Publications

  1. M.J. Simpson (2017). Calculating groundwater response times for flow in heterogeneous porous media . To appear.
  2. P. Haridas, J.A. McGovern, D.L.S. McElwain and M.J. Simpson (2017). Quantitative comparison of the spreading and invasion of radial growth phase and metastatic melanoma cells in a three-dimensional human skin equivalent model. To appear, PeerJ.
  3. W. Jin, C.J. Penington, S.W. McCue and M.J. Simpson (2017). A computational modelling framework to quantify the effects of passaging cell lines . PLOS ONE. 12: e0181941.
  4. A.P. Browning, S.W. McCue and M.J. Simpson (2017). A Bayesian computational approach to explore the optimal duration of a cell proliferation assay . Bulletin of Mathematical Biology. 79: 1888-1906.
  5. P. Haridas, C.J. Penington, J.A. McGovern, D.L.S. McElwain and M.J. Simpson (2017). Quantifying rates of cell migration and cell proliferation in co-culture barrier assays reveals how skin and melanoma cells interact during melanoma spreading and invasion. Journal of Theoretical Biology. 423: 13-25.
  6. O.M. Matsiaka, C.J. Penington, R.E. Baker and M.J. Simpson (2017). Continuum approximations for lattice-free multi-species models of collective cell migration. Journal of Theoretical Biology. 422: 1-11.
  7. W. Jin, E.T. Shah, C.J. Penington, S.W. McCue, P.K. Maini and M.J. Simpson (2017). Logistic proliferation of cells in scratch assays is delayed. Bulletin of Mathematical Biology. 79: 1028-1050.
  8. M. Zheng, F. Liu, Q. Liu, K. Burrage and M.J. Simpson (2017). A novel numerical approximation of the time fractional reaction-diffusion equation with a moving boundary. Journal of Computational Physics. 338: 493-510.
  9. M.J. Simpson, K-Y. Lo and Y-S. Sun (2017). Quantifying the roles of random motility and directed motility using advection-diffusion theory for a 3T3 fibroblast cell migration assay stimulated with an electric field. BMC Systems Biology. 11:39.
  10. S.T. Johnston, R.E. Baker and M.J. Simpson (2017). A new and accurate continuum description of moving fronts. New Journal of Physics. 19: 033010.
  11. S.T. Johnston, R.E. Baker, D.L.S. McElwain and M.J. Simpson (2017). Co-operation, competition and crowding: a discrete framework linking Allee kinetics, nonlinear diffusion, shocks and sharp-fronted travelling waves. Scientific Reports. 7: 42134.
  12. M.J. Simpson (2017). Critical time scales for morphogen gradient formation: Concentration or gradient criteria. International Journal of Heat and Mass Transfer. 106: 570-572.
  13. F. Jazaei, M.J. Simpson and T.P. Clement (2017). Understanding time scales of diffusive fluxes and the implication for steady state and steady shape conditions. Geophysical Research Letters. 44: 174-180.
  14. W. Jin, C.J. Penington, S.W. McCue and M.J. Simpson (2016). Stochastic simulation tools and continuum models for describing two-dimensional collective cell spreading with universal growth functions. Physical Biology. 13: 056003.
  15. A.J. Ellery, R.E. Baker and M.J. Simpson (2016). An analytical method for disentangling the roles of adhesion and crowding for random walk models on a crowded lattice. Fast Track Letter, Physical Biology. 13: 05LT02.
  16. P.R. Taylor, R.E. Baker, M.J. Simpson and C.A. Yates (2016). Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-comparment approaches. Journal of the Royal Society Interface. 13: 2016336.
  17. C.J. Penington, R.E. Baker and M.J. Simpson (2016). Exits in order: how crowding affects particle lifetimes. The Journal of Chemical Physics. 144: 244107.
  18. C.J. Andrews, L. Cuttle and M.J. Simpson (2016). Quantifying the role of burn temperature, burn duration and skin thickness in an in vivo animal skin model of heat conduction. International Journal of Heat and Mass Transfer. 101: 542-549.
  19. A.J. Ellery, R.E. Baker and M.J. Simpson (2016). Distinguishing between short-time non-Fickian diffusion, and long-time Fickian diffusion for a random walk on a crowded lattice. Communication, The Journal of Chemical Physics. 144: 171104.
  20. S.T. Johnston, R.E. Baker and M.J. Simpson (2016). Filling the gaps: A robust description of adhesive birth-death-movement processes. Physical Review E. 93: 042413.
  21. S.T. Johnston, J.V. Ross, B.J. Binder, D.L.S. McElwain, P. Haridas and M.J. Simpson (2016). Quantifying the effect of experimental design choices for in vitro scratch assays. Journal of Theoretical Biology. 400: 19-31.
  22. P. Haridas, J.A. McGovern, A.S. Kashyap, D.L.S. McElwain and M.J. Simpson (2016). Standard melanoma-associated markers do not identify the MM127 metastatic melanoma cell line. Scientific Reports. 6: 24569.
  23. R.N. Binny, P. Haridas, A. James, R. Law, M.J. Simpson and M.J. Plank (2016). Spatial structure arising from neighbour-dependent bias in collective cell movement. PeerJ. 4: e1689.
  24. B.J. Binder and M.J. Simpson (2016). Cell density and cell size dynamics during in vitro tissue growth experiments: Implications for mathematical models of collective cell behaviour. Applied Mathematical Modelling. 40: 3438-3446.
  25. A.J. Ellery, R.E. Baker, S.W. McCue and M.J. Simpson (2016). Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes. Physica A: Statistical Mechanics and its Applications. 449: 74-84.
  26. W. Jin, E.T. Shah, C.J. Penington, S.W. McCue, L.K. Chopin and M.J. Simpson (2016). Reproducibility of scratch assays is affected by the initial degree of confluence: expeirments, modelling and model selection. Journal of Theoretical Biology. 390: 136-145.
  27. F. Jazaei, M.J. Simpson and T.P. Clement (2016). Spatial analysis of aquifer response times for radial flow processes: Nondimensional analysis and laboratory-scale tests. Journal of Hydrology. 532: 1-8.
  28. C. Irons, M.J. Plank and M.J. Simpson (2016). Lattice-free models of directed cell motility. Physica A: Statistical Mechanics and its Applications. 442: 110-121.
  29. A.J. Ellery, R.E. Baker and M.J. Simpson (2015). Calculating the Fickian diffusivity for a lattice-based random walk with agents and obstacles of different shapes and sizes. Physical Biology. 12: 066010.
  30. P.R. Taylor, C.A. Yates, M.J. Simpson and R.E. Baker (2015). Reconciling transport models across scales: the role of volume exclusion. Rapid Communication, Physical Review E. 92: 040701(R).
  31. M.J. Simpson, J.A. Sharp, L.C. Morrow and R.E. Baker (2015). Exact solutions of coupled multispecies linear reaction-diffusion equations on a uniformly growing domain. PLOS ONE. 10(9): e0138894.
  32. M.J. Simpson and R.E. Baker (2015). Exact calculations of survival probability for diffusion on growing lines, disks and spheres: the role of dimension. The Journal of Chemical Physics. 143, 094109.
  33. S.T. Johnston, E.T. Shah, L.K. Chopin, D.L.S. McElwain and M.J. Simpson (2015). Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM assay data using the Fisher-Kolmogorov model. BMC Systems Biology. 9, 38.
  34. M.J. Simpson and L.C. Morrow (2015). Analytical model of reactive transport processes with spatially variable coefficients. Royal Society Open Science. 2, 140348.
  35. M.J. Simpson and R.E. Baker (2015). Spatial moment techniques for modelling biological processes. Bulletin of Mathematical Biology. 77, 581 - 585.
  36. D.C. Markham, M.J. Simpson and R.E. Baker (2015). Choosing an appropriate modelling framework for analysing multispecies co-culture experiments. Bulletin of Mathematical Biology. 77, 713-734.
  37. M.J. Simpson, J.A. Sharp and R.E. Baker (2015). Survival probability for a diffusive process on a growing domain. Physical Review E. 91, 042701.
  38. B.N. Vo, C.C. Drovandi, A.N Pettitt and M.J. Simpson (2015). Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation. Mathematical Biosciences. 263, 133 - 142.
  39. M.J. Simpson (2015). Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: Criteria for successful colonization. PLOS ONE. 10(2): e0117949.
  40. S.T. Johnston, M.J. Simpson and R.E. Baker (2015). Modelling the movement of interacting cell populations: A moment dynamics approach. Journal of Theoretical Biology, 370, 81 - 92.
  41. B.J Binder and M.J. Simpson (2015). Spectral analysis of pair-correlation bandwidth: Application to cell biology images. Royal Society Open Science, 2, 140494.
  42. M.J. Simpson and S.W. McCue (2015). ANZIAM 2015. Gazette of the Australian Mathematical Society. 42, 23 - 25.
  43. F. Jazaei, M.J. Simpson and T.P. Clement (2014). An analytical framework for quantifying aquifer response time scales associated with transient boundary conditions. Journal of Hydrology, 519, 1642 - 1648.
  44. S.T Johnston, M.J. Simpson, D.L.S. McElwain, B.J. Binder and J.V. Ross (2014). Interpreting scratch assays using pair density dynamics and approximate Bayesian computation. Royal Society Open Biology, 4, 140097.
  45. K.K. Treloar, M.J. Simpson, B.J. Binder, D.L.S McElwain and R.E. Baker (2014). Assessing the role of spatial correlations during collective cell spreading. Scientific Reports, 4, 5713.
  46. S.T. Johnston, M.J. Simpson and D.L.S McElwain (2014). How much information can be obtained from tracking the position of the leading edge in a scratch assay? Journal of the Royal Society Interface, 11, 20140325.
  47. K.K. Treloar, M.J. Simpson, D.L.S McElwain and R.E Baker (2014). Are in vitro estimates of cell diffusivity and cell proliferation rate sensitive to assay geomentry? Journal of Theoretical Biology, 356, 71 - 84.
  48. H.M. Young, A.J. Bergner, M.J. Simpson, S.J. McKeown, M.M. Hao, C.R. Anderson and H. Enomoto (2014). Colonizing while migrating: How do individual enteric neural crest cells behave? BMC Biology, 12. 23.
  49. M.J. Simpson and A.J. Ellery (2014). Exact series solutions of reactive transport models with general initial conditions. Journal of Hydrology. 513, 7 - 12.
  50. D.J.G. Agnew, J.E.F. Green, T.M. Brown, M.J. Simpson and B.J. Binder (2014). Distinguishing between mechanisms of cell aggregation using pair-correlation functions. Journal of Theoretical Biology. 352, 16 - 23.
  51. D.C. Markham, M.J. Simpson, P.K. Maini, E.A. Gaffney and R.E. Baker (2014). Comparing methods for modelling spreading cell fronts. Journal of Theoretical Biology. 353, 95 - 103.
  52. A.J. Ellery, M.J. Simpson, S.W. McCue and R.E. Baker (2014). Characterizing transport through a crowded environment with different obstacle sizes. The Journal of Chemical Physics. 140, 054108.
  53. M.J. Simpson, P. Haridas and D.L.S. McElwain (2014). Do pioneer cells exist? PLOS ONE.9(1): e85488.
  54. M.J. Simpson, J.A Sharp and R.E. Baker (2014). Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes. Physica A: Statistical Mechanics and its Applications. 395, 236 - 246.
  55. K.K. Treloar, M.J. Simpson, P. Haridas, K.J. Manton, D.I. Leavesley, D.L.S. McElwain and R.E. Baker (2013). Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies. BMC Systems Biology. 7, 137.
  56. S.T. Johnston, M.J. Simpson and M.J. Plank (2013). Lattice-free descriptions of collective motion with crowding and adhesion. Physical Review E. 88, 062720.
  57. A.J. Ellery, M.J. Simpson, S.W. McCue and R.E. Baker (2013). A simplified approach for calculating the moments of action for linear reaction-diffusion equations. Physical Review E. 88, 054102.
  58. D.C. Markham, M.J. Simpson, P.K. Maini, E.A. Gaffney and R.E. Baker (2013). Incorporating spatial correlations into multi-species mean-field models. Physical Review E. 88, 052713.
  59. M.J. Simpson, F. Jazaei and T.P. Clement (2013). How long does it take for aquifer recharge or aquifer discharge processes to reach steady state? Journal of Hydrology. 501, 241 - 248.
  60. L.G. Bowden, M.J. Simpson and R.E. Baker (2013). Design and interpretation of cell trajectory assays. Journal of the Royal Society Interface. 10, 20130630.
  61. M.J. Plank and M.J. Simpson (2013). Lattice-free models of cell invasion: discrete simulations and travelling waves. Bulletin of Mathematical Biology. 75, 2150 - 2166.
  62. B.J. Binder and M.J. Simpson (2013). Quantifying spatial stucture in experimental observations and agent-based simulations using pair-correlation functions. Physical Review E. 88, 022705.
  63. A.J. Ellery, M.J. Simpson and S.W. McCue (2013). Comment on Local accumulation times for source, diffusion and degradation models in two and three dimensions. The Journal of Chemical Physics. 139, 017101.
  64. D.C. Markham, M.J. Simpson and R.E. Baker (2013). Simplified method for including spatial correlations in mean-field approximations. Physical Review E. 87, 062702.
  65. K.K.Treloar and M.J.Simpson (2013). Sensitivity of edge detection methods for quantifying cell migration assays. PLOS ONE. 8(6): e67389.
  66. M.J.Simpson, B.H.Foy and S.W.McCue (2013). Travelling waves for a velocity-jump model of cell migration and proliferation. Mathematical Biosciences. 244, 98 - 106.
  67. M.J.Simpson, B.J.Binder, P.Haridas, B.K.Wood, K.K.Treloar, D.L.S.McElwain and R.E.Baker (2013). Experimental and modelling investigations of monolayer development with clustering. Bulletin of Mathematical Biology. 75, 871 - 889.
  68. M.J.Simpson, K.K.Treloar, B.J.Binder, P.Haridas, K.J.Manton, D.I.Leavesley, D.L.S.McElwain and R.E.Baker (2013). Quantifying the roles of cell motility and cell proliferation in a circular barrier assay. Journal of the Royal Society Interface. 10, 20130007.
  69. K.K.Treloar, M.J.Simpson and S.W.McCue (2013). Velocity-jump processes with proliferation. Journal of Physics A: Mathematical and Theoretical. 46, 015003. Highlighted by IOP Insights.
  70. M.J.Simpson, A.J.Ellery, S.W.McCue and R.E.Baker (2013). Critical timescales and time intervals for coupled linear processes. ANZIAM Journal. 54, 127 - 142.
  71. A.J.Ellery, M.J.Simpson, S.W.McCue and R.E.Baker (2012). Moments of action provide insight into critical times for advection-diffusion-reaction processes. Physical Review E. 86, 031136.
  72. M.J.Simpson and G.N.Mercer (2012). Infectious disease modelling. ANZIAM Journal. 54, 1 - 2.
  73. B.J.Binder, J.V.Ross and M.J.Simpson (2012). A hybrid model for studying spatial aspects of infectious diseases. ANZIAM Journal. 54, 37 - 49.
  74. S.T.Johnston, M.J.Simpson and R.E.Baker (2012). Mean-field descriptions of collective migration with strong adhesion. Physical Review E. 85, 051922.
  75. M.J.Plank and M.J.Simpson (2012). Models of collective cell behaviour with crowding effects: comparing lattice-based and lattice-free approaches. Journal of the Royal Society Interface. 9, 2983 - 2996.
  76. A.J.Ellery, M.J.Simpson, S.W.McCue and R.E.Baker (2012). Critical timescales for advection–diffusion–reaction processes. Physical Review E. 85, 041135.
  77. R.E.Baker and M.J.Simpson (2012). Models of collective cell motion for cell populations with different aspect ratio: diffusion, proliferation and travelling waves. Physica A: Statistical Mechanics and its Applications. 391, 3729 - 3750.
  78. M.J.Simpson and A.J.Ellery (2012). An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell. Applied Mathematical Modelling. 36: 3329 - 3334.
  79. K.K.Treloar, M.J.Simpson and S.W.McCue (2011). Velocity-jump models with crowding effects. Physical Review E. 84, 061920.
  80. S.W.Chang, T.P.Clement, M.J.Simpson and K-K.Lee (2011). Does sea-level rise have an impact on saltwater intrusion? Advances in Water Resources. 34: 1283 - 1291.
  81. M.J.Simpson and R.E.Baker (2011). Corrected mean-field models for spatially-dependent advection-diffusion-reaction phenomena. Physical Review E. 83, 051922.
  82. A.J.Ellery and M.J.Simpson (2011). An analytical method to solve a general class of nonlinear reactive transport models. Chemical Engineering Journal. 169: 313-318.
  83. M.J.Simpson, R.E.Baker and S.W.McCue (2011). Models of collective cell spreading with variable cell aspect ratio: A motivation for degenerate diffusion models. Physical Review E. 83, 021901.
  84. M.J.Simpson, C.Towne, D.L.S.McElwain and Z.Upton (2010). Migration of breast cancer cells: Understanding the roles of volume exclusion and cell-to-cell adhesion. Physical Review E. 82, 041901.
  85. R.E.Baker and M.J.Simpson (2010). Correcting mean-field approximations for birth-death-movement processes. Physical Review E. 82, 041905.
  86. M.J.Simpson, K.A.Landman and B.D.Hughes (2010). Cell invasion with proliferation mechanisms motivated by time-lapse data. Physica A: Statistical Mechanics and its Applications. 389: 3779 - 3790.
  87. A.E.Fernando, K.A.Landman and M.J.Simpson (2010). Nonlinear diffusion and exclusion processes. Physical Review E. 81, 011903.
  88. M.J.Simpson, K.A.Landman, B.D.Hughes and A.E.Fernando (2010). A model for mesoscale patterns in motile populations. Physica A: Statistical Mechanics and its Applications. 389: 1412 - 1424.
  89. M.J.Simpson, B.D.Hughes and K.A.Landman (2009). Diffusing populations: Ghosts or Folks? Australasian Journal of Engineering Education. 15: 59-68.
  90. M.J.Simpson, K.A.Landman and B.D.Hughes (2009). Pathlines in exclusion processes. Physical Review E. 79, 031920.
  91. M.J.Simpson (2009). Depth-averaging errors in reactive transport modelling. Water Resources Research. 45, W02505.
  92. M.J.Simpson, K.A.Landman and B.D.Hughes (2009). Distinguishing between directed and undirected cell motility within an invading cell population. Bulletin of Mathematical Biology, 71: 781-799.
  93. M.J.Simpson, K.A.Landman and B.D.Hughes (2009). Multi-species simple exclusion processes. Physica A: Statistical Mechanics and its Applications, 388: 399-406.
  94. B.J.Binder, K.A.Landman, M.J.Simpson, M.Mariani and D.F.Newgreen (2008). Modeling proliferative tissue growth: a general approach and an avian case study. Physical Review E. 78, 031912.
  95. K.A.Landman, M.J.Simpson and G.J.Pettet (2008). Tactically-driven nonmonotone travelling waves. Physica D: Nonlinear Phenomena. 237: 678-691.
  96. M.J.Simpson and K.A.Landman (2008). Theoretical analysis and physical interpretation of temporal truncation errors in operator split algorithms. Mathematics and Computers in Simulation, 77: 9-21.
  97. M.J.Simpson (2008). Discussion of Direct and split operator approaches with ELLAM for reactive transport equations. AIChE Journal, 54(2): 588-588.
  98. M.J.Simpson, A.Merrifield, K.A.Landman and B.D.Hughes (2007). Simulating invasion with cellular automata: connecting cell-scale and population-scale properties. Physical Review E. 76, 021918.
  99. M.J.Simpson and K.A.Landman (2007). Nonmonotone chemotactic invasion: High-resolution simulations, phase plane analysis and new benchmark problems. Journal of Computational Physics, 225(1): 6-12.
  100. M.J.Simpson and K.A.Landman (2007). Analysis of split operator methods applied to reactive transport with Monod kinetics. Advances in Water Resources, 30(9): 2026 - 2033.
  101. M.J.Simpson, K.A.Landman and K.Bhaganagarapu (2007). Coalescence of interacting cell populations. Journal of Theoretical Biology, 247: 525-543.
  102. K.A.Landman, M.J.Simpson and D.F.Newgreen (2007). Mathematical and experimental insight into the development of the enteric nervous system and Hirschsprung's Disease. Development, Growth and Differentiation, 49: 277-286.
  103. M.J.Simpson, D.C.Zhang, M.Mariani, K.A.Landman and D.F.Newgreen (2007). Cell proliferation drives neural crest cell invasion of the intestine. Developmental Biology, 302: 553-568. (Cover illustration article).
  104. M.J.Simpson (2007). Reply to comment on Computing residence times for flow towards a pumping well: Nomograph solution and validity of the small draw-down approximation. Hydrogeology Journal, 15: 431-432.
  105. M.J.Simpson, K.A.Landman, B.D.Hughes and D.F.Newgreen (2006). Looking inside an invasion wave of cells using continuum models: Proliferation is the key. Journal of Theoretical Biology, 243: 343-360.
  106. M.J.Simpson, K.A.Landman and D.F. Newgreen (2006). Chemotactic and diffusive migration on a non-uniformly growing domain: Numerical algorithm development and applications. Journal of Computational and Applied Mathematics, 192(2): 282-300.
  107. M.J.Simpson and K.A.Landman (2006). Characterizing and minimizing the operator split error for Fisher's equation. Applied Mathematics Letters, 19(7): 612-620.
  108. M.J.Simpson, T.P.Clement and F.E.Yeomans (2006). Erratum, Analytical model for computing residence times near a pumping well. Ground Water, 44(4): 509 - 510.
  109. M.J.Simpson, K.A.Landman and T.P.Clement (2005). Assessment of a non-traditional operator split algorithm for simulation of reactive transport. Mathematics and Computers in Simulation, 70(1): 44-60.
  110. M.J.Simpson (2005). Computing residence times for flow towards a pumping well: Nomograph solution and validity of the small draw-down approximation. Hydrogeology Journal, 13(5-6): 889 - 894.
  111. K.A.Landman, M.J.Simpson, J.L.Slater and D.F.Newgreen (2005). Diffusive and chemotactic cellular migration: smooth and discontinuous travelling wave solutions. SIAM Journal on Applied Mathematics, 65(4): 1420 - 1442.
  112. M.J.Simpson (2004). SEAWAT-2000: A Three-dimensional model for variable-density flow and transport processes. Ground Water, 42(5): 642 - 645.
  113. M.J.Simpson and T.P.Clement (2004). Improving the worthiness of the Henry problem as a benchmark for density-dependent ground water flow problems. Water Resources Research, 40(1) W01504.
  114. M.J.Simpson, T.P.Clement and F.E.Yeomans (2003). Analytical model for computing residence times near a pumping well. Ground Water, 41(3): 351 - 354.
  115. M.J.Simpson, T.P.Clement and T.A.Gallop (2003). Laboratory and numerical investigation of flow and transport near a seepage-face boundary. Ground Water, 41(5): 690 - 700.
  116. M.J.Simpson and T.P.Clement (2003). A theoretical analysis of the worthiness of Henry and Elder problems as benchmarks of density-dependent groundwater flow models. Advances in Water Resources, 26(1): 17-31.
  117. M.J.Simpson and T.P.Clement (2003). Comparison of finite difference and finite element solutions to the variably saturated flow equation. Journal of Hydrology, 270(1): 49 - 64.