david hormuth october 20, 2018 · • biomaterials: drugs, coatings/materials for implants,...
TRANSCRIPT
David HormuthOctober 20, 2018
What is biomedical engineering?• Biomechanics: Heart valves, knee replacements, prosthetics• Biomaterials: Drugs, coatings/materials for implants, anything that goes in or
on the body• Instrumentation: basically everything else….• Imaging, pacemakers, ECG machines, anything with computers, neuro-
stimulators, cochlear implants
Terre Haute, IndianaUndergraduate degree
Nashville, Tennessee Graduate degrees
Biomedical Engineering
Medical Imaging Mathematical Biology
Numerical Methods
High Performance Computing
Radiation Therapy
CancerResearch
Brain cancer
Computational Oncology
X-ray 1895
CT (Computed Tomography)The math ~1917The method 1963
Ultrasound1950-60s
Magnetic Resonance Imaging1973
Large magnet1 T (Tesla) = 10,000 Gauss
Fridge magnet ~ 100 Gauss. The Earth ~ .5 Gauss
3T Human (Clinical) Scanner 7T Small Animal (Pre-clinical) Scanner
Screening: Mammogram in breast cancer, dental x-rays (for cavities)
Diagnosis: Contrast-enhanced brain scan
Treatment planning: Biopsy placement, surgery, radiation therapyPredict how a patient will respond to therapy, change therapy if standard of care is not good enough.
Assessing Response: Is the tumor shrinking?Predict if a patient will respond before end of therapy.
What are some ways we can describethe tumor in this image?
Let’s assume it grows at a constant rate per day!
Volume Day 10 = 54.4 mm3
Volume Day 12 = 68.5 mm3
Difference: 14.1 mm3
(7.05 mm3/day)Predicted at Day 14 = 82.6 mm3
Measured at Day 14 = 114.4 mm3
Percent error = 27.8 % error
Error = 100% Model −MeasuredMeasured
⎛⎝⎜
⎞⎠⎟ 10 12 14 16
Time (Days)
0
50
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150
Volu
me
(mm
3 )
Model Measure
10 12 14 16Time (Days)
0
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Volu
me
(mm
3 )
Model Predicted Measure
Volume(t2) =Volume(t1)+ X t2 − t1( )
ΔVChange in volume!
Δtchange in time!
=Volume(t2)−Volume(t1)
t2 − t1( ) = XGrowth Rate
(Volume Increase per day)
!
Volume(t2)−Volume(t1) = X ⋅ t2 − t1( )10 12 14 16
Time (Days)
0
50
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Volu
me
(mm
3 )
Model Predicted Measure
Volume Day 10 = 54.4 mm3
Volume Day 12 = 68.5 mm3
Difference: 14.1 mm3
X = (7.05 mm3/day)
What is the change in volume over time?
What is a model?
Generic equation to find volume at any time point
Volume(ti ) =Volume(t1)+ (t − t1) ⋅X
What X works best to describe volume at both t2 and t3?
X = 7.05 X = 14 X = 21 X = 13Error at t1 0 -13.88 -27.87 -11.87Error at t2 31.86 4.06 -23.94 8.06
Total Squared Error 1015 209.02 1350 206
10 12 14 16Time (Days)
0
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me
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3 )
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10 12 14 16Time (Days)
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me
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10 12 14 16Time (Days)
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19% error
Volume(ti )Future Volume! "# $#
=Volume(t1)Initial Volume! "# $#
+Volume(ti−1)Previous Volume! "## $##
⋅X ⋅ ti − t1( )
ΔVChange in volume!
Δtchange in time!
=Volume(ti )−Volume(t1)
ti − t1( ) =Volume(ti−1) ⋅X
Constant growth didn’t work well…what else can we try?
Volume(t2) =Volume(t1)+Volume(t1) ⋅ 12( ) ⋅ 2( )Volume(t2) = 2 ⋅Volume(t1)
If X = ½ the tumor would double in volume in two days
What is the change in volume over time?
10 12 14 16Time (Days)
0
50
100
150
200
Volu
me
(mm
3 )
Model Predicted Measure
Generic equation to find volume at any time point
What X works best to describe volume at both t2 and t3?
X = 1 X = .5 X = .25 X = .125 X = .18Error at t1 -333 -79.3 -21.15 -1.32 -9.266Error at t2 -2854.5 -
287.35-33.37 24.8 3.218
Total Squared Error
8,259,300
88,858 1561 616.2 96.214 11% error
Volume(ti )Future Volume! "# $#
=Volume(ti−1)Previous Volume! "## $##
+Volume(ti−1)Previous Volume! "## $##
⋅X ⋅ ti − ti−1( )
10 12 14 16Time (Days)
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10 12 14 16 18Time (Days)
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10 15 20Time (Days)
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10 12 14 16 18Time (Days)
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10 15 20Time (Days)
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10 12 14 16Time (Days)
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10 12 14 16Time (Days)
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Prediction Error = 815 Model Error = 202
Prediction Error = 348 Model Error = 564
Prediction Error = 198 Model Error = 758
Prediction Error = 102 Model Error = 869
Prediction Error = 291 Model Error = 96
Prediction Error = 9 Model Error = 191
Prediction Error = 1925 Model Error = 195
Prediction Error = 5053 Model Error = 799
Line
arEx
pone
tial
Which model works best?
What can you tell us about how the model fits the curve?
ΔVChange in volume!
Δtchange in time!
=Volume(t2)−Volume(t1)
t2 − t1( ) =Volume(t1) ⋅X ⋅ 1−Volume(t1)Volumemax
⎛
⎝⎜⎞
⎠⎟
Growth rate changes with volume! "###### $######
10 12 14 16Time (Days)
0
50
100
150
200
250
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Volu
me
(mm
3 )
Model Predicted Measure
10 15 20Time (Days)
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me
(mm
3 )
Model Predicted Measure
10 12 14 16 18Time (Days)
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Model Predicted Measure
10 15 20Time (Days)
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me
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Shor
t Ter
m p
redi
ctio
nsLo
ng T
erm
pre
dict
ions
10 15 20 25 30Time (Days)
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me
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Model Predicted Measure
What does this plot remind you of?
What can we use this prediction for?
Volume is one thing….
What else can we model?
Hallmarks of Cancer
Modeling Immune system response
Modeling tumor genetic instability
Modeling tumor metabolism
Modeling Angiogenesis
Anderson et al Cai et al
Perez-Garcia et alEnderling et al
What can we measure non-invasively? How do these measures change with cancer?• Tumor size and shape
• Tumor cellularity
• Blood vessels, blood flow
• Oxygenation, or hypoxia
• Glucose usage
Diffusion-Weighted MRI• An imaging measurement sensitive to how freely water moves in tissue• How is that related to cells?
0 0.2 0.4 0.6 0.8 10.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Volume fraction
ADC
(x10
-3m
m2 /s
)
Diffusion-Weighted MRIb = 150 b = 300 b = 500
b = 700 b = 900 b = 1100
0( ) exp( )S b S b ADC= - ×ADC = 0.72 µm2/ms
Measure
Model
ΔVChange in volume!
Δtchange in time!
=Volume(t2)−Volume(t1)
t2 − t1( ) =Volume(t1) ⋅X ⋅ 1−Volume(t1)Volumemax
⎛
⎝⎜⎞
⎠⎟
Growth rate changes with volume! "###### $######
ΔNT
Change in cell number!
Δtchange in time!
=NT (t2)−NT (t1)
t2 − t1( ) = NT (t1) ⋅X ⋅ 1−NT (t1)NT ,max
⎛
⎝⎜⎞
⎠⎟
Growth rate changes with cell number! "#### $####
ΔNT x,y( )Change in cell number! "# $#
Δtchange in time!
=NT (x,y,t2)−NT (x,y,t1)
t2 − t1( ) = NT (x,y,t1) ⋅X ⋅ 1−NT (x,y,t1)NT ,max
⎛
⎝⎜⎞
⎠⎟
Growth rate changes with cell number% &##### '#####
Replace Volume with NTNT = the number of tumor cells
Add the location of each imaging point (x,y)
ΔNT x,y( )Change in cell number! "# $#
Δtchange in time!
=NT (x,y,t2)−NT (x,y,t1)
t2 − t1( ) = NT (x,y,t1) ⋅X ⋅ 1−NT (x,y,t1)NT ,max
⎛
⎝⎜⎞
⎠⎟
Growth rate changes with cell number% &##### '#####
BUT! Cells don’t stay put over time
ΔNT x,y( )Change in cell number! "# $#
Δtchange in time!
=NT (x,y,t2)−NT (x,y,t1)
t2 − t1( ) = Entering − Leaving +Staying( )Amount of cells moving around
% &###### '######+NT (x,y,t1) ⋅X ⋅ 1−
NT (x,y,t1)NT ,max
⎛
⎝⎜⎞
⎠⎟
Growth rate changes with cell number% &##### '#####
ΔNT x,y( )Change in cell number! "# $#
Δtchange in time!
= D ∇2NT (x,y,t)( )Amount of cells moving around
Diffusion! "###### $######
! "## $##+NT (x,y,t1) ⋅k ⋅ 1−
NT (x,y,t1)NT ,max
⎛
⎝⎜⎞
⎠⎟
Growth rate changes with cell numberProliferation
! "######## $########
! "##### $#####
We model cell movement using a diffusion term
Generic equation to find volume at any time point
What X works best to describe volume at both t2 and t3?
X = 1 X = .5 X = .25 X = .125 X = .18Error at t1 -333 -79.3 -21.15 -1.32 -9.266Error at t2 -2854.5 -
287.35-33.37 24.8 3.218
Total Squared Error
8,259,300
88,858 1561 616.2 96.214
Volume(ti )Future Volume! "# $#
=Volume(t1)Initial Volume! "# $#
+Volume(ti−1)Previous Volume! "## $##
⋅X ⋅ ti − t1( )
ΔNT x,y( )Change in cell number! "# $#
Δtchange in time!
= D ∇2NT (x,y,t)( )Amount of cells moving around
Diffusion! "###### $######
! "## $##+NT (x,y,t1) ⋅k ⋅ 1−
NT (x,y,t1)NT ,max
⎛
⎝⎜⎞
⎠⎟
Growth rate changes with cell numberProliferation
! "######## $########
! "##### $#####Instead of finding X, we are nowgoing to find K, D, and NT,max
The model doesn’t have any death terms…what can we add?
ΔNT x,y( )Change in cell number! "# $#
Δtchange in time!
=NT (x,y,t2)−NT (x,y,t1)
t2 − t1( ) = Entering − Leaving +Staying( )Amount of cells moving around
% &###### '######+NT (x,y,t1) ⋅X (x,y,t) ⋅ 1−
NT (x,y,t1)NT ,max
⎛
⎝⎜⎞
⎠⎟
Growth rate changes with cell number% &####### '#######
X (x,y,t) =X > 0growing! ,High NV
X ≤ 0Dieing! ,Low NV
⎧
⎨⎪⎪
⎩⎪⎪
ΔNT x,y( )Change in cell number! "# $#
Δtchange in time!
=NT (x,y,t2)−NT (x,y,t1)
t2 − t1( ) = Entering − Leaving +Staying( )Amount of cells moving around
% &###### '######+NT (x,y,t1) ⋅X ⋅ 1−
NT (x,y,t1)NT ,max
⎛
⎝⎜⎞
⎠⎟
Growth rate changes with cell number% &##### '#####
How can we change this model to add vasculature?What do blood vessels do?
We could connect it to the proliferation rate!
Dynamic Contrast Enhanced MRI (DCE-MRI)
ΔCTissueΔt
= KTransCBloodAmount entering
the tissue
! "# $#− K
Trans
veCTissue
Amount leavingthe tissue
! "# $#
ΔNT x,y( )Change in cell number! "# $#
Δtchange in time!
=NT (x,y,t2)−NT (x,y,t1)
t2 − t1( ) = Entering − Leaving +Staying( )Amount of cells moving around
% &###### '######+NT (x,y,t1) ⋅X (x,y,t) ⋅ 1−
NT (x,y,t1)NT ,max
⎛
⎝⎜⎞
⎠⎟
Growth rate changes with cell number% &####### '#######
ΔNV x,y( )Change in blood vessels! "# $#
Δtchange in time!
=NV (x,y,t2)−NV (x,y,t1)
t2 − t1( ) = Entering − Leaving +Staying( )Amount of cells moving around
% &###### '######+NV (x,y,t1) ⋅XV (x,y,t) ⋅ 1−
NV (x,y,t1)NV ,max
⎛
⎝⎜⎞
⎠⎟
Vasculature Growth or Death Rate% &####### '#######
We can use a very similar model to describe how the vasculature grows, dies, and moves over time
We now have 2 equations we need to at each time point
Measured tumor cells Predicted tumor cells
t1 t2 t3
t4 t5 t6
t7
t1 t2 t3
t4 t5 t6
t7
Measured vasculature Predicted vasculature
t1 t2 t3
t4 t5 t6
t7
t1 t2 t3
t4 t5 t6
t7
What is missing in this model that nearly every patient gets?
Treatment!
• Chemotherapy
• Radiation Therapy
• Surgery
• Immunotherapy
When and what type of drugs should the patient receive?
When and how much radiation should the patient receive?
Will this person respond to the treatment?
Tumors are unique, they grow uniquely, the respond uniquely.
Website: cco.ices.utexas.eduEmail: [email protected]