  Background and Objective: Computational ultrasound imaging has become a
well-established methodology in the ultrasound community. Simulations of
ultrasound sequences and images allow the study of innovative techniques in
terms of emission strategy, beamforming, and probe design. There is a wide
spectrum of software dedicated to ultrasound imaging, each having its
specificities in its applications and the numerical method.
  Methods: We describe in this two-part paper a new ultrasound simulator
(SIMUS) for MATLAB, which belongs to the MATLAB UltraSound Toolbox (MUST). The
SIMUS software simulates acoustic pressure fields and radiofrequency RF signals
for uniform linear or convex probes. SIMUS is an open-source software whose
features are 1) ease of use, 2) time-harmonic analysis, 3) pedagogy. The main
goal was to offer a comprehensive turnkey tool, along with a detailed theory
for pedagogical and research purposes.
  Results: This article describes in detail the underlying linear theory of
SIMUS and provides examples of simulated acoustic fields and ultrasound images.
The accompanying article (part II) is devoted to the comparison of SIMUS with
several software: Field II, k-Wave, FOCUS, and the Verasonics simulator. The
MATLAB open codes for the simulator SIMUS are distributed under the terms of
the GNU Lesser General Public License, and can be downloaded from
https://www.biomecardio.com/MUST.
  Conclusions: The simulations described in the accompanying paper (Part II)
show that SIMUS can be used for realistic simulations in medical ultrasound
imaging.
