
Resonance guidance. Proc Natl Acad Sci 2003;100:13549–
13554.
Leader J. Numerical analysis and scientific computation.
Boston: Pearson Education, Inc.; 2004. pp 455–467.
Bhowmick S, Bischof JC. Supraphysiological thermal injury
in Dunning AT-1 prostate tumor cells. J Biomech Engr 1998;
122:51–59.
Bhowmick S, Coad JE, Swanlund DJ, Bischof JC. In vitro
thermal therapy of AT-1 Dunning prostate tumours. Int J
Hyperthermia 2004;20:73–92.
Wulff W. The energy conservation equation for living tissue.
IEEE Trans Biomed Eng 1974;21:494–495.
Klinger HG. Heat transfer in perfused biological tissue. I.
General Theory Bull. Math Biol 1974;36:403–415.
Chen MM, Holmes KR. Microvascular contributions in tissue
heat transfer. Ann N Y Acad Sci 1980;335:137–150.
Weinbaum S, Jiji L, Lemons DE. Theory and experiment for
the effect of vascular temperature on surface tissue heat
transfer. 1. Anatomical foundation and model conceptualization. J Biomech Eng 1984;106:246–251.
Weinbaum S, Jiji L, Lemons DE. Theory and experiment for
the effect of vascular temperature on surface tissue heat
transfer. II. Model formulation and solution. J Biomech Eng
1984;106:331–341.
Weinbaum S, Jiji LM. A new simplified bioheat equation
for the effect of blood flow on average tissue temperature.
J Biomech Eng 1985;107:131–139.
Wissler EH. Comments on Weinbaum and Jiji’s discussion of
their proposed bioheat equation. J Biomech Eng 1987;109:
355–356.
Charney CK, Weinbaum S, Levin RL. An evaluation of
the Weinbaum-Jiji bioheat equation for normal and hyperthermic conditions. J Biomech Eng 1990;112:80–87.