Line spreads of W(2n-1, q), q even

Let q be an even prime power and n \ge 2. We construct line spreads of the symplectic polar space W(2n-1,q) by replacing pairwise disjoint reguli in a Desarguesian line spread. The construction is based on partitions of the points of PG(n-1,q^2) into points of a nondegenerate Hermitian variety and Baer sublines meeting that variety in exactly one point. In the plane case, the partition is invariant under a cyclic group of order q^2-q+ 1.