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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):'1209–1217
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''