Exhibit 31.1**CERTIFICATION**I, Nassib G. Chamoun, certify that: 1. I have reviewed this Quarterly Report on Form 10-Q of Aspect Medical Systems, Inc.;  2. Based on my knowledge, this report does not contain any untrue statement of a materialfact or omit to state a material fact necessary to make the statements made, in light ofthe circumstances under which such statements were made, not misleading with respect to theperiod covered by this report;  3. Based on my knowledge, the financial statements, and other financial informationincluded in this report, fairly present in all material respects the financial condition,results of operations and cash flows of the registrant as of, and for, the periodspresented in this report;  4. The registrant’s other certifying officer and I are responsible for establishing andmaintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e)and 15d-15(e)) and internal control over financial reporting (as defined in Exchange ActRules 13a-15(f) and 15d-15(f)) for the registrant and have: a) Designed such disclosure controls and procedures, or caused such disclosurecontrols and procedures to be designed under our supervision, to ensure that materialinformation relating to the registrant, including its consolidated subsidiaries, is madeknown to us by others within those entities, particularly during the period in whichthis report is being prepared;  b) Designed such internal control over financial reporting, or caused such internalcontrol over financial reporting to be designed under our supervision, to providereasonable assurance regarding the reliability of financial reporting and thepreparation of financial statements for external purposes in accordance with generallyaccepted accounting principles;  c) Evaluated the effectiveness of the registrant’s disclosure controls andprocedures and presented in this report our conclusions about the effectiveness of thedisclosure controls and procedures, as of the end of the period covered by this reportbased on such evaluation; and  d) Disclosed in this report any change in the registrant’s internal control overfinancial reporting that occurred during the registrant’s most recent fiscal quarterthat has materially affected, or is reasonably likely to materially affect, theregistrant’s internal control over financial reporting; and 5. The registrant’s other certifying officer and I have disclosed, based on our mostrecent evaluation of internal control over financial reporting, to the registrant’sauditors and the audit committee of the registrant’s board of directors (or personsperforming the equivalent functions): a) All significant deficiencies and material weaknesses in the design or operationof internal control over financial reporting which are reasonably likely to adverselyaffect the registrant’s ability to record, process, summarize and report financialinformation; and  b) Any fraud, whether or not material, that involves management or other employeeswho have a significant role in the registrant’s internal control over financialreporting.Dated:May 8, 2008              /s/ Nassib G. Chamoun   Nassib G. Chamoun   *Chief Executive Officer(Principal Executive Officer)*