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Clinical Insights from Mathematical Modelling of Biological Systems

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Clinical Insights from Mathematical Modelling of Biological Systems
Clinical'Insights'from'Mathematical'
Modelling'of'Biological'Systems'
Tom$Kelsey
Professor$of$Health$Data$Science
twk@st-andrews.ac.uk
Paediatric Visiting$Club$(PVC)$North$Berwick$
13th$to$15th$of$September$2019$
Colleagues'&'competing'interests
Evelyn'Telfer,'Reproductive'Physiology,'Edinburgh,'UK
W'Hamish'B'Wallace,'Oncology,'Edinburgh,'UK
Richard'A'Anderson,'OBGYN'&'Endocrinology,'Edinburgh,'UK
Scott'M'Nelson,'OBGYN'&'Endocrinology,'Glasgow,'UK
Waljit Dhillo,'Assisted'Conception,'Imperial'College,'London,'UK
Claus'Yding Andersen,'Reproductive'Physiology,'Copenhagen,'DK
oI'have'no'competing'financial'interests'to'declare
oMy'research'is'funded'exclusively'by'UK'Research'Councils'and'Cancer'Charities
Overview
Modelling'ovarian'reserve
Radiotherapy'implications
Modelling'ovarian'volume
Combining'these'to'predict'follicle'density'in'a'healthy'ovary'of'
known'age
Modelling'AMH
Clinical'implications
Summary
Non-Growing'Follicles
Ovarian'reserve''
Born'with'a'population'that'declines'until'menopause''
NGFs'are'selected'for'maturation
Impossible'to'measure'in'vivo''
Using'current'technologies''
Populations'are'counted'in'vitro'
Histological'examination'of'stained'tissue
NGFs
Age-Related'NGF'Models
All'based'on'histology
Ovaries'are'sliced,'stained'and'either'photographed'or'observed'
directly
NGFs'counted'in'only'a'sample'of'the'tissue
if'10%'is'sampled'(say)'then'multiply'the'count'by'10'to'get'the'
population
This'assumes'that'NGFs'are'distributed'evenly'in'the'tissue
which'we'know'not'to'be'the'case'
NGFs'-WHB'Wallace,'MD'Thesis'1989
1,000
10,000
100,000
1,000,000
0 5 10 15 20 25 30 35 40 45 50 55
NGFs
log10
Age (years)
NGFs'Faddy'&'Gosden 1992
Faddy MJ, Gosden RG'et'
al.'Hum'Reprod.'1992'
Nov;7(10):1342-6
Aggregated'data
Broken'stick'
biexponential
Age'38?
NGFs'Hansen'et#al.,'2008
Hansen'KR et'al.
Hum'Reprod.'2008'
Mar;23(3):699-708
Single'centre data
Differential'equation
Forced'through'
known'age'at'
menopause
NGFs'Wallace'&'Kelsey,'2010
Wallace'WH,'Kelsey$TW.
PLoS One.'2010'Jan'
27;5(1):e8772
Aggregated'data
Holistic'modelling
Z-score'for'any'age
Agrees'with'
menopausal'ages
NGFs'Wallace'&'Kelsey,'2010
Kelsey$$et$al.
Mol Hum'Reprod.'
2012'Feb;18(2):79-87
Despite'the'wide'
ranges'in'population,'
loss'is'believed'to'
occur'at'a'similar'rate'
in'most'women'and'
children
NGFs'Wallace'&'Kelsey,'2010
Uses'all'the'data'we'know'about
Includes'the'population'increase'phase
Does'not'assume'an'age'at'menopause
other'studies'forced'the'curve'through'an'end-point
Has'a'lower'population'at'birth'than'the'others'
300,000'NGFs'per'ovary
Can'it'be'validated?
Can'it'be'used'to'make'clinical'predictions/decisions?
NGF'Model'Validation
All'models'are'wrong,'but'some'are'useful”
Box,'G.'E.'P.,'and'Draper,'N.'R.,'(1987),'Empirical'Model'Building'
and'Response'Surfaces,'
Does'the'model'accurately'predict'
age'at'menopause?
Mean'Follicle'Densities'in'ovarian'tissue?
both'from'studies/data'not'used'to'derive'the'model
If'so,'we'can'consider'the'model'externally'validated
unless'and'until'new'data'arrives'that'contradicts'the'model'
predictions
Age'at'Menopause
Predicted'NGF'numbers'and'distribution'of'menopausal'ages'from'
the'Prospect-EPIC'cohort'(n'='4,037)'were'compared
The'distributions'of'observed'age'at'natural'menopause'and'
predicted'age'at'natural'menopause'showed'close'conformity
Since'the'Prospect-EPIC'data'were'unavailable'at'time'of'model'
derivation,'we'have'external'validation'for'the'NGF'model
This'constitutes'external$validation
Depmann M,'et'al,
J'Clin Endocrinol Metab.'
2015;100(6):E845-51.
Clinical'Implication'RXT
Collect'data'on'ages'at'POI'after'known'doses'of'radiotherapy'for'
survivors'of'childhood'cancer
Assume'that'the'gap'between'normal'menopausal'age'and'age'at'POI'
is'due'to'the'treatment
Derive'a'model'of'the'LD50'for'NGF'cells'about'2'GY
Apply'the'model'to'
1. Estimate'the'age-related'effective'sterilising dose'
2. Predict'age'at'POI'after'a'known'dose
Use'the'model'to'plan'RXT,'counsel'families,'and'inform'oncofertility
strategies
Clinical'Implication'RXT
R'A'Anderson'et'al
The'Lancet'
Diabetes'and'
Endocrinology'3(7):'
556-567,'2015
Dose'to'least-affected'
ovary'that'will'induce'
POI'in'98%'of'subjects
Clinical'Implication'RXT
R'A'Anderson'et'al
The'Lancet'
Diabetes'and'
Endocrinology'3(7):'
556-567,'2015
Predicting'POI'
after'5Gy
Clinical'Implication'RXT
R'A'Anderson'et'al
The'Lancet'
Diabetes'and'
Endocrinology'3(7):'
556-567,'2015
Predicting'POI'
after'14.4Gy
(i.e.'Total'Body'
Irradiation)
Indirect'Measures'of'Ovarian'Reserve
Ideally,'we’d'have'a'machine'that'counted'NGFs'safely'in'vivo
this'machine'isn’t'going'to'exist'any'time'soon
There'are'currently'three'things'that'can'be'measured'that'suggest'a'
high,'average'or'low'ovarian'reserve
Ovarian'volume'(OV)
Antral'follicle'counts'(AFC)
Anti-Müllerian'Hormone'(AMH)
Each'has'strengths'and'weaknesses
Age-related'model'of'Ovarian'Volume
Kelsey'TW'et'al.'
Ovarian'volume'
throughout'life:'a'
validated'normative'
model.'PLoS ONE.'
2013;8(9):e71465.
Simulated'data
Aggregated'data
Holistic'modelling
Z-score'for'any'age
Mean'Follicle'Density'Prediction
Mean'NGF'density'values'were'obtained'from'13'ovarian'cortical'
biopsies'(16-37'years).'These'values'were'compared'to'age-matched'
model'generated'densities
And'checked'against'Danish'MFD'data
Age-related'NGF'and'ovarian'volume'models'were'combined,'
assuming'that'a'large'ovary'contains'more'NGFs'than'a'small'one
Simply'guess'the'volume'of'the'cortex,'then'divide'predicted'NGFs'by'
predicted'cortical'volume'for'that'age
Mclaughlin M,'Kelsey'
TW'et'al..'J'Assist'
Reprod Genet.'
2015;32(7):1089-95
MFD'Model,'2015'
Mclaughlin M,'Kelsey'
TW'et'al..'J'Assist'
Reprod Genet.'
2015;32(7):1089-95
Validation'of'both'
models
Validation'of'the'
modelling'assumption
Clinical'Implications'Chemotherapy
McGlaughlin et'al.'
Hum'Reprod. 2017'Jan;32(1):165-174.
Black'predictions''''''''''''''''Blue'controls'
Green'-COPDAC''''''''''''''''''''Red'-ABVD
Age-Related'Model'of'AMH
Kelsey'et'al.'A'validated'
model'of'serum'anti-
müllerian hormone'from'
conception'to'menopause.'
PLoS ONE.'
2011;6(7):e22024.
Simulated'data
Aggregated'data
Holistic'modelling
Z-score'for'any'age
Age-Related'Model'of'AMH
Fleming'R, Kelsey$TW,'
Anderson'RA,'Wallace'WH,'
Nelson'SM.
Fertil Steril.'2012'
Nov;98(5):1097-102
AMH
From'about'25'years,'AMH'declines'in'line'with'the'rate'of'
recruitment'of'NGFs'towards'maturation
justifying'the'use'of'AMH'in'adult'infertility
Up'to'about'9'years,'AMH'increases'in'line'with'the'rate'of'
recruitment
For'intermediate'ages'the'picture'is'less'clear
Kelsey'TW,'Anderson'RA,'
Wright'P,'Nelson'SM,'
Wallace'WH.'
Data-driven'assessment'of'
the'human'ovarian'reserve.'
Mol Hum'Reprod.'
2012;18(2):79-87
Uses'of'the'AMH'model
Comparison'od'women'with'germline'BRCA1'
and'BRCA2'mutations
Prediction'of'live'birth'after'assisted'conception'
cycles
Prediction'of'loss'of'ovarian'function'after'
chemotherapy'for'early'breast'cancer
Diagnosis'of'polycystic'ovarian'syndrome'
(PCOS)
Diagnosis'of'menstrual'disturbance'due'to'
PCOS
And'many'more
Phillips'KA'et'al.'Hum'Reprod.'2016'
31(5):1126-32
Iliodromiti S, Kelsey'TW, et'al.'Hum
Reprod Update.'2014'20(4):560-70
Anderson'RA''et'al.'Eur'J'Cancer.'
2013'49(16):3404-11
Iliodromiti S'et'al.'JClin Endocrinol
Metab.'Aug;98(8):3332-40
Abbara A'et'al.'Frontiers'in'
Endocrinology,'in'press
Summary
“It'is'difficult'to'make'predictions,'especially'about'the'future”'
Danish'proverb
Complex'and'multidisciplinary'process
Data'identification,'assessment,'interpretation
Modelling'techniques'&'technologies
Internal'and'external'validation
Understanding'of'implications
Does'a'model'reliably'predict'new'instances?
If'so,'keep'using'it
If'not,'seek'an'improved'model
When'successful,'the'process'provides'useful'clinical'&'biomedical'insights
Thank'you!
Clinical'Implications'Turner'Syndrome
Mamsen et'al.
Fertil Steril. 2019'
Jun;111(6):1217-1225
Clinical'Implications'Galactosemia
Mamsen et'al.
J'Assist'Reprod Genet.'2018'
Jul;'35(7):'12091217
Clinical'Imp.'TG'exposure'to'Testosterone
McGlaughlin et'al.'
Hum'Reprod. 2019'
(under'review)
Variation'from'the'line'at'
identity'suggests'a'difference'
between'cases'and'the'general'
population'
Amount'of'variation'can'be'
calculated
Clinical'Imp.'TG'exposure'to'Testosterone
McGlaughlin et'al.'
Hum'Reprod. 2019'
(under'review)
Total'observations'are'close'to'
the'total'prediction'line,'
externally'validating'the'model'
Healthy'observations'are'
significantly'below'the'healthy'
predicted'line,'suggesting'that'
the'proportion'of'healthy'
follicles'in'TG'ovaries'is'much'
lower'than'expected''
ResearchGate has not been able to resolve any citations for this publication.
  • R Fleming
  • T W Kelsey
  • R A Anderson
  • W H Wallace
  • S M Nelson
Fleming R, Kelsey TW, Anderson RA, Wallace WH, Nelson SM. Fertil Steril. 2012 Nov;98(5):1097-102
  • K A Phillips
Phillips KA et al. Hum Reprod. 2016 31(5):1126-32
  • R A Anderson
Anderson RA et al. Eur J Cancer. 2013 49(16):3404-11
  • Clinical Implications -Galactosemia Mamsen
Clinical Implications -Galactosemia Mamsen et al. J Assist Reprod Genet. 2018
It is difficult to make predictions, especially about the future" • Danish proverb • Complex and multidisciplinary process • Data identification, assessment, interpretation • Modelling techniques & technologies • Internal and external validation • Understanding of implications
  • A Abbara
Abbara A et al. Frontiers in Endocrinology, in press Summary • "It is difficult to make predictions, especially about the future" • Danish proverb • Complex and multidisciplinary process • Data identification, assessment, interpretation • Modelling techniques & technologies • Internal and external validation • Understanding of implications