Optimization of Biopsy Protocols for Detection of Prostate Cancer

1
Optimization of Biopsy Protocols for Detection
of Prostate Cancer

• Ariela Sofer , George Mason University
• Jianchao Zeng, Georgetown University
• Brett Opell, Georgetown University
• With acknowledgement to
• John J. Bauer, Xiaohu Yao, Wei Zhang, Isabel A.
  Sesterhenn
• Judd W. Moul, John Lynch, Seong K. Mun
• GU, Walter Reed Army MC, AFIP, CPDR USUHS

2
Prostate Cancer Biopsy

• Prostate cancer is the second leading cause of
  cancer-related death among American men.
• In US alone, about 220,900 new cases are expected
  to be diagnosed in 2003, and 28,900 men are
  expected to die of the disease.
• Unfortunately, no imaging modality can
  effectively differentiate cancerous tissue from
  normal prostate tissue
• Gold standard for prostate cancer detection
  transrectal ultrasound guided needle biopsy
• Problem current biopsy protocols are not
  adequate in terms of detection rate

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Systematic Prostate Biopsy

• A biopsy protocol designates the number of
  needles to be used and their location on the
  prostate.
• Currently adopted protocol is the sextant
• misses 20 or more of cancers
• Recently some alternative protocols have been
  shown empirically to have better detection rates
• 
  
• Our goal determine an optimal needle biopsy
  protocol

4
The Approach

• Use real prostate specimens obtained from
  prostatectomies to reconstruct 3-D prostate
  models (currently 301 prostate specimens)
• Superimpose a 3-D grid over each model and
  calculate cancer presence within the grid
• Develop a 3-D distribution map of tumor location
• Use the map to determine the biopsy protocols
  that maximize the probability of detection.
  Protocols should be identifiable by the
  physician to within the resolution of ultrasound
• Develop a 3-D simulation platform for comparing
  the optimal protocol to existing protocols.
  System allows for automatic simulation by
  computer and interactive virtual biopsy by
  urologists

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3-D Surface Modeling
b
a
c
d
6
Prostate Division for Biopsy Protocols48 Zones
Y
Anterior
X
A
Z
Posterior
Base
Mid
Apex
Right
Left
7
Prostate as Seen by Physician in Biopsy
8
Distribution Map of Cancer By Zone 301 Patients

No. of Patients
Base
Mid
Apex
9
Optimal Protocol for a Prescribed Number of
Needles

• Our goal to determine the protocol that
  maximizes the probability of detecting cancer in
  a biopsy with a prescribed number of needles.
• Some restrictions
• Physicians want left-right symmetry in probes
• The anterior regions are harder and more
  uncomfortable to probe. Biopsies restricted to
  the posterior, or to the rear 3/4s (posterior
  rear half of anterior) would be desirable

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What is the Probability of Detecting Cancer in a
Zone?

• A probe in a cancerous zone will
• not necessarily yield a positive
• (cancerous) diagnosis
• Given that a zone is cancerous,
• what is the probability that a probe
• will detect cancer?
• Difficulties
• Prostates have varying volumes
• Variability in physicians placement
• of needle
• Cancer is not distributed randomly in
• zone
• Needle does not draw a random selection of cells

0.5-1.2 cm
Typical zone 0.14 -1.7 cc
Needle core 1.6 cm long 0.16cm diameter 0.016 cc
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Estimating the Probability of Detection in a Zone

• Partition each zone into a sufficiently large
  number of
  subzones, with each subzone
  small enough in volume
  to be contained
  in a needle core.
• Identify the presence of cancer for each
  patient in
  each sub-zone
• Assume that
• the longitudinal position (z) of the needle
  insertion point
• the depth (y)
• the firing angle of the needle (only one degree
  of freedom)
• are independent Gaussian variables.
• Combine the above model with the prostate volume
  and needle core volume information to estimate
  the probability that a needle probe in a zone
  will be positive

z
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Initial Approximation

• Divided each zone into 53 125 sub-zones for a
  total gridof 6000 sub-zones.
• The table below summarizes
• Proportion of patients who had cancer in each
  zone (blue)
• Estimated probability that a needle in zone will
  detect cancer (black)

Base
Mid
Apex
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Optimal Protocol for a Prescribed Number of
Needles

• Given that a patient has cancer, determine the
  protocol that maximizes the probability of
  detection in a biopsy of k needles.
• Our decision variables
• Let pij probability that a needle in zone j
  detects cancer in patient i.
• Let qij 1 - pij
• Here i 1,,m and j 1,,n
• where m number of prostates models in
  study (m 301) n number of zones in
  3-D map (n 48)

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Maximizing the Probability of Detection

• Then
• Thus the probability of diagnosing cancer in
  patient i is
• The k-biopsy protocol that maximizes the
  probability of detection solves

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Maximizing the Probability of Detection (Contd)

• Equivalently
• Denote
• Then the protocol solves the nonlinear integer
  program

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NLIP via Generalized Benders Decomposition

Assume that f is convex and g is concave for each
fixed x. Then problems are equivalent
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Generalized Benders Decomposition (contd)

Termed the primal problem. Assume for simplicity
it has a solution for all x.
Gives an upper bound on f
Relax these constraints Rather than all ? and
the best y, just choose previous ?s and the
related ys Resulting problem termed the master
problem
Get a lower bound on f
If f and g are linear in x, the master problem is
an IP easy
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The Algorithm

• Given an initial feasible point ,
  and an upper bound UB on the objective
• Iteration t 0, 1,
• Solve primal for xt. Set
• Solve the IP (relaxed master problem)
• Set
• If (UB - LB) lt ? terminate.

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Our NLIP Generalized Benders Decomposition

Problems are equivalent
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The NLIP Generalized Benders Decomposition

Termed the primal problem Solution
Gives an upper bound on f
Relax these constraints Rather than all ? and
the best y, just choose previous ?s and the
related ys Resulting problem termed the master
problem
Get a lower bound on f
21
The Algorithm

• Given an initial feasible point ,
  and an upper bound UB on the objective
• Iteration t 0, 1,
• Set
• Solve the IP (relaxed master problem)
• Set
• If (UB - LB) lt ? terminate.

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Results

• Estimated detection rate for sextant method
  67.3
• Estimated detection rated for optimized biopsies
• Note that in 6 of the patients cancer is
  restricted to anterior

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Updated Biopsy Protocols
6-Needle Biopsy. Estimated Probability of
Detection 79.3
8-Needle Biopsy. Estimated Probability of
Detection 82.9
10-Needle Biopsy. Estimated Probability of
Detection 85.5
Base
Mid
Apex
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Further Work Patient Specific Groups

• We are studying the detection rate of our
  optimized protocols on patient-specific groups
  classified by age, race, PSA level and prostate
  size.
• Preliminary analysis of detection rates of the
  optimal schemes for a crude division to small-
  and large- size prostates

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Future Research

• Enhance the current distribution model by
• Using finer division for probability estimates
• Increasing the number of prostate models
• Perform more comprehensive study for biopsy
  protocols by race, age, prostate size, grade of
  cancer re-biopsy
• Test protocols via interactive virtual biopsy by
  urologist using biopsy simulation system
• Apply the 3-D prostate tumor distribution map
  protocol to real-time in vivo image-guided biopsy
  procedures
• Apply distribution map for dose escalation in
  brachytherapy

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A New Generation of Image-Guided Prostate Biopsy

• Biopsy guidance

A patient-specific 3-D prostate model is
reconstructed from the prostate outlines and
matched to the 3-D tumor distribution map with
optimal biopsy protocols. The tumor distribution
information, and the optimal biopsy protocols are
highlighted or color-coded as grids on top of the
ultrasound images during biopsy.
US Probe
Tracker