The　purpose　of　this　research　is　to　establish　the　generalised　fractional　Bloch-Torrey　equation　for　better　simulating　anomalous　diffusion　in　heterogeneous　biological　tissues.　The　introduction　of　the　distributed-order　time　fractional　derivative　allows　for　an　improved　interpretation　of　the　complex　diffusion　behaviours　with　multi-scale　effects.　The　use　of　variable　coefficients　in　the　model　increases　its　applicability　for　describing　the　spatial　heterogeneity　evident　in　the　cellular　structures.　The　proposed　distributed-order　time　and　space　fractional　Bloch-Torrey　equation　is　discretised　in　time　and　space　by　the　L2-1σ　formula　and　the　finite　element　method,　respectively.　The　stability　and　convergence　analyses　of　these　numerical　methods　are　provided.　To　further　improve　the　computational　efficiency,　a　reduced-order　extrapolation　scheme　is　developed.　We　verify　the　effectiveness　of　the　proposed　methods　by　numerical　examples.　Moreover,　the　coupled　fractional　dynamic　system　solution　behaviour　is　explored　on　a　human　brain-like　domain　divided　into　the　white　matter　and　grey　matter　regions.　Compared　with　the　model　having　constant　coefficients,　solution　behaviours　suggest　that　variable　diffusion　coefficients　offer　an　effective　way　to　differentiate　the　distinct　diffusion　phenomena　evolving　in　different　tissue　micro-environments.　Furthermore,　to　evaluate　the　impacts　of　the　weight　function　in　the　distributed-order　operator,　we　choose　three　types　of　beta　distributions　with　the　same　mean　but　different　values　of　the　variance.　The　results　indicate　that　the　larger　value　of　the　variance　leads　to　a　more　remarkable　fluctuation　and　a　slower　decay　of　the　transverse　magnetisation.　This　generalised　distributed-order　fractional　model　may　provide　further　insights　into　capturing　anomalous　diffusion　in　heterogeneous　media.　©　2024　Elsevier　Inc.