Cell accelerated cryoablation simulation.

Abstract

Tumor cryoablation is a clinical procedure where supercooled probes are used to destroy cancerous lesions. Cryoablation is a safe and effective palliative treatment for skeletal metastases, providing immediate and long term pain relief, increasing mobility and improving quality of life. Ideally, lesions are encompassed by an ice ball and frozen to a sufficiently low temperature to ensure cell death. "Lethal ice" is the term used to describe regions within the ice ball where cell death occurs. Failure to achieve lethal ice in all portions of a lesion may explain the high recurrence rate currently observed. Tracking growth of lethal ice is critical to success of percutaneous ablations, however, no practical methods currently exist for non-invasive temperature monitoring. Physicians lack planning tools which provide accurate estimation of the ice formation. Simulation of ice formation, while possible, is computationally demanding and too time consuming to be of clinical utility. We developed the computational framework for the simulation, acceleration strategies for multicore Intel x86 and IBM Cell architectures, and performed preliminary validation of the simulation. Our results demonstrate that the streaming SIMD implementation has better performance and scalability. Both accelerated and non-accelerated algorithms demonstrate good agreement between simulation and manually identified ice ball boundaries in phantom and patient images. Our results show promise for the development of novel cryoablation planning tools with real-time monitoring capability for clinical use.

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Cell Accelerated Cryoablation Simulation
Daniel J. Blezek1, David G. Carlson2, Lionel T. Cheng1, Matthew R.
Callstrom1, and Bradley J. Erickson1
1blezek.daniel@mayo.edu, Mayo Clinic, Rochester MN, 55905, USA
2IBM, Rochester MN 55901, USA
Abstract. Tracking growth of lethal ice is critical to success of percu-
taneous ablations using supercooled probes introduced into cancerous
lesions. Physicians lack planning tools which provide accurate estima-
tion of the ice formation. Simulation is computationally demanding, but
must rapid for clinical utility. We develop the computational framework
for the simulation, acceleration strategies for multi-core Intel x86 and
IBM Cell architectures, and preliminary validation of the simulation.
Our data shows streaming SIMD implementation has better performance
and scalability, with good agreement between simulation and manually
identified ice ball boundaries.
1 Introduction
Minimally-invasive methods of lesion ablation, utilizing image guidance, have
become increasing popular in recent years. One key procedure is destruction of
neoplastic lesions through freezing, or cryoablation. It is often used for tumors
in patients where surgical extirpation is not a viable option [1].
Skeletal metastases are often painful. The current standard of care is radia-
tion therapy. However, relief from pain lags treatment and 20 to 30% of patients
do not experience relief at all. Palliative cryoablation has emerged as an imme-
diate source of relief [2]. To the best of our knowledge, no clinically oriented
simulation systems exist for musculo-skeletal (MSK) cryoablation procedures.
The procedure is illustrated in Fig. 1; bone and cryoprobe isosurfaces are ren-
dered with the 0◦C isotherm.
Suitable lesions are accurately localized through radiological imaging tech-
niques. One or more thin probes (cryoprobes) are introduced into the body
via a small skin puncture, and positioned within the lesions under real-time
imaging guidance [3]. Recent advances in cryoprobe technology have provided
unprecedented flexibility to the physician; insulated probes allow percutaneous
approaches and elimination of cryogens allow fine control over the heat flux. Once
probe positions are confirmed, expansion of argon gas near the probe tip (the
Joule-Thompson effect) progressively freezes the adjacent tissue, forming an “ice
ball”. The temperature for ensuring cell death is “lethal ice” at −20 to −40◦C.
Ice formation, changes in cellular volume and loss of blood supply induce cell
death in lethal ice. Current clinical practice is a 10 minute freeze, 10 minute
thaw and 10 minute re-freeze.

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2D.J. Blezek and D.G. Carlson
(a) Left illiac bone(b) Right superic pubic ramus
Fig.1. MSK cryoablation procedures. Cryoprobes may be used in parallel (a)
or in a “spoke” pattern (b). Four cryoprobes are used in both examples.
Imaging plays a key role in the planning, intra-procedural monitoring and
subsequent follow-up of cryoablation cases. Planning consists of lesion visualiza-
tion and careful selection of probe trajectory to maximize tumor destruction and
minimize injury to normal tissue. Parallel (Fig. 1(a)) and crossing (Fig. 1(b))
probe configurations are common. The interventional radiologist integrates many
factors when formulating his plan, i.e., location of the lesion relative to criti-
cal structures, heat conducting properties of surrounding structures, amount of
blood perfusion that might carry heat away from the region, and lesion shape.
During the procedure, ice ball growth is monitored through serial imaging stud-
ies, allowing the operator to modify growth rate by titration of gas flow.
Physicians performing MSK cryoablation estimate the number and position
of cryoprobes from general manufacturer specifications and prior experience.
This suggests the need for tools to assist in planning cryoablation procedures,
which in turn is expected to improve clinical outcomes. To be useful, a simula-
tion system must rapidly provide accurate temperature maps based on physical
properties of cryoprobes and tissue-specific thermal characteristics. This point
can not be overstated: if the system does not provide adequate response, no
matter how accurate, it can not be clinical useful. Once a plan is submitted for
simulation, physicians expect immediate visualization of the temperature maps.
Seconds of run time for each simulated minute are expected. In this work, we
have endeavored to develop and validate a highly accelerated solver first on the
Intel x86 architecture and then on IBM’s Cell Broadband Engine architecture.
2 Methods
2.1 Solution to the Bioheat Equation
Based on the plan configured by the planning interface, the simulation system
solves the heat transfer equations. The planning system provides the location,
size, and heat flux of each cryoprobe. The simulation determines tissue properties
for each voxel in the CT image and boundary conditions for a partial differen-
tial equation (PDE) system. The simulation incorporates models of cryoprobe

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Cryoablation Simulation3
Table 1. Bioheat equation symbols and units
Symbol Description
Cspecific heat
T temperature
kthermal conductivity
˙ wb
blood perfusion
Cb
specific heat of blood
Tb
blood temperature
˙ qmet
metabolic heat generation
βrelaxation parameter
W˙ wbCb/C
N(Tt) neighborhood of Tt
∆x2
i
square distance from Tt to Ti
Tissue specific temperature-dependent
˜C(T)effective specific heat
˜k(T)effective thermal conductivity Wm−1K−1
˜ qmet(T) effective metabolic heat
˜ wb(T)effective blood perfusion
Units
MJm−3K−1
K
Wm−1K−1
unitless
MJm−3K−1
K
K
unitless
unitless
tmm
MJm−3K−1
K
unitless
physical properties and intrinsic tissue properties include thermal conductivity,
specific heat, perfusion, etc. Our derivation follows the work of Rabin [4] and
Deng [5].
Our simulation model incorporates the important liquid-solid phase transi-
tion [5]. Tissue moves from “fresh” to “mush” to “frozen”, each state having
different thermal properties[6]. Symbols and unites used in this work are defined
in Table 1. The bioheat equation [7] is given in (1). The time rate of change in
temperature is governed by the divergence of the temperature gradient (Lapla-
cian for scalar fields), blood perfusion and metabolic heat generation. Using
finite differences (2) with a relaxation parameter β, (1) can be iteratively solved
as shown in (3). The solution domain is divided into isotropic 1mm3elements,
resulting in a time step (∆t) of 0.3 sec. or 180 iterations per minute of simu-
lated freezing (see [5] for details). Associated with each tissue class are several
temperature dependent parameters(˜C(T),˜k(T),˜ qmet(T), and ˜ wb(T) in Table 1)
modeling phase change.
C∂T
∂t= ∇ · (k∇T) + ˙ wbCb(Tb− T) + ˙ qmet
(1)
Tt= βTt+∆t+ (1 − β)Tt
(2)
Tt+∆t=
1
1 − Wβ∆t
+
?
k∆t(Ti
1 − W(1 − β)∆tTt+(˙ qmet+ ˙ wbCbTa)∆t
t− Tt)
C∆x2
i
C
?
Ti
t∈N(Tt)
?
(3)

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4D.J. Blezek and D.G. Carlson
2.2 Implementation
CT images are acquired approximately every 2 minutes during the procedure. For
each subject, the CT image corresponding to the end of the first freeze cycle were
identified. All CT volumes were resampled to 1mm3isotropic resolution, forming
the Ttvolume for t = 0. A volume of tissue classes (Ctissue) was initialized. Initial
conditions were constructed from manually identified cryoprobe voxels fitted to
a line and assigned the “tissue class” of probe; each voxel’s temperature was
fixed at −170◦C for the duration of the simulation. The remaining tissue was
initialized to 37◦C and assigned to the generic tissue class.
The basic algorithm for solving the heat transfer equation is shown in Algo-
rithm 1. For each slice, row pointers are initialized, including the neighborhood
rows N(Prow) around Prow. Tt+∆tis calculated by the Update(·) function. The
algorithm iterates until the simulation time Tsimis reached.
Algorithm 1 Basic simulation algorithm.
Initialize volumes Tt, Tt+∆t and Ctissue
while t < Tsim do
for slice = 1 to Nslices do
for row = 1 to Nrows do
Prow = Tt.getSlice(slice).getRow(row)
Load pointers N(Prow) = {Pabove,Pbelow,Prow+,Prow−}
for idx = 1 to Ncolumns do
{the Update(·) function implements (3)}
Tt+∆t[idx] = Update(constants[Ptissue[idx]],N(Prow[idx]))
end for
end for
end for
t = t + ∆t
end while
2.3Acceleration strategies
Symmetric multi-processors are ubiquitous. OpenMP has emerged as a simpli-
fied alternative to explicit management of threads [8,9]. The main strength of
OpenMP lies in the ability to convert serial loops to parallel through #pragma
compiler directives. The resulting code is readily understandable, and may be ex-
ecuted in serial for debugging/validation purposes. OpenMP naturally fits into
medical image processing by allowing loops over all the slices in a volume to
be executed on all the available SMP cores. Both commercial high-performance
compilers, e.g. the Intel compiler, and open source compilers, e.g. GCC imple-
ment the OpenMP standard. Our initial acceleration strategy augments Algo-
rithm 1 with OpenMP directives, processing slices in parallel on all available
CPUs (Algorithm 2). The code was compiled by the Intel compiler and GCC on

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Cryoablation Simulation5
an server (IBM HS21 Blade, CentOS 5). Table 2 shows compiler parameters and
versions.
Algorithm 2 OpenMP algorithm.
while t < Tsim do
for all Core in available CPUs do {Execute in parallel}
for all slice ∈ Coreslices[Core] do
for row = 1 to Nrows do
Prow = Tt.getSlice(slice).getRow(row)
Load pointers N(Prow) = {Pabove,Pbelow,Prow+,Prow−}
for idx = 1 to Ncolumns do
{the Update(·) function implements (3)}
Tt+∆t[idx] = Update(constants[Ptissue[idx]],N(Prow[idx]))
end for
end for
end for
end for
t = t + ∆t
end while
Table 2. Compiler details
Name / Version
GNU GCC 4.1.2 20070626
Intel Compiler for Linux version 10.1 20080112
XL C/C++ for Multicore Acceleration V9.0
Parameters
-O3 -fopenmp
-O3 -ipo -no-prec-div -xT -openmp
-O5 (SPU compilation only)
IBM’s Cell Broadband Engine [10] is a useful platform for acceleration of
medical image registration [11], and shows potential for broad applicability.
Though the Cell is akin to a general purpose CPU, i.e., Intel x86, understanding
of its strengths and weaknesses are critical to successful acceleration. Current
generations of the Cell have 16 synergistic processing units (SPU). Each SPU
has 256KiB of local storage and a single-instruction, multiple-data (SIMD) vec-
tor processor. Data must be explicitly moved from the main memory into the
local store. The Cell has excellent direct memory access (DMA) abilities; up
to 16 asynchronous DMA requests may be simultaneously pending per SPU.
While the small local storage may seem like a significant limitation, relative to
graphical processing units, it is spacious. The SPU local storage is, in essence,
an explicitly managed L1 cache.
Development to a streaming SIMD algorithm for Cell was our second accel-
eration phase (Algorithm 3). Data-starvation and CPU-starvation pitfalls have
been avoided by overlapping computation and asynchronous DMA requests. In
parallel, each SPU processes an independent regions of interest (ROI). SPUs are