Table 1 Equations to model HD-MEA signals in isotropic media.

Volume conductor theory

Equation 1 \({{\rm{\varphi }}}_{{{\rm{\sigma }}}_{{\rm{s}}}}({\rm{x}}^{\prime} ,{\rm{y}}^{\prime} ,{\rm{z}}^{\prime} )=\frac{{\rm{I}}}{4{\rm{\pi }}{\rm{\sigma }}\sqrt{{({\rm{x}}^{\prime} -{\rm{x}})}^{2}+{({\rm{y}}^{\prime} ,-{\rm{y}})}^{2}+{({\rm{z}}^{\prime} -{\rm{z}})}^{2}}}\) where σ = σ_s.

No boundaries

First-order approximation of extracellular recordings without the MEA surface

Semi-infinite MoI

Equation 2 \({{\rm{\varphi }}}_{{\rm{se}},{{\rm{\sigma }}}_{{\rm{s}}}}({\rm{x}}^{\prime} ,{\rm{y}}^{\prime} ,0)=2\ast {\varphi }_{{{\rm{\sigma }}}_{{\rm{s}}}}({\rm{x}}^{\prime} ,{\rm{y}}^{\prime} ,0)\)

Single boundary (HD-MEA surface as insulator)

First-order approximation of in vitro MEA signals

Bounded MoI, (z < h_s)

Equation 3 \({{\rm{\varphi }}}_{{\rm{bo}},{\rm{z}} < {{\rm{h}}}_{{\rm{s}}}}({\rm{x}}^{\prime} ,{\rm{y}}^{\prime} ,0)={\varphi }_{{\rm{se}},{{\rm{\sigma }}}_{{\rm{s}}}}({\rm{x}}^{\prime} ,{\rm{y}}^{\prime} ,0)+{{\rm{\gamma }}}_{{\rm{s}}}\) where \({{\rm{\gamma }}}_{{\rm{s}}}=2\sum _{{\rm{n}}=1}^{\infty }\,{{\rm{W}}}_{{\rm{SA}}}^{{\rm{n}}}[{\varphi }_{{{\rm{\sigma }}}_{{\rm{s}}}}({\rm{x}}^{\prime} ,{\rm{y}}^{\prime} ,-\,2{{\rm{nh}}}_{{\rm{s}}})+{\varphi }_{{{\rm{\sigma }}}_{{\rm{s}}}}({\rm{x}}^{\prime} ,{\rm{y}}^{\prime} ,2{{\rm{nh}}}_{{\rm{s}}})]\), W_SA = 1 and h_s is the height of the saline.

Double boundaries (HD-MEA surface and liquid-air interface as insulators)

In vitro MEA model considering liquid column height