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Sensing of signals from biological processes, such as action potential propagation in nerves, are essential for clinical diagnosis and basic understanding of physiology. Sensing can be performed electrically by placing sensor probes near or inside a living specimen or dissected tissue using well established electrophysiology techniques. However, these electrical probe techniques have poor spatial resolution and cannot easily access tissue deep within a living subject, in particular within the brain. An alternative approach is to detect the magnetic field induced by the passage of the electrical signal, giving the equivalent readout without direct electrical contact. Such measurements are performed today using bulky and expensive superconducting sensors with poor spatial resolution. An alternative is to use nitrogen vacancy (NV) centres in diamond that promise biocompatibilty and high sensitivity without cryogenic cooling. In this work we present advances in biomagnetometry using NV centres, demonstrating magnetic field sensitivity of approximately 100 pT/$\sqrt{Hz}$ in the DC/low frequency range using a setup designed for biological measurements. Biocompatibility of the setup with a living sample (mouse brain slice) is studied and optimized, and we show work toward sensitivity improvements using a pulsed magnetometry scheme. In addition to the bulk magnetometry study, systematic artifacts in NV-ensemble widefield fluorescence imaging are investigated.