Modelli bio -matematici per lo studio delle

dinamiche dell ’infezione cronica

da HCV

Piero Colombatto

UO Epatologia - Azienda Ospedaliero Universitaria Pisana

Centro di Riferimento Regionale per la diagnosi e cura delle epatopatie croniche e del tumore di fegato

Box, George E.P. & Draper, N.R. Empirical Model-Building and Response Surfaces. Wiley (1987) p. 424.

All models are simplified reflections of reality, but, despite their inherent falsity, they are nevertheless extremely useful.

All models are simplified reflections of reality, but, despite their inherent falsity, they are nevertheless extremely useful.

A model is a conceptual representation of some phenomenon. A model is a conceptual representation of some phenomenon.

Definition

Showing by dynamic simulation over time how a particular variable or phenomenon will behave

Showing by dynamic simulation over time how a particular variable or phenomenon will behave

Working as a substitute for directmeasurement and experimentationWorking as a substitute for directmeasurement and experimentation

Scopes of scientific modelling

Systems Engineering Fundamentals. Defense Acquisition University Press, 2003

Building of a model

Analysis of the process making assumptions and

hypothesis that can explain the phenomenon .

Mathematical description of the

relations between the variables playing a role

in the process

Mathematical solution of the

equations / fit to empirical data

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The discovery of Neptun

1612 -13 Galileo had recorded it as a fixed star.

1846: a French mathematician, Urbain Joseph Le Verrier, proposed the position and mass of another as yet unknown planet that could cause the observed changes to Uranus' orbit.

Sept. 23rd 1846: using the predicted parameters of Le Verrier, Johann Galle discovered the planet at the Berlin Observatory, who found Neptune on his first night of searching.

Modelling study to investigate the mechanism of action of IFN therapy

From a single exponential to the biphasic viral load decline

Viral Load

Target Cells

InfectedCells

Infected CellLoss

Free virion clearance

Two compartments model of chronic HCV infection

Block of viral production efficacy:

IFN (0-99.9%)

RBV (5-10%)

DAAs (90-99.99%)

Viral Load vs. Time

1,E+03

1,E+04

1,E+05

1,E+06

1,E+07

1,E+08

-7 7 21 35 49 63 77 91 105 119 133 147 161 175

Time (days)

Vira

l Lo

ad (

cp/m

l)

1st

phase

2nd

phase

The different clearance rate constants of the free vi rions(1st phase) and of the infected cells (2 nd phase) explains

the biphasic decline of the Viral Load

Block of virion production

Clearance of infected cells

1,E-04

1,E-03

1,E-02

1,E-01

1,E+00

1,E+01

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1,E+06

1,E+07

04/04/01 02/05/01 30/05/01 27/06/01 25/07/01 22/08/01 19/09/01 17/10/01 14/11/011

10

100

1000

1000026 weeks

STOP

?

SVR

or

Relapse

HCV-RNA ALT4 weeks

Application of the biphasic model to HCV RNA decline during effective antiviral treatment

1,E-04

1,E-03

1,E-02

1,E-01

1,E+00

1,E+01

1,E+02

1,E+03

1,E+04

1,E+05

1,E+06

1,E+07

04/04/01 02/05/01 30/05/01 27/06/01 25/07/01 22/08/01 19/09/01 17/10/01 14/11/011

10

100

1000

1000026 weeks

STOP

HCV-RNA ALT4 weeks

The simple biphasic model of HCV RNA decline can not predict treatment outcome with accuracy

y = 224321e-0,1588x

y = 57,709e-0,0372x

1,E+00

1,E+01

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1,E+04

1,E+05

1,E+06

0 5 10 15 20 25 30 35days

V(t

) [c

p/m

l];

AL

T(t

) [U

I/l]

V(t)

ALT(t)-20

A discrepancy in Log decrease of ALT and HCV-RNA is present during the 2nd phase attributed to the infected cell clearance.

� the discrepancy betwen ALT and HCV-RNA Log decline is attributed to a further decrease of the virus production rate constant (Ψ0) during the 2ndphase

� the infected cell clearance rate constant (δ0) is computed by fitting the ALT decline during the 1st month

NEW MODEL

Combined analysis of ALT and HCV RNA kinetics

Colombatto P et al.. Antiv Ther, 2003

kinetics of the inhibition of virus replication / production according to the new model

0,001

0,01

0,1

1

10

-5 5 15 25 35 45 55 65

days

Com

pute

d V

iral P

rodu

ctio

n C

oeffi

cent Ψο

(1−ε)....Ψο

(1−ε)....γ.... Ψο DAAs

Viral kinetics during an initial 14 Day study of the Hepatitis C Virus Protease Inhibitor VX 950

(Telaprevir)

Levin J. EASL Conference, 2006, Vienna, Austria

A rebound or plateau in viral response was observed in 4 of 8 patients due to the emergence of resistant variants

1,E-07

1,E-05

1,E-03

1,E-01

1,E+01

1,E+03

1,E+05

1,E+07

-5 95 195 295 395days

HC

V-R

NA

(cp

/ml)

k = 0

k = 0,1

k = 0,2

k = 0,3

k = 0,5

Measuredvalues

IFN stop

HCV-RNA 100 cp/ml sens itivity limit

Colombatto P et al.. Antiv Ther, 2003

Model of long term viral kinetics

V (t) = γ*I (t)

dI/dt = δ0*I (t)

dI/dt = δ0*I (t)*(I(t)/I0)k

0,1

1

10

100

1000

10000

100000

1000000

10000000

100000000

I eot 5,000 Ieot

250 Ieot

peg-IFN: 2a 2b 2a 2b 2a 2b NR REL SVR

Ieot <250 has

93% PPV of SVR

Colombatto P et al, Clin Pharm Ther, 2008

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Months

Num

ber

of p

ts w

ith I

eot<

250

Genotype 1 or 4 (31 pts)

Genotype 2 or 3 (29 pts)

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Months

Num

ber o

f pts

with

Ieo

t<25

0 Gt 1-4 CC (17 pts)

Gt 1-4-CT/TT (14 pts)

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Months

Num

ber o

f pt

s w

ith I

eot<

250 Gt 2-3 CC (15 pts)

Gt 2-3 CT/TT (14 pts)

Genotype 1 or 4 Genotype 2 or 3

Time to reach model computed I eot<250

76% pts

56% ptsIL28B

CCIL28B CC

Colombatto P et al. AISF 2011

Prospective Randomized Trial (EudraCT: 2006−002483−26)

After stratification by:

- HCV genotype (1 - 4 vs 2 - 3)

- treatment exposure (Naives vs Relapsers)

- peg-IFN type (alpha-2a vs alpha-2b)

Random

Model Tailored GuidelineMT GL

ALT + HCV-RNA at day: 0, 2, 4, 7, 14, 21 and 28

HCV-RNA at day: 0, 28, 84

Week 6: Ieot < 5000* Ieot > 5000*

∆∆∆∆ Log < 2 ∆∆∆∆ Log > 2 Week 12 STOP (NR)

* Ieot >5000 at GL duration: 6 mo. for G2-3 and 12 mo. for G1-4.

Continue

(6-12 mo.)

STOP (NR)

Continue to

Ieot<250

(3-18 mo.)

117 pts

Model Tailored: 60 Guideline: 57

No model fit: 10 (16%)

50 57

not included in the analysis

Randomized patients

Drop out due to

AE: 8 5

Prot. Viol.: 6 5

36 47Complete Prot. pts:

SVR 58% 66%

REL 8% 19%

NR 33% 15%

p = NS

IL28B CC prevalence33% 43%

0,0%

20,0%

40,0%

60,0%

80,0%

100,0%

Model Tail. 87,5% 12,5%

Guideline 77,5% 22,5%

SR Rel

Outcome in EVR patients who completed treatment according to Model or Guideline duration

Cost-efficacy analysis in pts who completed the treatment protocol, taking into account the 5 additional ALT and HCV-RNA assays required for viral kinetics, showed a lower cost for SVR in responder patients ( MT: 15.425 Euro vs GL: 19.191 Euro ).

24

40

Rel 3

Rel 6

NR 11

NR 8

0

5

10

15

Model Tailored Standard GL

Pts

14 pts 14 pts

= 21.5 %

= 43.0 %

Analysis of treatment failures in the two different decisional alghoritms

Modelling HCV viral dynamics can be used in clinical practice for selecting patients or tailoring individual treatment with

DAAs?

Modelling of HCV infection dynamics in a rapidlyevolving treatment paradigm

Study

To assess the predictive performance of modelling ALTand HCV-RNA decline during the first 4 weeks ofPegIFN+RBVtherapy in a large cohort of HCVgenotype1 patients

To test its potential application in the selection of patientscandidates to triple therapy after the 4 week lead-in phase.

Colombatto et al. AISF Annual Meeting, Rome 2013

Bio -mathematical prediction of SVR with P/R

treatment

0

2

4

6

8

Time

Log IU/ml

I phase II phase

Drug effectiveness Immune system activity

Block on virus production (εεεε) Infected cells clearance (δδδδ0000)

1−ε1−ε

HCV-RNA

ππ

δδδδ0

ALT

δδδδ0

ALTφφφφφφφφ

Day 0 2 week 4

Model for early viral kinetics analysis

Colombatto P et al.. Antiv Ther, 2003

3rd phase?3rd phase?

Study cohort: 155 consecutive HCV genotype 1 patient s

AssaysALT and HCV-RNA (Cobas Taqman, LLQ 25 IU/ml) were measured at 0-2-4-7-14-21-28 days during the first 4 weeks of P/R therapy

ModelingALT and HCV-RNA were fit into a bio-mathematical model simulating virusand infected-cell decline during therapy to compute:- Infected cells at the end of therapy (Ieot)- Viral load at the end of therapy (Veot)

Infected cells

clearance

Direct

antiviral

activity

ε = 0.872

φ = 0.05

Ieot and Veot distribution in 149 patients (6 pts no model)

Outcome: NR PR Rel SVR

Pts 26 19 38 66

NR PR Rel SVR

26 19 38 66

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Ieot_Real

1,E-05

1,E-04

1,E-03

1,E-02

1,E-01

1,E+00

1,E+01

1,E+02

1,E+03

1,E+04

1,E+05

1,E+06

1,E+07

Veot_RealIeot Veot

Bio -mathematical prediction of SVR with P/R

1,E-04

1,E-02

1,E+00

1,E+02

1,E+04

1,E+06

1,E+08

1,E+10

1,E+12

1,E+14

I*Veot_real

AUROCs of Ieot , Veot and of Veot*Ieotto discriminate SVR from NO SVR pts

Area SE lower upper lim.

Ieot 0,906 0,025 0,857 0,956

Veot 0,930 0,022 0,887 0,973

Ieot*Veot 0,941 0,021 0,900 0,981

Veot*Ieot distribution by treatment outcome

Outcome: NR PR Rel SVR

Pts 26 19 38 66

800

7 58

876

= 65

= 84

Bio -mathematical prediction of SVR with P/R

Prediction of SVR in 149/155 (*) patients

* 6 pts excluded (2 NR, 1 PR, 1 Rel and 2 SVR) beca use “no model fit”

Pts at risk

% of Total

Pts SVRWeek 4

predictorSensitivity Specificity PPV NPV DA

65 43,6% 58 Ieot*Veot<800 87,9% 91,6% 89,2% 90,5% 89,9%

28 18,8% 26 RVR 39,4% 97,6% 92,9% 66,9% 71,8%

Prediction of NO SVRPts at risk

% of Total

Pts SVRWeek 4

predictorSensitivity Specificity PPV NPV DA

84 56,4% 8 Ieot*Veot>800 91,6% 87,9% 90,5% 89,2% 89,9%

27 18,1% 1HCV-RNA drop <1 Log week 4

31,3% 98,5% 96,3% 53,3% 61,1%

Bio -mathematical prediction of SVR with P/R

1,E-04

1,E-02

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I*Veot_real

1,E-02

1,E+00

1,E+02

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1,E+10

1,E+12

1,E+14

I*Veot_real

HCV- RNA week 4 vs Biomath. predictiondrop < 1 Log drop > 1 Log

Outcome: NR PR Rel SVR

Pts 23 1 2 1

NR PR Rel SVR

3 18 36 65

7 pts 74 pts

Ieot*Veot

Ieot*Veot

800

65 pts

(28 RVR)

Study conclusions

The Biomath. Prediction by Ieot*Veot index has:• predictive performance superior to that of the single variables

(AUROCs of 0.941 and 90% DA in the identification of SVR).

• positive predictive value of SVR similar to RVR (≈90%)

• sensitivity for SVR much higher than RVR (87.9% vs 39.4%).

The Ieot*Veot 800 threshold helps to better identify:

• pts with higher chance of SVR with P/R among those withoutweek 4 RVR

• patients who are more likely to reach SVR adding the PIsamong those with week 4 HCV-RNA decline < 1 Log

Simplified Biomathematical Prediction of SVR in HCV G1 patients treated with P/R (lead -in)

Model computed parameters of the antiviral efficacy by ALT (0-1-2-4 weeks) and HCV-RNA (0-4 weeks)

Infected cells

clearance

(2)- 7- 14 - 28 days

TVR/Peg-IFN/RBV Peg-IFN/RBV

Wks 0 4 12 24

HCV-RNA IU/ml >1000 >1000 detectable Stopping rules

HCV-RNA IU/ml <10-25 <10-25 Tailoring duration

HCV-RNA IU/ml ≤1000 ≤1000

Viral load monitoring during Peg-IFN, RBV and DAAs

Peg-IFN/RBV/BOCIFN/ RBV

Wks 0 4 8 12 24

HCV-RNA IU/ml ≥100 detectable Stopping rules

HCV-RNA IU/ml <10 <10 STOP

HCV-RNA IU/ml <1log decline Tailoring duration

24 w

48 w

Comparison of viral load decline

Peg135+R1000 TVR+P180->135+R1000

HCV-RNA LLQ (15 IU/ml)

ε = 0.872

ε = 0.999

φ = 0.05

φ = 0.39

TVR increased:

>120 fold the block of viral replication ((((ε)ε)ε)ε)

~ 8 fold the 2nd phase RNA clearance (φ)(φ)(φ)(φ)

Early viral kinetics in a prototype cirrhotic patie nt relapser after P/R therapy retreated with P/R+TVR

Comparison of ALT decline

Peg135+R1000 TVR+P180->135+R1000

Infected cell half-life: 9.4 days (SOC) 7.5 days (TVR+SOC)

Infected cell clearance rate was only 25% faster !!

Early viral kinetics in a prototype cirrhotic patie nt relapser after P/R therapy retreated with P/R+TVR

Individual HCV RNA Profiles of Treatment-experience d Patients in REALIZE LI T12/PR48 Group (2 of 2)

Late vBT Relapse

LLOQ (25 IU/mL) LLOQ

(25 IU/mL)

6

4

2

0

8

Log

10H

CV

RN

A (IU

/mL) 6

4

2

0

8

Log

10H

CV

RN

A (IU

/mL)

PRdisc

TVR/Pbo disc

TVR start

PRdisc

TVR/Pbo disc

TVR start

G. Picchio, EASL 2012

Boosting anti-HCV immune response by combining SOC and Therapeutic Vaccines

treatment

0

2

4

6

8

Time

HCV-RNALog10 gen Eq/ml

I phase II phase

Drug effectiveness Immune system activi tyBlock on virus production (εεεε) Infected cells clearance (δδδδ0000)

2 days 2 – 4 weeks

Therapeutic Vaccine (E1E2-MF59)

Peg-IFN + RBV

εεεε

δδδδ0

Colombatto et al., ISVHLD Washington 2009 (JVH, 2013, in press)

2,42

1,03

0

1

2

3

4

5

6

7

-28 0 28 56 84 112 140

Days of Therapy

HC

V-R

NA

Log

IU/m

l

Mean e>0,8 STD

Mean e>0,8STD+V

12 pts: 3 NR; 3 PR; 6 Rel

12 pts: 2 DO; 1 NR; 6 Rel; 3 SVR (SVR rate PP: 30%)

Viral dynamics: 2 nd phase HCV-RNA decline in patientswith ε ε ε ε > 0.8

V V V V

ε ε ε ε

Conclusions

Bio-mathematical modelling of HCV infection in the:

PAST helped to understand the physical reasons for chr onicity and the roleplayed by the different mechanisms of the antiviral res ponse induced by IFN

PRESENT helps to- charactherize the antiviral response to PegIFN/RBV at th e single patient

level to predict therapy outcome, tailor treatment dura tion and managedecision of PIs add-on

- hypotesize new therapeutic approaches in patients diffic ult to treat or with previous failures

- analyse and compare the antiviral effects of different treatment schedules

FUTURE might help to- investigate the reasons for viral persistance in patie nts not cured with the

DAAs (if any !)- define cost/effective strategies to optimize the use of the new therapeutic

approaches

Pisa ’s Viral Kinetics Group

MDs:- Filippo Oliveri- Pietro Ciccorossi- Veronica Romagnoli- Barbara Coco- Beatrice Cherubini- Carlotta Rastelli- Gabriele Ricco- Lidia Surace

PhDs:- Daniela Cavallone- Francesco Moriconi

Bio-Physics / Mathematicians:- Luigi Civitano- Ranieri Bizzarri- Laura Manca

Ferruccio Bonino and Maurizia Rossana Brunetto