Computational Mathematical and Informatics Challenges to ... · n indexes states of current i, m indexes states connected to state n i indexes voltage-gated currents Gi is total conductance

Mathematical and Informatics Challenges to Translating Cardiovascular Models to Clinical Care

⪥Raimond L Winslow Institute for Computational Medicine Department of Biomedical Engineering The Johns Hopkins University Whiting School of Engineering & School of Medicine

Computational

What I Will Talk About


• Biophysical modeling of the cardiac myocyte


• Biophysical modeling of the cardiac myocyte• Structural imaging and modeling of cardiac anatomy

and its variations



and its variations• Electrophysiological modeling of cardiac tissue and

heart



and its variations• Electrophysiological modeling of cardiac tissue and

heart• Along the way, comments and questions relating to

personalization of models

Biophysical Modeling of the Cardiac Myocyte

Tipping the Balance

HFN

~ 40 pA difference of inward Ca2+ current

N HF

Work towards more accurate modeling of membrane currents, transporters, and their regulation

Ionic Currents: From HH to Markov Models

INa (t) = GNam(t)3h(t) v(t) − ENa (t)[ ]!m(t) = 1− m(t)[ ] ⋅αm[v(t)]− m(t) ⋅ βm[v(t)]!h(t) = 1− h(t)[ ] ⋅αh[v(t)]− h(t) ⋅ βh[v(t)]

HH Equations

Equivalent Continuous Time Markov Chain

m0h1[ ] 3αm

βm! ⇀!!↽ !!! m1h1[ ] 2αm

2βm! ⇀!!↽ !!!! m2h1[ ] αm

3βm! ⇀!!↽ !!! m3h1[ ]

βh $α h βh $α h βh $α h βh $α h

m0h0[ ] 3αm

βm! ⇀!!↽ !!! m1h0[ ] 2αm

2βm! ⇀!!↽ !!!! m2h0[ ] αm

3βm! ⇀!!↽ !!! m3h0[ ]

Open State

activation/inactivation processes independent

Closed Non-Inactivated States

Non-Conducting Inactivated States

Independent Gating of Sub-Units

Experiments show independence doesn’t hold

i indexes voltage-gated currents j indexes membrane transporter currents (algebraic functions) Cm is membrane capacitance v(t) is membrane potential

Itrj (t)

dv(t)dt

= −1

Cm

Iioni

i∈ ion currents∑ (t) + Itr

j

j∈ transporters∑ (t)

⎡

⎣⎢

⎤

⎦⎥

dC jk (t)

dt= −

ITotalk (t)

zFVjeff

Equations for the time-evolution of state occupancy probabilities for current i n indexes states of current i, m indexes states connected to state n

i indexes voltage-gated currents Gi is total conductance for current i is open state occupancy probability at time t for membrane current i v(t) is membrane potential at time t and are external and internal concentrations of the ion to which conductance i is permeable

PO

i (t)

Time rate of change of concentration of ion k in compartment j

is total current for ion k

is volume of compartment j Vj

eff

Time Varying Membrane Potential

Voltage-Gated Membrane Currents

j indexes transporter currentsMembrane Transporter Currents

State Occupancy Probabilities

Time-Varying Concentrations

6

Generic State Equations

LCC

15 nm

Diad

Cytosol

RyR

Sarcolemma JSR Membrane

7

JSR LumenExtracellular

Ca2+ Signaling is Intimately Involved in Cellular Arrhythmias

L-Type Ca2+ Channels (LCCs)

Ryanodine-Sensitive Ca2+

Release Channels (RyRs)

LCC

15 nm

Diad

Cytosol

RyR

Sarcolemma JSR MembraneVoltage-Dependent Activation (VDI)

Ca2+

Ca2+

+

7






LCC

15 nm

Diad

Cytosol

Ca2+-Dependent Inactivation (CDI)

Ca-Induced Ca-Release (CICR)

RyR


7






LCC

15 nm

Diad

Cytosol



RyR


7

Voltage-Dependent Independent (VDI)






LCC

15 nm

Diad

Cytosol



RyR


7

Voltage-Dependent Independent (VDI)






• VDI is slow and weak • CDI is strong and fast • LCCs and RyRs are so tightly coupled they

gate as a single “macro-channel”

Ca2+ extrusion by serca pump Recovery from CDI Re-activation of LCCs

CDI

CDI

Many Different Properties of Ca2+ Signaling Linked With EADs

• Slowed VDI, reduced CDI (LCC mutation - Timothy Syndrome)

• Reduced JSR Ca2+ load (serca down-regulation, RyR leak in HF)

• CaMKII phosphorylation of LCCs, (increased mode 2 gating), ischemia & HF

• CaMKII phosphorylation of Na channels, incomplete inactivation, late current

• ROSm ⇒ H2O2 ⇒ CaMKII • PKA phosphorylation of LCCs, increased

mode 2 gating• Drug block of IK’s • Mutations

• loss of function mutations IKs (LQT1), IKr (LQT2)

• Incomplete inactivation of Ina (late Na current, LQT3)

“Indirect” “Direct”

CDI

Spontaneous RyR Openings, NCX Current, and Delayed Afterdepolarizations (DADS)

Cardiovascular Physiology (Pappano & Wier)

RyR Po Increases with JSR Ca2+ LoadDADs Upon Increased JSR Ca2+ Load

Dulhunty et al (2011) Proc. Austr. Physiol. Soc. 42: 47

CDI

Spontaneous RyR Openings, NCX Current, and Delayed Afterdepolarizations (DADS)

Cardiovascular Physiology (Pappano & Wier)

RyR Po Increases with JSR Ca2+ LoadDADs Upon Increased JSR Ca2+ Load

Dulhunty et al (2011) Proc. Austr. Physiol. Soc. 42: 47

Cellular Mechanisms of Ca2+ Triggered Activity, Z. Song, (2013) Ph.D. Thesis, Northeastern University

The Metabolic Sink Hypothesis

Maack & Bohm (2011) JACC 58(1): 83

Cortassa et al (2004) Biophys J 87(3): 2060

ROS-Induced ROS-Oscillations

Loss of ⍦m, Low ATP, Increased Po KATP Channels, Conduction Block

Comments & Questions


• As we quantify more and more of the biology of the cardiac myocyte, it is becoming clear that there are many routes to cellular arrhythmia, involving many processes



• In light of this, the extent to which the perturbed biology of individuals differ may be large




• Substantial experimental and clinical data link afterdepolarizations to ventricular arrhythmias





• How do these cellular arrhythmias trigger ventricular arrhythmias?





• How do these cellular arrhythmias trigger ventricular arrhythmias?• multiple regions of partial EAD synchronization (Sato et al 2009

PNAS 106(9): 2983)





• How do these cellular arrhythmias trigger ventricular arrhythmias?• multiple regions of partial EAD synchronization (Sato et al 2009

PNAS 106(9): 2983)• something simpler ? - afterdepolarizations arising in electrically

isolated tissue (Purkinje fibers, trabecular muscle fibers, viable cells within necrotic regions) propagate into ever larger tissue masses

Model phosphorylation using Michaelis-Menten methods

Phosphorylation is a function of cytosolic CaMKII activity

Torrent-Guasp et al (2005). Euro. J. Cardio-Thor. Surg. 27(2): 191

Hunter, P. J. and Smaille, B. H. (1988). Prog. Biophys. Mol. Biol. 52(2):101 Nielsen, P. M. F. et al (1991). Am. J. Physiol. 260: H1365

Manual Dissections Quantitative Histology & Fiber Mapping

Legrice et al (1995) Am. J. Physiol. 269: H571 Legrice et al (1997) Am. J. Physiol. H272: 2466

Sheet Reconstruction

Young et al (1998) J Microsc. 192: 139

MicrostructureThe Auckland Heart Finite Element Model

Anatomical Modeling of the Heart

DTMRI & Fiber Inclination Angle

Transmural Inclination Angle Histologic & DTMRI Reconstruction

Reese et al (1995) Magn. Reson. Med. 34(6): 786

% Distance Epi - Endo

Scollan et al (1998) Am. J. Physiol. 275(44): H2308 Holmes et al (2000) Magn. Reson. Med. 44: 157

DTMRI-Based Anatomic Reconstruction and Cardiac Computational Anatomy

Scollan et al (2000). Ann. Biomed. Eng. 28(8): 934

DTMRI and Sheet Orientation

Helm et al (2005) Magn. Reson. Med. 54(4): 850!   11 normal, 12 failing canine hearts !   1 normal human heart !  All data available at www.ccbm.jhu.edu www.bme.jhu.edu

Average DTMRI ϕ: - 45° and 117° Experimental ϕ: Dokos et al 45° and 110°; Ashikaga et al 36° and 116°

Diffusion Imaging

http://www.bme.jhu.edu

Cardiac Atlasing Using the Large Deformation Diffeomorphic Metric Mapping Algorithm (LDDMM)

Cardiac Atlasing Using the Large Deformation Diffeomorphic Metric Mapping Algorithm (LDDMM)

Miller, Trouvé, Younes (2002) On the Metrics and Euler-Lagrange Equations of Computational Anatomy. Ann Rev BME 4:3 75 Beg et al (2004) Computational Cardiac Anatomy Using MRI Mag Res Med 52: 1167 Helm et al (2006) Measuring and Mapping Cardiac Fiber Architecture Using Diffusion Tensor MRI Circ Res 98: 125

Top: Normal canine voxel-by-voxel mean values on atlas Middle: Failing canine voxel-by-voxel mean values on atlas Bottom: Statistically significant differences (p=.01) between normal

and failing populations

Relative Wall Thickness Fiber Inclination Angle Sheet Angle

Structural Analysis of the Failing Canine Heart Ex-Vivo

Helm et al (2006) Measuring and Mapping Cardiac Fiber Architecture Using Diffusion Tensor MRI Circ Res 98: 125

Between “Subject” Variability of Fiber Inclination Angle

• Fiber inclination angle (6 hearts) mapped onto atlas • Sampled multiple corresponding anterior, lateral posterior regions • Standard deviation about mean across hearts at corresponding

locations < 7o

Helm et al (2005) Ann N Y Acad Sci 1047: 296

Comments

Comments

• Diffusion imaging is the gold standard (ex-vivo)

Comments

• Diffusion imaging is the gold standard (ex-vivo)• Magnet field strength increasing, new imaging techniques emerging

Comments

• Diffusion imaging is the gold standard (ex-vivo)• Magnet field strength increasing, new imaging techniques emerging• While data suggest that the tertiary eigenvector of the diffusion tensor

may be the surface normal to cardiac sheets, this has not been proven

Comments


may be the surface normal to cardiac sheets, this has not been proven• Modeling anatomy and it’s variations by using 1:1 diffeomorphic

mappings to place images into a common coordinate system is a powerful tool for ex-vivo analyses of anatomic remodeling in disease

Comments




• Root mean square displacement of a water molecule calculated using measured ADCs and imaging times for DTMRI is 10’s of um.

Comments





• It is therefore unlikely that fiber structure can be measured in the beating heart. Measurements may represent residual fiber strain

Comments





• It is therefore unlikely that fiber structure can be measured in the beating heart. Measurements may represent residual fiber strain

• Low subject to subject variability of fiber structure may mean that diffeomorphic mapping of atlas fiber structure to individual hearts may be reasonable

Repeat in x-y plane (Optical Cross Section)

Collect Optical Stack Slice & Stack Image Processing & Volume Reconstruction

Langendorff-Perfused Heart Ischemia, Hoechst & Mito-Red Labeling

Two-Photon Imaging & Microtome Reconstruction

High Resolution Heart Reconstruction

Long QT Syndrome 1 (LQT1)

• 34 known mutations of KCNQ1

• LQT1 ⇒ risk for sudden death

• 633 LQT1 Subjects

• Functional characterization of each KCNQ1 mutant

• AP model ionic model based on genotype

• 1-D model of transmural conduction and ECG

KCNQ1 Sub-Unit

Study

Hoefen et al (2012) JAC 60: 2182

Transmural Repolarization Prolongation

Electrophysiological Modeling of Cardiac Tissue and Heart

Image-Based Modeling for Surgical Ablation Therapy

Ashikaga et al (2013) Feasibility of image-based simulation to estimate ablation target in human ventricular arrhythmia, Heart Rhythm, 10(8): 1109-16

Surgical abla+on outside PAZ

Surgical abla+on inside PAZ

Predicted Abla+on Zone (PAZ)

Op+mal Abla+on Zone

Pa+ent-‐Specific Design of Cardiac Abla+on Therapy

Ashikaga et al (2013) Heart Rhythm, 10(8): 1109-16

MRI-‐Based Anatomical Models of 12 Pa+ent Hearts

Scar

Simula+ons Reveal Op+mal Abla+on Site per Pa+ent

Normal

What do simulations predict re burns outside the predicted/optimal ablation zone? How can the physician be guided to the right location with error < 5 mm in a beating heart ? Is this practical ?

Surgical abla+on outside PAZ

Surgical abla+on inside PAZ

Predicted Abla+on Zone (PAZ)

Op+mal Abla+on Zone

Pa+ent-‐Specific Design of Cardiac Abla+on Therapy

Ashikaga et al (2013) Heart Rhythm, 10(8): 1109-16

MRI-‐Based Anatomical Models of 12 Pa+ent Hearts

Scar

Simula+ons Reveal Op+mal Abla+on Site per Pa+ent

Normal

What do simulations predict re burns outside the predicted/optimal ablation zone? How can the physician be guided to the right location with error < 5 mm in a beating heart ? Is this practical ?

• 16 replicates • Local protein controls • 10% expression change • 80% power

Anderson et al (2009) Proteomics 9(24): 9962

Subject to Subject Transmural Molecular Heterogeneity

Transmural Protein Expression 4 Canines, LV Lateral Wall

SERCA2A NCX1 CX430.20.0

0.40.60.8

- 0.2- 0.4- 0.6- 0.8

% Distance Epi to Endo0.2 0.4 0.6 0.8 1.00.2 0.4 0.6 0.8 1.0

Log2

(Exp

ress

ion

to C

ontr

ol)

N1

N2N3!

N4

N1

N2

N3!

N4

SERCA2a ~ Δ30%, JSR Ca2+ Δ 30%, APD90 Δ 50 mSec!

NCX1 ~ same!

CX43 Δ ~ 40%, CV 60-70 cm/Sec (LV lateral), 45-70 cm/Sec (LV anterior)

Anderson et al (2011) Mol. Cell. Proteomics 10(7): M111.008037-1


Comments & Questions• What can we measure in patients ?


- We can image shape


- We can image shape- We can image regional fibrosis and infarct geometry


- We can image shape- We can image regional fibrosis and infarct geometry- “Metabolic imaging” - metabolites, regional O2 consumption


- We can image shape- We can image regional fibrosis and infarct geometry- “Metabolic imaging” - metabolites, regional O2 consumption- genotype (useful if functionally characterized)



• What we can’t measure in patients



• What we can’t measure in patients- Fiber and sheet structure



• What we can’t measure in patients- Fiber and sheet structure- Disease-induced, spatial remodeling of cellular and molecular

processes




processes• Is patient-specific EP modeling of the heart to deliver individualized

therapy a “massively under-determined” problem?





therapy a “massively under-determined” problem?- This question is particularly important in non-structural heart disease





therapy a “massively under-determined” problem?- This question is particularly important in non-structural heart disease- Ablation therapy study - structure rules





therapy a “massively under-determined” problem?- This question is particularly important in non-structural heart disease- Ablation therapy study - structure rules- LQT study - generic models suffice






• Delivering real, working diagnostics/therapies is a very hard problem with long event horizon that includes FDA






• Delivering real, working diagnostics/therapies is a very hard problem with long event horizon that includes FDA- Use animal models, where much more can be probed, to test ideas and

approaches

Thanks to all who have contributed

Myocyte Modeling!Saleet Jafri

Jeremy Rice Joe Greenstein

Laura Doyle Mark Walker Lulu Chen

Yasmin Hashamboy Pegy Foteinou

Claire Zhou !

Mitochondrial Modeling!Sonia Cortassa

An-Chi Wei Laura Doyle Lufang Zhou

Genomics & Proteomics!Christina Yung Troy Anderson

!Structural Imaging!

David Scolllan Alex Holmes

Pat Helm Siamak Ardekani Rob Kazmierski

Aagam Shah !

Experimental Collaborators!Brian O’Rourke

Miguel Aon David Yue

Eduardo Marban

Work supported by the NHLBI

Documents

Computational Mathematical and Informatics Challenges to ... · n indexes states of current i, m indexes states connected to state n i indexes voltage-gated currents Gi is total conductance