Formal Computational Modelling of Bone Physiology and Disease Processes Candidate: Nicola Paoletti Supervisor: Emanuela Merelli Examiners: Luca Bortolussi, Guido Sanguinetti PhD course in Information Science and Complex Systems - XVI cycle - University of Camerino Camerino, 24 March 2014
Formal Computational Outline Modelling of Bone Physiology and Disease Processes N. Paoletti
ANALYSIS BIOLOGICAL LANGUAGES MODELS TECHNIQUES PROPERTIES Sect 1.1 Shape Calculus Stochastic Bone micro Simulation (Spatial PA) ABM structure METHODS Probabilistic Osteopo- CTMC Model Checking rosis Simulation Osteomy- ODE Sect 1.2 elitis Sensitivity Analysis Parameter Synthesis Hybrid Ap- Stabili- proximation zation Model Checking Controlled STI Switched Optimal Control (Therapy Systems Scheduling) Sect 2 D − CGF Stochastic (extension Hybrid of CGF PA) Automata
Formal Computational The bone remodelling process Modelling of Bone Physiology and Disease Processes N. Paoletti
Formal Computational The bone remodelling process Modelling of Bone Physiology and Disease Processes N. Paoletti Bone remodelling. . . why? • Multiscale process: multiscale effects, from the molecular signalling level to the tissue level • A paradigm for other physiological systems (like epithelium renewal and haematopoiesis) • Clinical and social impact: for diseases like osteoporosis, Paget’s disease, osteomyelitis. • Collaboration with IOR (Istituto Ortopedico Rizzoli)
Shape Calculus (Spatial PA) 1.1- Shape Stochastic ABM Calculus & agent-based simulation Simulation Bone micro Osteopo- structure rosis
Formal Computational Shape Calculus Modelling of Bone Physiology and Disease Processes N. Paoletti • A bio-inspired spatial process algebra for describing 3D processes, entities characterized by a behaviour B (` a la Timed CCS) and a shape S . • We extend the calculus with additional terms: Iteration , Thanatos and Duration S ∈ S - 3D shape σ = � V , m , p , v � Basic shape S � X � S Complex shape P ∈ 3DP - 3D process B ∈ B - Behavior S [ B ] S ∈ S , B ∈ B nil Null behavior P � a , X � P Composed 3D process � α, X � . B Bind ω ( α, X ) . B Weak split N ∈ N - 3D network ρ ( L ) . B Strong split nil Empty network ǫ ( t ) . B Delay P P ∈ 3DP B + B Choice N � N Parallel 3D processes ( B ) i Iteration Θ Thanatos δ ( t , B ) Duration K Process name
Formal Computational Shape Calculus Modelling of Bone Physiology and Disease Processes N. Paoletti S 1 [ B 1 ] S 1 [ B ′′ 1 ] � a , X 1 � � a , X 0 � � b , X ′ 1 � � a , Y � � c , X ′ 0 � � P 0 , P 1 , Y � ∆ ρ t S 0 [ B ′′ 0 ] S 0 [ B 0 ] S 0 [ B ′ 0 ] � a , Y � S 1 [ B ′ 1 ] Evolution of 3D processes in the Shape Calculus. Processes S 0 [ B 0 ] and S 1 [ B 1 ] are involved in a bind on the channel � a , Y � and in a subsequent strong split.
Formal Computational Shape Calculus model for BR Modelling of Bone Physiology and Disease Processes N. Paoletti • Cells communicate • Cells as 3D Processes , each other via direct communicating by binding contact • Biochemical signals as • RANK/RANKL/OPG channels exposed at the are surface-bound surface of the 3D process proteins
Formal Computational Shape Calculus model for BR Modelling of Bone Physiology and Disease Processes N. Paoletti • Cells communicate each • Cells as 3D Processes , other via direct contact communicating by binding • RANK/RANKL/OPG are • Biochemical signals as channels surface-bound proteins exposed at the surface of the 3D process RANKL/OPG signaling. (pre-osteoblast, mature osteoblast) → (mature osteoblast, active osteoblast) S Ob S Ob S Ob � rankl , X 1 � � rankl , X 2 � ρ (rankl , X 1 ) � rankl , Y � S Ob ρ (rankl , X 2 ) B Ob � rankl , X 2 � S Ob S Ob S Ob [ � rankl , X 1 � .ρ (rankl , X 1 ) . B OPG ] � S Ob [ � rankl , X 2 � .ρ (rankl , X 2 ) . B Ob ] ↓ S Ob [ ρ (rankl , X 1 ) . B OPG ] � rankl , Y � S Ob [ ρ (rankl , X 2 ) . B Ob ] ↓ S Ob [B OPG ] � S Ob [B Ob ]
Formal Computational BR specification Modelling of Bone Physiology and Disease Processes N. Paoletti Tissue, BMU def i =1 � ( � QBMU j ) q ( � ABMU i ) a Tissue = j =1 n Oy def i =1 � ( � Oc j ) n Oc j =1 � ( � Ob k ) n Ob ABMU = ( � Oy i ) k =1 n Oy def QBMU = ( � Oy i ) i =1 Osteocyte def S Oy [( � can , X � + � can , X � ) k Oy + � consume , X � . Θ] Oy = Osteoclast def Oc = S Oc [B Oc ] def δ (t Oc , ( � consume , X � . resorb ) ∞ ) . Θ . � mineral , X � k Oc B Oc = Osteoblast def Ob = S Ob [ � rank , X � .ρ (rank , X) . B OPG + ǫ (t Pb ) . B OPG ] def B OPG = � rank , X � .ρ (rank , X) . B Ob + B Ob def B Ob = δ (t Ob , ( � mineral , X � . form ) ∞ ) . Θ
Formal Computational Encoding of 3D processes as agents Modelling of Bone Physiology and Disease Processes N. Paoletti • Stochastic actions Binding affected by the rates of the actions involved (rated output/passive input) • Perception distance Agents can communicate within a given radius • Prototype in Repast Simphony : support for Shape Calculus models (simplified shapes), stochastic simulation implemented through discrete-event scheduler A B a , λ a , w 1 a , w 2
Formal Computational Encoding of 3D processes as agents Modelling of Bone Physiology and Disease Processes N. Paoletti • Stochastic actions Binding affected by the rates of the actions involved (rated output/passive input) • Perception distance Agents can communicate within a given radius • Prototype in Repast Simphony : support for Shape Calculus models (simplified shapes), stochastic simulation implemented through discrete-event scheduler a , w 2 C − − → ( a ,λ ) d A − − − → a , w 1 B − − → a , w 3 D − − → d
Formal Computational Encoding of 3D processes as agents Modelling of Bone Physiology and Disease Processes N. Paoletti • Stochastic actions Binding affected by the rates of the actions involved (rated output/passive input) • Perception distance Agents can communicate within a given radius • Prototype in Repast Simphony : support for Shape Calculus models (simplified shapes), stochastic simulation implemented through discrete-event scheduler
Formal Computational BR model Modelling of Bone Physiology and Disease Processes N. Paoletti Motion • Output channels release “molecule concentrations” (RANKL and Oc death factors) diffusing according to a CA-like rule • Cells move according to a biased random walk , influenced by compatible molecular bias Parametrization • cells number, lifetime, size, resorption and formation rate taken from experimental works • diffusion coefficients and perception radii tuned for having realistic remodelling times
Formal Computational Results Modelling of Bone Physiology and Disease Processes N. Paoletti Experimental evidence: RANKL concentration inversely related to bone turnover and density. Aging affects bone structure. Two parameter configurations • healthy , with regular RANKL production and cellular activity; • pathological , with an overproduction of RANKL and a reduced cellular activity (i.e. aging). BMD [mg/cm 2 ] H ealthy O steoporotic Stdev H Stdev O time [days] 40 simulations of agent-based model, 1 remodelling cycle
Formal Computational Results Modelling of Bone Physiology and Disease Processes N. Paoletti Experimental evidence: RANKL concentration inversely related to bone turnover and density. Aging affects bone structure. Two parameter configurations • healthy , with regular RANKL production and cellular activity; • pathological , with an overproduction of RANKL and a reduced cellular activity (i.e. aging). Normal Osteopenia Osteoporosis After 7 remodelling cycles ( ∼ 7 years), pathological patient goes osteoporosis.
Formal Computational Results Modelling of Bone Physiology and Disease Processes N. Paoletti 1 st cycle 2 nd cycle 3 rd cycle H O H O H O Positioning of signalling osteocytes affect bone microstructure
Formal Computational Conclusion Modelling of Bone Physiology and Disease Processes N. Paoletti • Extension of Shape Calculus • New agent-based, stochastic and spatial model of BR, based on formal language specification, and able to reproduce normal and defective dynamics • Too many parameters if using the full expressive power of the calculus. Practically, simplifications are needed. [1] N. Paoletti, P. Li` o, E. Merelli and M. Viceconti. Multi-level Computational Modeling and Quantitative Analysis of Bone Remodeling. In IEEE/ACM TCBB , 9(5), pp. 1366-1378, 2012. [2] N. Paoletti, P. Li` o, E. Merelli and M. Viceconti. Osteoporosis: a multiscale modeling viewpoint. In CMSB 2011 , 9(5), ACM, pp. 183-193, 2011. [3] P. Li` o, E. Merelli, N. Paoletti and M. Viceconti. A combined process algebraic and stochastic approach to bone remodeling. In CS2Bio 2011 , ENTCS 277, pp. 41-52, 2011.
1.2- Formal Analysis of Bone Pathologies Probabilistic Osteopo- CTMC Model Checking rosis Simulation Osteomy- ODE elitis Sensitivity Analysis Stabili- Model Checking zation Hybrid Ap- proximation Parameter Synthesis
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